BepiColombo

Posted on August 5, 2022 by janstu

A few weeks ago I read this in the news:

BepiColombo Spacecraft Makes Second Gravity Assist of Planet Mercury – Captures Spectacular Close-Ups

Here is one of those close-ups.

The BepiColombo spacecraft? I am interested in space missions and have written several blogs about space travel and spacecrafts, but I must have missed this one.

So here is a post about BepiColombo. And about Mercury. And about Gravity Assists.

Let me start with Mercury, the smallest of the eight planets in our solar system. And the fastest, orbiting the Sun in 88 days. Its orbit is the most elliptical of all planets, the distance to the Sun varies between 46 and 70 million km. (For comparison, the similar distances for Earth are 147 and 152 million km).

Mercury is not easy to observe from Earth, because the planet orbits so close to the Sun. For a long time, it was thought that Mercury was tidally locked to the Sun, in the same way as the Moon is tidally locked to Earth. It was only in 1965 that radar observations of Mercury showed that it was actually rotating with a period of 59 days. An Italian scientist, Giuseppe Colombo noticed that this value is 2/3 of the orbital period and suggested that Mercury and the Sun are in a so-called 2:3 resonance, with Mercury rotating 3 times during 2 orbital periods. More about tidal locking and resonances in the appendix.

In the nineteen sixties space travel started, in the USA with the Mariner program from 1962 to 1973. Here are a few of the Mariners. The Mariner 2 was the first spacecraft to reach another planet (Venus), It had not yet a camera on board! The Mariner 4 flew by Mars and took 20(!) pictures of the red planet. .

The Mariner 10 mission had a novelty, after its launch it passed very close to the planet Venus. The gravitation of this planet changed the speed and direction of the Mariner in such a way that it continued its course in the direction of Mercury. This is called a gravity assist, often (confusingly) called a gravitational slingshot. See the appendix for more details.

.In the left diagram you see the effect. Three months after launch the Mariner 10 passes Venus at a distance of less than 6000 km. It brings the spacecraft in an elliptical orbit around the Sun with a period of 176 days. On 29 March it passes Mercury at a distance of 700 km. For the first time in history pictures were taken of Mercury’s surface!, A big surprise was that Mercury had a (weak) magnetic field, so it should have a liquid iron core.

The gravity assist was suggested by the same Giuseppe Colombo and was so successful that it is now a standard procedure for spaceflight.

It took almost 30 years before the next mission to Mercury started. In 2004 the MESSENGER spacecraft was launched and its mission was to go into orbit around Mercury and study its structure and magnetic field. Going into orbit around Mercury is not an easy job because of the strong pull of the Sun. Not less than seven gravity assists were needed to slow down the spacecraft enough, one flyby with Earth itself (!), two with Venus and four with Mercury. Here is a diagram of the flight path. Just to show how complicated it is.

The advantage of gravity assists is that you don’t need fuel to change the course, only minor DSM’s (Deep Space Maneuvers). The “disadvantage” is that it takes considerably more time to reach the target. In this case more than six years.

After this lengthy introduction, let’s go back to the BepiColombo mission. Giuseppe (Bepi) Colombo died in 1984, this mission must have been named BepiColombo in his honor, as he was the first to identify the 2:3 resonance of Mercury and also the first to suggest a gravity assist for the Mariner 10 to reach Mercury..

BepiColombo is a joint mission of the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA). BepiColombo was launched in October 2018. The spacecraft contains two orbiters, one MMO) to study the magnetic fields of Mercury, the other one MPO) will study structure and geology of the planet.

In this animation, you can follow the flight path of BepiColombo (pink) from the launch in 2018 until it goes into orbit around Mercury in 2025. The orbits of Earth, Venus and Mercury are in dark blue, light blue and green, respectively. The spacecraft will use a total of nine(!) gravity assists before it goes into orbit.

As it may be difficult to see where and when the flybys occur, I have taken a few screenshots from a very informative video created by ESA: BepiColombo – orbit and timeline .Worth watching. In the screenshots the flyby is indicted with a circle.

The photo of Mercury at the begining of thos post was, taken during the 2nd flyby of Mercury on 23 June 2022.

When BepiColombo goes into orbit around Mercury, it will have travelled more than 10 billion km. Only then it will deploy the two orbiters.

So we will have to wait more than three years before the two orbiters start collecting scientific data.

Appendix: Tidal locking

As probably everybody knows about tides on earth, we will start there. Twice a day the sea will have a high tide and a low tide. Those tides are caused by the gravitational attraction between Earth and Moon. This force depends on the distance between the two bodies. It is a bit stronger on the side of the earth facing the moon, than on the opposite side, resulting in the tides.

The friction caused by these tidal forces, will slow down the rotation of the Earth, increasing the length of a day. Not much, about 2 milliseconds per century. But when Earth and Moon were formed, about 4.5 billion year ago, the length of a day was much shorter only a few hours.

A similar story holds for the Moon, but here the slowing down has been so effective that for billions of years the moon is “tidally locked”, the rotation if the moon (its “spin) is equal to its orbital period around Earth. The technical term is that the Moon is in a 1:1 spin-orbit resonance with Earth. From Earth we always see the same side of the Moon.

Most other moons in our Solar System are also tidally locked to their planet. For example the four Jupiter moons, discovered by Galileo in 1609.

An interesting case is Pluto (no longer a planet) and its moon Charon. Charon is a large moon and Pluto a small “minor planet”.. Both moon and planet are tidally locked to each other! Here is an animation.

The gravitation of the Sun aldo causes tidal forces on the planets. On Earth we are aware of that, but the Sun’s tidal forces are smaller than those of the moon. During full moon and new moon the two tides enhance each other, the high tide is stronger and called a spring tide. During first and last quarter they work against each other, the high tide is weaker and called a neap tide. See the diagram below

Because Mercury is orbiting so close to the Sun, the tidal forces are a lot stronger. Until 1965 it was thought that Mercury was tidally locked to the Sun, rotating in 88 days, same as the period of its orbit => a 1:1 resonance. Now we know that it is a 2:3 resonance, Mercury rotates faster, 1.5 times during one orbit. The reason is that Mercury’s orbit is quite elliptical, so its (orbital) speed is not constant, moving faster when it is close to the Sun. Here is link to a good explanation: Mercury’s 3:2 Spin-Orbit Resonance. .

The length of a day is commonly defined as the time between successive sunrises or sunsets. 24 hours for Earth, slightly more then the rotation period of 23.9344696 h. With 1:1 tidal locking there is no more sunset/sunrise, the concept of a day has no meaning or you could say that the length of a day is infinite ;-). The animation below shows Mercury orbiting the Sun. The red point represents an observer on Mercury. Note that this observer rotates three times during two orbits. Dawn, midday, dusk and midnight are marked. A day on Mercury takes 176 (earth) days, much longer than the rotation period of 59 (earth) days!

Appendix: Gravity Assists

After launch, a spacecraft will move under the influence of gravitation, primarily the attraction of the Sun. Using the precious fuel on board, it can maneuver a bit to reach its destination. When its course brings it close to a planet, the gravity of this planet can change direction and speed of the spacecraft, without using fuel. Depending on how the spacecraft approaches the planet, its speed can increase or decrease. This use of a planet’s gravity is called a gravity assist or a gravitational slingshot.

Here is a somewhat misleading analogy of a gravity assist. “Space balls” are shot at a train with speed of 30 MPH. If the train is at rest, they bounce back with a speed of 30 MPH. But the train is not at rest, it approaches with a speed of 50 MPH. The balls hit the train now with 30 + 50 = 80 MPH and bounce back with the same speed. For the observer along the rails, the balls now have a speed of 80 + 50 = 130 MPH.

This analogy, from Charley Kohlhase, an important NASA engineer, illustrates a few important points. 1).The balls are interacting with a moving object and 2). the mass of the moving object is so large, that its loss of energy can be neglected.

My own favorite example is that of a tennis player, who hits an incoming ball, before it bounces (a volley). When he keeps his racket still, the ball will bounce back with (about) the same speed (block volley). When he moves his racket forward, the speed will be larger (punch volley), when he moves it backwards, the ball will go back slower (drop volley). In this case his own mass is less than the train, so he will feel the impact of the ball.

In space there are no contact forces, everything moves under the influence of gravity, therefore I always found the analogy unsatisfactory. The influence of gravity on the motion of two bodies in space has been described by Kepler using Newton’s gravitation law. We assume that the mass of one body (a planet) is much larger than the mass of the other one (a spacecraft) Here are a few possible orbits. The red one is part of an ellipse, the green one a parabola and the blue one a hyperbola.

On the Internet you can find numerous videos explaining gravity assist. Pick your choice here. Many of them I found confusing and/or too complicated. So I decided to give it a try myself ;-). Here are three images I have created.

The left image shows the course of a spacecraft under the influence of a planet’s gravitation. It is a hyperbolic orbit, where the speed increases until the spacecraft is closest to the planet (called the periapsis), after which its speed will decrease again. The initial speed and the final one are equal, only the direction has changed (the red arrows). If the planet would be at rest relative to an observer (for example Earth), that would be all.

But that is not the case, the planets move around the Sun. In the second image, a planet moves to the right (blue arrow). The gravitation between spacecraft and planet is still the same (the red arrows) but an outside observer will now see the effect of the two speeds: the green arrows. The change of direction of the red arrows now has a clear effect, the final speed is larger than the initial one: here we have a gravity assist to increase the speed of the spacecraft!. This happens when the spacecraft passes “behind” the planet.

In the last image I have reversed the speed of the planet, so now the spacecraft passes “in front of” the planet. With an opposite effect, now the final speed is less than the initial one, The gravity assist in this case reduces the speed of the spacecraft.

Spacecraft exploring the outer planets have to overcome the gravitation of the sun and will need an “extra push” from gravity assists, passing at the rear of planets. BepiColombo is getting closer to the Sun and has to break to be able to go into orbit around Mercury. Therefore it needs gravity assists, passing in front of a planet, reducing its speed.

For me, this explanation of a gravity assist is satisfactory, I am curious about the opinion of others. Comments are welcome 😉

Kumari Kandam & Lemuria

Posted on June 10, 2022 by janstu

Recently I came across an article The Lost Continent of Kumari Kandam in which I found this map:

I had never heard about Kumari Kandam and had to check Wikipedia: Kumari Kandam, “a mythical continent, believed to be lost with an ancient Tamil civilization” The Wikipedia article is interesting and worth reading.

Kumari Kandam never existed. The concept of a lost continent with a Tamil civilisation is the result of Tamil Nationalism . As I want to avoid this sensitive topic, I will give in this blog only some background information, starting with Lemuria.

In 1864 the English zoologist Philip Sclater explained the presence of lemur fossils in Madagascar and India, but not in Africa and Arabia by assuming that in the past Madagascar and India were connected by a landmass , which later was submerged by the ocean., He named this lost continent Lemuria.

A couple of years later this idea of a lost continent was picked up by the German scientist Ernst Haeckel, a staunch defender of Darwinian evolution. He suggested that this lost continent could have been the cradle of human evolution. Here is a map drawn by Haeckel.

Here is a detail. Notice the alternate name Paradise for Lemuria!

The “Out of Asia”” theory of human evolution was quite popular in those days.

We know now that Lemuria never existed and have a much more fascinating explanation: continental drift. I will write a separate blog about this topic. Continents (tectonic plates) have not a fixed location ,but move slowly. Here is a video of the continental drift the last 100 million years. India was still connected to Madagascar, but moved north until it collided with Asia (the collision caused the Himalayas). Also notice how at the start of the video Australia is still connected to Antarctica.

The classical Tamil literature (Sangam) mentions the occurrence of flooding, resulting in the loss of land. At the end of the 19th century Tamil scholars and nationalists suggested that Lemuria was the center of Tamil civilisation and named it Kumari Kandam. After its submersion Tamils had to migrate to other parts of the world, bringing there civilisation and language.

The submersion is often explained by the rise in sea levels after the last Ice Age. More than 100 meter. In itself that makes sense, as you can see in the Google image below where I have roughly indicated a contour line 120 m below sea level. Considerable amounts of land were lost to the sea during the past ~ 20.000 years.

But not a continent.

Lagrange points

Posted on January 31, 2022 by janstu

On 25 December 2021, the James Webb Space Telescope (JWST) was successfully launched. It has now reached its destination at the L2 Lagrange point of the Sun-Earth system. For many years I have considered writing a blog about the five L:agrange points, but I was not sure if I could do that in a relatively simple way.

I am still not sure, but in this blog I will give it a try.

Here is a diagram of the Sun-Earth system (not to scale). The five Lagrange points are marked.

Earth and all other planets orbit the Sun because of the gravitational attraction between a planet and the Sun. Earth orbits the Sun in ~365 days at a distance of 150 million km. The other planets do the same, but at different distances and with different periods. Here is the solar system (not to scale).

It was Kepler who studied the planetary motion. He found a relation between the period and the distance, which is now called Kepler’s Third Law: The square of a planetary period is proportional to the third power of its distance. Let’s take Mars as an example. The distance to the Sun is ~228 million km and a Mars year is ~687 days. The distance is a factor 228/150 = 1.52 larger. The third power of 1.52 is 1.52×1.52×1.52 = 3.512. Kepler’s 3rd law predicts that a Mars year will be √ 3,512 = 1.88 times longer than an Earth year. = 1,88 x 365 = 686 days.

Now let us consider a spacecraft in the Sun-Earth system. It’s mass is so small compared to the mass of Sun and Earth, that it will not influence their motion. But it will feel the gravitational attraction from the Sun and also from the Earth. Is it possible that the combined attraction of Sun and Earth will result in a period of 1 year?

The answer is yes, there are exactly 5 points where this is the case, the 5 Lagrange points!

Here is the explanation for L2. This point lies farther away from the Sun than Earth, so the attraction from the Sun is weaker and would result in a longer period. But Earth also attracts the spacecraft in the same direction as the Sun and in L2 they give together enough attraction to let this point orbit in 1 year. Calculation gives that L2 is located 1.5 million km from Earth, 151.5 million km from the Sun

For L1 the explanation is similar. Here the attraction of the Sun is stronger resulting in a shorter period. But now Earth “pulls back” and together they give the right amount of attraction. The location of L1 is also 1.5 million km from Earth, 148.5 million km from the Sun (the figure above is not to scale).

L3 lies at the opposite side of the Sun, Here the attraction from Earth is minimal, it contributes only little to the attraction of the Sun, so L3 lies only slightly further away than 150 million km from the Sun.

Before we describe the points L4 and L5, we will first look in a bit more detail at the solar system. When we say that the planets orbit the Sun, it suggests that the Sun doesn’t move itself, while the planets orbit around it. And that is not true. The Sun and a planet both orbit around their common center of mass, often called their barycenter. In this image the barycenter is shown for the Sun and Jupiter. Because the Sun is much more massive than Jupiter, their barycenter lies close to the Sun.

Here are a few animations for different situations, where the barycenter is marked with a red cross. The animations are not to scale. The first image shows the situation of for example two stars of equal mass. The next one shows minor planet Pluto and its large moon Charon. The last image shows Earth and Sun. The mass of Earth is so small that the barycenter lies within the Sun.

Of course the resulting force in the Lagrange points has to be directed to the barycenter and for L1, L2 and L3 this is automatically the case, because these points lie all three on the line connecting Sun and Earth. These points were already found by the famous mathematician Euler in 1720.

In 1772 Lagrange discovered two more “stable” points, where the attraction of Sun and Earth are not in the same direction, but together point to the barycenter. of the Sun-Earth system. .

The mathematics is complicated, I will use some hand waving to make the existence of L4 (and L5) plausible. In the diagram below, the masses of Sun and Earth are S and E , the barycenter is indicated as b, it lies within the Sun because the Sun is much more massive than the Earth. The location of b depends on the ratio of the two masses S and E;.

L4 is the top of a triangle with all sides equal to the distance between Earth and Sun. Because L4 has an equal distance to Earth and Sun, the gravitational forces on L4 are in the same ratio of S and E. Therefore the resulting force is directed to b ! Note that L4 lies outside Earth’s orbit. Similar to L1, the two combined forces give L4 a period of 1 year, same as Earth.

Actually the barycenter of the Sun-Earth system lies extremely close to the Sun’s center of mass, The radius of the Sun is 670.000km and b lies about 450 km from its center! In this diagram this distance has been strongly exaggerated to show the process. In the usual diagrams of the Lagrange points, L4 and L5 are located so close to the Earth orbit, that it is not possible to see their separation.

Until now we have described the 5 Lagrange points as points that orbit the Sun in one year, same as the Earth. Another description is often used, a rotating coordinate system. In such a coordinate system, centered in the barycenter and rotating once a year, Sun, Earth and the 5 Lagrange points are stationary. But it comes at a cost. Because such a coordinate system is not an inertial system, fictitious forces have to be introduced, for example the centrifugal force,

In the diagram below the Lagrange points are indicated, in such a rotating frame. The contour lines give the gravitational field energy. Compare it with the contour lines on a topo map. The blue and red arrows indicate the direction of the force (the direction of the slope in a topo map). In topo map terminology L4 and L5 are located on the top a hill, while the other three are located in so-called saddle points. On first sight it would seem that all Lagrange points are unstable, For the L1-L3 points a small displacement in the x-direction, and for L4 and L5 a small displacement in any direction would be enough to disturb the balance (like a pencil on its tip).

Careful and complicated mathematical analysis (see for example here) leads to a surprising result: the regions around L4 and L5 are actually stable, objects in a large region around these Lagrange points will move in orbits and stay in that region. The regions around the other three Lagrange points are unstable, objects can orbit for a while, but will eventually escape. That is illustrated in the two diagrams below. The left diagram. shows the Sun-Earth system in an inertial frame, the right one in a rotating frame The 5 Lagrange points are marked in red.

Notice the moving tiny points, They are test masses. released near the various Lagrange punts. Look carefully and you will see that the test masses released near L1 and L2 quickly move away. For L3 it takes a bit longer. All these three Lagrange points are unstable. But around L4 and L5 the test masses do not “escape”, these points are stable.

In the introduction of this blog I wrote that the JWST had reached its destination at the L2 Lagrange point of the Sun-Earth system. Actually the space telescope is not positioned in :the Lagrange point itself but orbiting L2. And what an orbit it is! Elliptical, the distance to L2 varies between 250.000 km and 832.000 km. One period takes about 6 months. The orbit is not stable, about every 21 days the thrusters of the JWST must perform minor course corrections.

A more detailed explanation of the WEBB launch and orbit can be found in this brilliant YouTube video: How James Webb Orbits “Nothing”

There also satellites orbiting L1. At the moment for example the SOHO satellite to study the Sun and the DSOVR to study the Earth. Here are two pictures taken by these two spacecraft.

In 1978 the International Sun-Earth Explorer-3 (ISEE-3). was the first spacecraft that went into an orbit around a Lagrange point. It studied the Sun and Earth for 4 years and also here the unstable orbit had to be corrected regularly. Here is a diagram of the launch process.

After its mission was completed, the spacecraft got a new target, to study comets! It was renamed International Cometary Explorer, left its orbit and via amazingly complicated manoeuvres went on its way to a comet., Click on the screenshot to see an animation of the mission. Very informative and fascinating..

What about L3? This Lagrange point is permanently behind the Sun, as seen from the Earth. No scientific use, but it has played a role in science fiction. . Here is an example, a science fiction movie Journey to the Far Side of the Sun, released in 1969 (the same year that humans landed on the Moon). Click on the screenshot to watch the movie.

Synopsis of the movie: In 2069 a planet is discovered in L3 and the director of Eurosec (named Jason Webb !) organises a mission to what turns out to be a mirror-earth. Very interesting to watch.

We now know that L3 is unstable, with a “decay time” of about 150 year. It would be a suitable location for alien enemies to hide, while preparing for an attack 😉

L4 and L5 are stable (under certain conditions) but have no use for science. Possibly in the far future, these regions could be used to build human colonies.

Until here we have concentrated on the Lagrange points of the Sun-Earth system, but the Earth-Moon system has also its Lagrange points and so do for example the Sun and Jupiter.

Jupiter has collected thousands of asteroids around its L4 and L5 points. They are called trojans because they are named after heros of the Trojan war. Here is an animation. The asteroids in front of Jupiter are called the Greeks and the ones trailing Jupiter are called the Trojans.

The name trojan is now generally used for objects in the L4 and L5 points of other planets. In the L4 and L5 points of the Earth until now “only” two Earth trojans. have been observed.

But there may have been one in the early history of Earth!. I will end this blog with a fascinating theory about the origin of the Moon! The theory is called the Giant-Impact Hypothesis. When the Sun and the planets were born, about 4.5 billion year ago, Earth was not alone. It had a Mars-sized sister planet in the L4 (or L5) Lagrange point. About 20-30 million year later, this hypothetical planet, named Theia, possibly disturbed by the other planets, left the L4 region and collided with Earth. It must have been a cataclysmic event From this collision the Moon was born.. Here is the scenario.

And a visualisation

Here is the Wikipedia List of Objects at Lagrange Points

All the images are taken from the Internet, many from Wikipedia.

The DART mission

Posted on November 23, 2021 by janstu

Two years ago I published a detailed blog post: Will an asteroid hit Earth? In that post I discussed the scenario that an asteroid had been discovered on a collision course with Earth and what could be done to avoid such a possibly catastrophic collision. One option is to send a spacecraft to the asteroid and let it crash with it. The impact should change the course of the asteroid, so it would no longer hit Earth.. The DART mission will test the feasibility of this “kinetic impactor” technique. DART will be launched on 24 November, so it is time for an update.

The acronym DART stands for Double Asteroid Redirection Test. Target for DART is the minor asteroid Didymos, discovered in 1996. It has a diameter of 780 meter and orbits the sun in 2.11 year. In 2003 it was discovered that Didymos has a small moon with a diameter of 160 meter. This moon has been named Dimorphos , it orbits Didymos in about 12 hour at a distance of 1.2 km. DART will crash into this moon at a speed of 6.6 km/s. and change its orbit slightly. In the infographic this change is hugely exaggerated. It is estimated that the crash will change the speed of Dimorphos only about 0,4 mm/s and its orbital period about 10 minutes

Originally DART was part of the much more ambitious AIDA mission. The crash will take place at about 11 million km from Earth. How to observe the effects of the crash? The solution was to launch another spacecraft earlier than DART, which would reach Didymus and go into orbit around the asteroid. This AIM spacecraft , to be developed by the European Space Agency (ESA), would observe the crash and send data back to Earth. It would even deploy a small lander, MASCOT2 to study the properties of Dimorphos.

But in December 2016, AIM was cancelled by ESA, after Germany withdrew the 60 million Euro funding for the project. I commented in the above mentioned blog:

As an European I feel rather ashamed that Europe has acted this way.

NASA decided to continue with DART., which will be launched by a SpaceX Falcon 9 rocket. A fascinating feature from the Falcon 9 is that part of it (the first stage) will return to Earth, land vertically (!) and can be used again for other missions. It will land on a so-called drone ship, an unmanned platform in the ocean. There are three of these drone ships active at the moment, all with poetic names. The Falcon 9 will land on “Of Course I Still Love You” Here is the ship.

And here is a video of the take off and landing. You must see it to believe it ;-).

DART will arrive at the asteroid end of September 2022. The spacecraft will use autonomous navigation to point itself to the moon. It has a camera on board, the DRACO that takes high-resolution photos. On-board software will analyse these photos, be able to distinguish between Dimorphos and Didymos and point Dart to Dimorphos.

About 10 days before reaching its destination, DART will deploy a tiny spacecraft, a so-called CubeSat . This LICIACube has been developed by ASI, the Italian Space Agency and will take pictures of the crash. So at least images of the collision will be sent to Earth.

Here is a short YouTube video of the DART mission. I will point out a few details.

0:07 The nose cone of the Falcon 9 opens to deploy DART
0:15 the solar arrays are unrolled, a new technique. Each one is 8,5 m ;long
0:22 The lens cover of DRACO opens
0:26 Didymos in the center, Dimorphos to the right
0:32 The orbits of Earth and Didymos. They comes close, but are still 11 million km away from each other when DART crashes.
0:37 The Xenon thruster will steer the spacecraft
0:41 The LICIACube is deployed
0:54 DRACO will find the target
0:58 Found the target
1:02 On collision course
1:04 The end of DART

My next update about DART will probably be in October next year.

We are Star Children

Posted on June 13, 2021 by janstu

Twelve years ago I started an ambitious project, a series of webpages to explain that we can be considered to be Star Children, in the sense that all the atoms forming our body (with the exception of hydrogen), have been formed in the interior of stars.

The project was too ambitious, here is a screenshot of he small part I managed to complete. It is still available on my website. Click on the screenshot to have a look.

An adult human body (70 kg) contains roughly 7×10²⁷ atoms. Written out a 7 with 27 zeros: 7,000,000,000,000,000,000,000,000,000. That is a lot, actually much more than the estimated number of stars in the observable universe (10²³-10²⁴).

Most of those atoms are hydrogen atoms. The human body consists roughly of 60% water and each water molecule contains 2 hydrogen atoms and 1 oxygen atom. Oxygen comes second and carbon third. Together with nitrogen these four elements form more than 99% of the human body. For the graphs I have used data from the Wikipedia article Composition of the Human Body. Most of the graphs you find on the Internet give mass percentages, in that case oxygen takes first place. I prefer a representation in atomic percentages.

In this graph some of the other elements are shown. About 25 elements are considered to be essential for human life, some in minuscule percentages. For example Cobalt (in vitamin B12) contributes only 3.0×10⁻⁷ %

How, where and when were all these elements formed? The scientific name for the formation of the various elements is called nucleosynthesis.

Let’s start with the beginning, the Big Bang.

About 13.77 billion year ago our Universe came into being. That is the present estimate, with an uncertainty of ± 40 million year. It was unbelievably dense and hot, a “soup” of quarks gluons and photons. Immediately it started expanding and cooling and after a few minutes protons and neutrons could form. Some of these protons and neutrons fused into alpha particles ( two protons and two neutrons) until after about 20 minutes the temperature was too low for fusion.

But still way too hot for (neutral) atoms to form, it was a plasma (protons, alpha particles and electrons). If an electron and a nucleus would combine, the photons would immediately break it up again. Only after ~380.000 year, when the temperature had dropped to ~ 3000 K, electrons could recombine with protons and alpha particles to form H and He atoms. Roughly about 92% hydrogen atoms and 8% helium atoms. (usually mass percentages are given, 25% He and 75% H).

From that time onwards the photons did not interact anymore with matter, the universe was still bathing in an orange glow (3000K) but as the universe kept expanding and cooling, this radiation went from visible light to infrared , microwave etc. It is what we now still detect as the cosmic background radiation at a temperature of 2.275 K. About 1 million year after the Big Bang, the universe was COMPLETELY DARK!

These cosmic Dark Ages lasted for many million years. But small fluctuations in matter density caused gravity to form concentrations of matter. Inside these matter concentrations the temperature was rising until a level (many millions of degrees) that fission became possible again. The first stars were born and there was again light in the universe. Later also galaxies developed and after about 1 billion years the universe was basically like it is now.

Here is an impression of the development of the universe.

We will now concentrate on the evolution of these stars. First a few general remarks. Basically everything that happens in the universe is the result of four fundamental forces.

The strong nuclear force between nucleons, only active when the nucleons are very close together,”short-range”
The electromagnetic force, ~100 times weaker, but “long range”, holds atoms together.
The weak nuclear force, ~ 1 million times weaker, “short-range”, responsible for radioactivity.
The gravitational force, extremely weak, ~10³⁹ times weaker, “long-range”.

Back to the new-born star. All four forces are active here. The gravitational force tries to contract the star further. The strong force generates counter pressure, by fusing nucleons together, but those nucleons need to move fast (= high temperature) to overcome the electromagnetic repulsion. The weak nuclear force is needed to transform protons into neutrons. Here is how four protons can produce an alpha particle. Other options are also possible.

Our Sun was born 4.6 billion years ago as a relatively small star, a yellow dwarf. At the moment it is still “burning” hydrogen in its core and will continue to do that for another 5 billion years.

More massive stars will burn a lot faster to counteract gravity. The first stars may have had masses a few hundred times the solar mass, finishing the hydrogen it its core in only a few million years. What next? The core will contract and the temperature will increase. You might expect that fusion would start of two alpha particles into Beryllium (4 protons and 4 neutrons). But there is a problem, that Be isotope is not stable , it has a half live of only 8×10⁻¹⁷ s and decays back into two alpha particles. What will happen occasionally is that during its short lifetime, another alpha particle will collide and form Carbon (6p and 6 n). This is called the triple-alpha process and I will give more details in a separate appendix.

When this helium burning starts in the core, hydrogen burning will still continue in a shell around the core.

In the next phase, when the carbon core has been formed, carbon nuclei will fuse with alpha particles into Oxygen (8p and 8n) surrounded by a helium burning shell. And so on, Neon, Magnesium, Silicon etc. These fusion processes generate less energy than the hydrogen fusion and when iron is reached the fusion stops, fusion to heavier elements would cost energy! The star looks like an onion with its skins.

When there is no more energy to counteract gravity, the star will die in a spectacular fashion, releasing so much energy that for a short time it can be brighter than a whole galaxy. It is called a supernova. A large part of its mass will be ejected into the surrounding space and in the cataclysmic explosion many of the elements heaver than iron are formed. What remains of the star is a neutron star or a black hole.

Recently I have written a blog about the Witch’s Broom nebula, the remnants of a supernova explosion. More details in that blog. The most famous of these supernova remnants is the Crab Nebula. The supernova has been recorded by Chinese astronomers in 1054. The center of the nebula contains a neutron star.

Here are a few more examples. They are all false-color images (see my Witch’s Broom blog). Here is a List of Supernova Remnants.

As a result of these supernova explosions the clouds of interstellar gas became more and more “polluted”, no longer consisting of only hydrogen and helium. . It is from these clouds that new stars are born. For example our Sun, 4.9 billion year ago. Still mostly hydrogen and helium but about 0.1 % of the other elements. The big gas planets are also mostly H and He, but the rocky inner planets (Mercury, Venus, Earth and Mars) consist mainly of this 0,1 % other elements, as the hydrogen and helium have been “blown” away by the Sun.

Here is Earth, our Blue Marble, the iconic picture was taken by the crew of the Apollo 17 in 1972. Basically all its atoms have been forged in the interior of stars.

And the same holds for all living creatures, including us. Life on Earth is carbon-based, and each carbon atom has been fused in the interior of a star through the triple-alpha process.

We are Star Children
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APPENDIX

The energy that is released when particles are fused is called the binding energy of that particle. For nuclear processes this energy is usually given in MeV (Million electronVolt). 1 MeV = 1.6×10^-13 Joule. An alpha particle has a binding energy is 28.3 MeV. It is this (large) energy which generates pressure to counteract gravity in the interior of stars.

To fuse two alpha particles into beryllium is a different story. You have to add energy (it has a negative binding energy). Not much, 0.092 MeV, but as a result it is unstable, it will decay in two alpha particles. When the British astronomer Fred Hoyle in the 1950s studied the process how elements were formed in the interior of stars, he and others discovered this bottleneck.

During its short lifetime beryllium may fuse with another alpha particle into carbon and that will release energy, 7.367 MeV. The fiery furnace in the core of the star where fusion occurs would contribute another 0.3 MeV. Hoyle calculated that in most cases this “excited” carbon nucleus will decay into alpha particles instead of releasing the extra energy as gamma rays and settling down in its ground state. It could not explain the large amount of carbon found iin the universe.

UNLESS the carbon nucleus would have a so called resonance at an energy of ~7.7 MeV, Think about a soprano who can break a glass by letting it resonate with the frequency of her singing! But at that time no such resonance in the carbon nucleus was known.

Hoyle convinced his friend and colleague William Fowler, an experimental nuclear physicist, to search for such a resonance . And they found this excited level exactly at the energy predicted by Hoyle. This resonance level is now called the Hoyle state,

Was this a coincidence? Without this resonance level, carbon would not have been formed and carbon-based life would have been impossible.

Do we live in a Fine-tuned Universe ? Is the universe custom-made for “us” , the Anthropic Principle . Food for thought 😉

The Witch’s Broom Nebula

Posted on May 22, 2021 by janstu

In April the ESA/NASA project published this stunning image as its Picture of the Week. In this blog I will first show some pictures and then give an explanation and some background information.

The image was taken by the Wide Field Camera 3 of the Hubble Space Telescope.

The image shows a very small part of the Witch’s Broom Nebula, also called the Western Veil Nebula. I have marked the (tiny) location of the detailed image with an x (click to enlarge)

This nebula is in its turn part of the Cygnus Loop. Upper right the Witch’s Broom Nebula, lower left the Eastern Veil Nebula.

Getting confused? Here is the relation between the various images. Left the Cygnus Loop, in the middle the Witch’s Broom and right the detail.

The Cygnus Loop is located in the constellation Cygnus (the Swan). Deneb and Vega are very bright stars. The Cygnus Loop (Veil Nebula) is marked in the lower left

This YouTube video may also help

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About the Cygnus loop and the Veil Nebula

The Cygnus loop and the Veil Nebula are the remnants of a supernova. Many thousands year ago a massive star (much more massive than our Sun) had used up all its “fuel” and exploded in a final spasm before dying. In that explosion, much of the star material is ejected, leaving behind a neutron star or even a black hole. For a short period the star can outshine its whole galaxy!

In this NASA infogram, the development of such a massive star is given. It contains lots of information, but you can skip the details for this blog.

Much research has been done about the Cygnus Loop, the Veil nebula and the star that caused it. The Cygnus Loop is huge, its diameter is about six times the diameter of the moon. You need basically a telescope to see it.

It is a so-called emission nebula. The gas and dust in the nebula is ionised by the shockwave of the exploded star and the light we observe is the light emitted by the atoms in the nebula. The color of the emitted light depends on the kind of element. Very simplified: hydrogen emits reddish light, oxygen bluish light etc. When you look at the image of the Witch’s Broom nebula, you see that it mainly consists of (ionised) hydrogen and oxygen.

Determining the distance of the Cygnus Loop is a complicated process and you will find many values on the Internet. A distance of ~ 2400 lightyear is nowadays accepted by most astronomers. This would give the actual size of the Cygnus Loop as 130 lightyear! The loop is still expanding with a speed of ~ 1.5 million km/h

When did the star explode? Many different estimates. In the release of the first picture above a value of ~10000 year is given ( and a distance of 2100 lightyear). Humans living in that time would have observed the sudden appearance of a very bright “new” star, brighter than Venus and probably even visible in broad daylight. That explains the name (super)nova with nova meaning new in Latin. Supernovae are very rare, the last one in our own Milky Way, visible from Earth, was observed and studied by Kepler in 1604.

Scientists are still searching for a neutron star, or a blackhole in the center of the nebula, but until now nothing has been found.

A lot more can be said about supernovae. In the infogram above they are called “Engines of Creation” and that is an apt description. After the Big Bang the Universe consisted of hydrogen and helium, there was no oxygen no sulfur, no calcium, no iron etc. But Earth and all living creatures are built from those elements. How come? The answer is simple, all those elements have been formed inside stars! We are literally Star Children.

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About the pictures

The Wide Field Camera of the Hubble Space Telescope takes colorful pictures. Wrong! It takes black and white pictures as do basically all other telescopes. But it uses a filter to select only a specific color (range). And it takes pictures of the same object using other filters, selecting different colors. For the picture above with the stunning details of the Witch’s Broom five filters were used. And those filters are not just simple pieces of red, green or blue glass. A widely used filter is the H-alpha filter, that only lets through the red light of hydrogen (technically: a wavelength of 656 nm, bandwidth a few nm). Here is a picture of the Cygnus loop, using a H-alpha filter.

Compare it with this photo, taken with a color camera without any filters. Dominated by the numerous stars, the Witch’s Broom nebula is (almost) invisible,

Other popular filters in astrophotography are SII and OIII filters They select the colors of ionised Oxygen blueish and Sulfur (reddish) respectively and block all the other colors.

Combining pictures, taken with different filters, you must assign colors to the black and white images. One option is to choose colors that correspond closely to the color of the filter. In that case the result will look more or less “natural”. The red-blue image of the Cygnus loop is a result of combining the H, O and S filters. But of course you can assign different colors to the B&W pictures. Like in the image below, where hydrogen is green(!), oxygen blue and sulfur red.

The Hubble Space Telescope can also use infrared or ultraviolet filters. Here is the Cygnus loop in ultraviolet, blue has been assigned to the B&W image.

The Hubble website has a very informative section The meaning of color in Hubble Images. It shows how the B&W images can be combined in various ways. Very readable, with examples. Here are three.

Left is Mars, where the three filters have been assigned their “real” color. In the middle the famous “Pillars of Creation”, a star forming region. The red hydrogen is depicted in green, the red sulfur light in red and the green oxygen light in blue. The last example shows Saturn in unusual colors, because the B&W pictures were taken with various infrared filters. Near infrared is shown as blue, the middle range as green and the far infrared as red.

Finally here is again April’s Picture of the Week . The text says that It is a combination of five B&W images, Hydrogen in red, oxygen in blue and sulfur in green. No information about the other two.

Perseverance

Posted on March 7, 2021 by janstu

Are you staying up tonight?, a friend asked me a few weeks ago. No, why? , I replied. He knows about my interest in space travel and expected that I was aware of the landing of a spacecraft on Mars that night. But I was not 😉

I checked the timing, the Perseverance would land at 4:55 am in the morning of 19 February (Malaysian time). In this blog I will explain why I decided to enjoy my sleep and check the next morning if the landing had been successful 😉

In 2018 I wrote a blog Landing on Mars, in which I described the various Mars missions, concentrating on the Curiosity Mission of 2012. The procedure to land the Curiosity was new, using a so-called sky-crane for the last phase.

Here is a diagram of what is called the Entry, Descent and Landing (EDL) process. The spacecraft enters the (thin) Martian atmosphere with a velocity of ~ 20.000 km/h. About 7 minutes later it must land on the surface with a velocity of less than 1 m/s. As signals between Earth and Mars take about 11 minutes, EDL can not be controlled from Earth, the whole process must have been programmed in the computers on board. Mission Control can only wait and see. That’s why these 7 minutes have been called the seven minutes of terror.

In my 2018 blog I describe the three phases in more detail, here is an very informative animation.

In 2012 everything went well, the Curiosity is actually still operational at the moment, much longer than originally planned.

The Perseverance that landed last week, has followed the same EDL procedure. Of course it must have been a relief for Mission Control that it was again a smooth process, but to keep calling it seven minutes of terror is exaggerated. That’s why I decided to enjoy a good night’s sleep. Here is the EDL process for the Perseverance. As you see it is basically the same as for Curiosity.

The two rovers also look the same. To the left Curiosity, the official name of the mission is Mars Science Laboratory (MSL). The Perseverance, to the right, is part of the Mission 2020 project.

Of course there are differences. The wheels have been redesigned, the robotic arm is heavier and the rover carries more cameras, 23 in total. Notice the “hazcams” at the front and the back of the rover, to avoid obstacles. Sherloc, Watson and Pixl are science cameras, I will tell a bit more about them later.

Some of the cameras have not a real science function, but have been added mainly to please the general public 🙂 . The back shell has a camera looking up to see how the parachute deploys. The camera of the sky-crane is looking down and can follow how the rover is being lowered to the ground. And the rover has a camera looking upwards to see the sky-crane. And a camera looking downward to the ground. That one is important, the spacecraft has a digital map of the surface and uses the camera images with a lot of AI to steer to the right location.

Keep in mind that all these images can only be transmitted back to Earth, after the spacecraft has landed. During the EDL, Mission Control only receives telemetry signals (altitude, speed etc). NASA has published a spectacular video where those messages are combined with the camera images. This is a YouTube video your really should watch (several times!). No wonder that this video has already been viewed more than 14 million times.

This map of Mars gives the location of the NASA missions. Insight and Curiosity are still operational. For a list of all Mars missions, click here.

Perseverance has landed in the Jezero crater. In this picture, taken by the Mars Express orbiter, I have marked the landing location with a cross.

This amazing photo has been taken by the Mars Reconnaissance Orbiter, one day after the landing. During the EDL the heat shield, the parachute and the sky-crane (descent stage) have to be jettisoned away from the rover. When you enlarge the picture above, you can just see the two small craters.

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Perseverance’s mission

Now that Perseverance has landed successfully on the Red Planet, what is it going to do? The missions of Curiosity and Perseverance are basically the same, to determine whether Mars ever was, or is, habitable to microbial life.

When Mars was a young planet, billions of years ago, water was abundant, there were lakes and rivers, similar to young Earth. On Earth life started about 3,5 billion years ago in the form of microbes. Fossil remains of these microbial colonies are called stromatolites. Here is an example, found in Australia, ~ 3.4 billion year old.

Could primitive microbial life have started on Mars in a similar way? Curiosity landed in the Gale crater, created about 3.7 billion year ago by a gigantic meteor impact. The crater became a lake, rivers deposited sediments. Curiosity collected surface material with its robotic arm, pulverised and heated it, before using a variety of analysing tools. Many organic molecules were found, for example thiophenes. which, on Earth at least, are primarily a result of biological processes.

Mars Mission with the Perseverance will continue this research with advanced technology.

Here is an artist impression how the Jezero crater may have looked like, when it was filled with water. Notice the river, top left, flowing into the lake. That river deposited a lot of sediments in the lake and it is near these sediments that Perseverance has landed.

A detailed map of the landing region, with the various geological structures in different colors. The “valley” of the former river and the delta are clearly visible The location of the rover again marked with a cross. The scientists have already made a proposal how the rover will explore the region (yellow line). The mission will take at least one Mars year (687 Earth days). If you want more information why the Jezero crater was chosen, click here.

The robotic arm has three scientific instruments, the PIXL, SHERLOC and WATSON. PIXL stands for Planetary Instrument for X-ray Lithochemistry . SHERLOC is an acronym for Scanning Habitable Environments with Raman & Luminescence for Organics & Chemicals and WATSON represents a Wide Angle Topographic Sensor for Operations and eNgineering . Engineering sense of humor.

PIXL is the main instrument. It points a very narrow X-ray beam at a piece of rock and detects the reflected light (fluorescence ), which is characteristic for the chemical elements in the rock. By analysing this reflected light, PIXL hopes to find biosignatures. Here is an artist impression of PIXL in action.

SHERLOC searches for organics and minerals that have been altered by watery environments and may be signs of past microbial life . Its helper Watson will take close-up images of rock grains and surface textures.

Suppose that Perseverance finds promising locations during its traveling. Wouldn’t it be wonderful if scientists on Earth could study the material at these locations in greater detail?

Well, that is exactly the most ambitious part of the Mars 2020 project, to bring back rock and regolith back to Earth. When you are a follower of my blog, you may remember that Hayabusa2 has brought back material from the asteroid Ryugu, and of course moon rocks have been brought back. But never yet material from a planet.

The robotic arm of Perseverance contains a drill, which can collect core samples. Here it is ready to start drilling.

The core sample (comparable in size with a piece of chalk) is put in a sample tube and taken over to the body of the rover where a few measurements are made. Then it is hermetically sealed to avoid any contamination, and temporally stored in a cache container. The container has space for 43 tubes. Here is an example of a sample tube.

Watch the video to follow the complicated process. Three robotics arms are used!.

How to get these sealed tubes back to Earth? NASA and ESA (the European equivalent will work together in what at first sight looks almost like science fiction. Actually it is still partly fiction at the moment! Here is the plan.

In July 2026 (!) a spacecraft will be launched, consisting of a lander and a rover. In August 2028 it will land near the Perseverance.

Here the spacecraft has landed on the surface of Mars, the rover still has to be deployed.

The only function of the rover is to fetch the sample tubes and bring them back to the lander. In this artist impression it is suggested that the sample tubes are scattered around, but that doesn’t make sense to me. Probably Perseverance will have created a few depots, or even kept all tubes in its own storage. The various descriptions I have found on the Internet, are not clear about this. The whole Return Mission is very much work in progress.

Here the tubes are handed over by the “fetch rover” to the lander, where they are put in the Sample Return Container.

The Sample Return Container might look like this. It will be designed so that the temperature of the samples will be less than 30 degrees Celsius.

The container will be loaded in a rocket, the Mars Ascent Vehicle, which will be launched in spring 2029.

The rocket will bring the container in a low Mars orbit and release it there..

In the meantime In October 2026 the Earth Return Orbiter has been launched, it will arrive at Mars in 2027 and lower its orbit gradually to reach the desired altitude in July 2028. There it will wait to pick up the container.

After the Earth Return Orbiter has caught the container, it will “pack” it in the Sample Return Capsule (SRC) and then go back to Earth, where it will arrive in 2031, ten years from now. It is this SRC that will will be released and finally land on Earth.

Here is a simulation of the procedure.

The primary mission of Mars2020 is to determine if Mars was habitable in the past. But there are also secondary missions. On board of the Perseverance there is one experiment, called MOXIE, that will produce oxygen from the carbon dioxide in the Martian atmosphere. Just a proof of concept experiment, important for future human missions to Mars.

Quite spectacular is that Perseverance is bringing a small helicopter, the Ingenuity. The Mars atmosphere is thin, but the helicopter should be able to fly. A bit similar to a drone, flying a few meter high, and maximum 50 m away. At the moment it is still hanging under Perseverance, planning is to test it after a few months. Here is an animation

At the moment Perseverance is testing al its components. It has made its first test drive, only a few meters. Here is a picture, you can clearly see the tyre tracks.

If there is more news about the Mars2020 mission, I will update this blog or write a new one.

Let me end this blog with an animation created in 1988 (!) , describing a Sample Return Mission to Mars. Fascinating to watch.

Dust Grabbers

Posted on December 3, 2020 by janstu

Two years ago I have written a post, Hayabusa2 , about a Japanese spacecraft and a few months later an update, Solar System Explorers, in which I mentioned the American spacecraft Osiris-Rex.

The two spacecraft have in common that they have a similar mission: travel to an asteroid, collect some surface material from it and bring that back to Earth. That’s why I have given this post the frivolous title of Dust Grabbers.

When I wrote the two posts, both spacecraft had arrived at their respective destinations, but had not yet collected asteroid material. Now they have, so it is time for an update.

First about Hayabusa2. Here are asteroid Ryugu and the Hayabusa2 spacecraft.

After reaching Ryugu, Hayabusa2 had already successfully dropped two Minerva rovers and the Mascot lander on the surface of the asteroid (see my first report). The surface of the asteroid was much rougher than expected, here is a picture taken by one of the Minerva’s.

For the touchdown, Hayabusa2 needed a flat surface, without boulders or big rocks and it was difficult to find a suitable location. In my first report I have described the touchdown, here is a very informative animation of the process. Two screenshots, left just before the touchdown, right just after. Notice how flat the asteroid surface is in the animation.

The touchdown was originally planned for October 2018 but postponed, to give the scientists time to redesign the touchdown procedure and check if navigation could be made accurate enough to land in a very small region.

On 6 February JAXA (the Japanese equivalent of NASA) published an extensive pdf-file for the press, Asteroid explorer, Hayabusa2,reporter briefing with a detailed description of the redesigned touchdown. A location had been selected and a target marker (TM) had been dropped near the chosen location. A TM is a small (10 cm) ball of reflecting material, you can see it in the animation screenshots above, left in the foreground.

The actual touchdown finally took place on 22 February 2019. One day earlier Hayabusa2 had already descended slowly from its home position (HP) at 20 km altitude to an altitude of 45 m. Here is a time diagram of the touchdown phase. Notice that between 7:07 and 7:50 JST time, there is no communication between the spacecraft and mission control.

Also keep in mind that the touchdown is an autonomous process, because it takes 15 minutes for a signal from Earth to reach the spacecraft. All steps have been programmed by the scientists and engineers.

Try to imagine the tension in Mission Control during this “blackout” period. And the explosion of joy when the first signals from the spacecraft showed that it was still alive.

At first this is the only thing they know, that Hayabusa2 is still alive. Only later images and data were coming in. A small video camera was mounted next to the collecting horn and recorded the touchdown. Have a look at the video Here are two screenshots, before and after touchdown. I have indicated the position of the target marker, it is the white stip inside the blue circles. Also notice the surprising amount of rubble whirled up after the touchdown, mostly caused by the thrusters firing.

Originally a second touchdown was planned at a different location, but this was cancelled because of the rugged surface of Ryugu. Instead the scientists concentrated on the most ambitious part of the program. The first touchdown had collected some surface material of the asteroid. Technically called regolith . This material has the same age as the asteroid itself, but has been exposed during millions of years to solar wind and radiation.

Of course it would be very interesting to collect some asteroid material from BELOW the surface. Here is the ingenuous plan developed by the Japanese scientists:

shoot a projectile to Ryugu to create an artificial crater.
touchdown later in the crater to collect some newly exposed material.

And that’s what they did! I have described the working of the so-called SCI (Small Carry-on Impactor) in my first post. Basically it is a copper projectile (2 kg) that hits the surface of Ryugu with a speed of 2 km/s, creating a crater of several meters diameter. Here is a diagram of the operation. Lots of details, I will point out a few. The operation took place on 5 April 2019.

Hayabusa2 descends from HP to an altitude of 500 m and releases the SCI with a downward speed of 20 cm/s. Here you see a time-lapse of the deployment. It takes about 40 minutes for the SCI to reach the surface and detonate. The detonation will cause a lot of debris, so Hayabusa2 must take shelter and does that by moving horizontally away and then down into the “shadow” of Ryugu.

Before disappearing below Ryugu’s horizon Hayabusa2 deployed a camera (DCAM3) to take pictures of the explosion. Here are some images. Not that spectacular for a layman, but apparently the scientists were able to draw conclusions from the vague plumes of debris that are visible.

Because of Ryugu’s weak gravitation it takes days before the debris of the explosion settles down. Notice times and distances in the diagram, Hayabusa2 moves away horizontally for about 100 km before “climbing up” again and finally reaches HP more than 10(!) days after the deployment of the SCI.

After the successful creation of an artifical crater, Hayabusa2 descended a few times above the crater to explore the new situation. Was it feasible to touchdown in or near the crater to collect material, exposed by the explosion, without jeopardizing the success of the first touchdown? On 8 July Jaxa published a very readable report discussing the pros and cons of a second touchdown: To go or not to go . It was decided to go and have a touchdown in the region C01-Cb, not really inside the crater but on the rim. Here are two images to show the touchdown area. The left image shows the artifical crater at the bottom right, the right image gives details about the size of rocks near the touchdown.

The procedure for the second touchdown was basically the same as for the first one. During one of the descends a target marker was released and on 11 July 2019 the touchdown took place. A sample was collected successfully.

Mission accomplished, time to go home. How to deliver the two samples to Earth? Have another look at the Hayabuss2. I have indicated the Sampler Horn and the SRC, the Sample Return Capsule. In this tiny (40 cm diameter) capsule the two samples have been stored (right diagram) and it is this capsule that will be released when Hayabusa2 arrives back at Earth.

After leaving Ryugu on 13 November 2019,Hayabusa2 l will reach Earth on 6 December 2020, using its ion engines for navigation.

Here is a diagram of the SRC return. The capsule will enter the Earth atmosphere with a speed of 12 km/s, the heat shields will protect the sample container. At 10 km altitude a parachute will be deployed.

The planned landing location is the Woomera desert in Australia, about 450 km north-west of Adelaide. Expected landing 6 December between 2:47-2:57 JST. It will take time to find the capsule, hopefully within one day. Here is a photo of the Woomera desert.

JAXA is maintaining a monumental website about Hayabusa2, updated with the latest news: JAXA Hayabusa2 Project.

After this long report about Hayabusa2, I will be much shorter about the Osiris Rex mission. Here is asteroid Bennu, smaller (~500 meter) than Ryugu (~ 900 meter). Both asteroids are spinning fast (~ 4 and ~ 8 hours respectively) and that might partly explain their similar shape of a “spinning top”. Although the material of these asteroids is about 4.5 billion years old, both were probably formed after a catastrophic collision of parent asteroids, millions of years ago.

The Osiris Rex spacecraft has a similar design as the Hayabusa2, with a SRC csapsule for the collected asteroid material. But there is one big difference, instead of a sampler horn, the Osiris Rex has a robotic arm, which can be unfolded and grab regolith while the spacecraft is hovering above the surface.

This has its advantages. The Hayabusa2 has to touch the surface (through its horn) and therefore has to worry about rocks nearby. The robotic arm is longer (about 3 meter) and more flexible. Another advantage is the way of collecting regolith. The Hayabusa2 fires a tiny bullet inside the horn and catches the regolith that is swirling upwards. That will not be much, the team is hoping for 1 gram (!) of material. Only after the capsule is opened the mass of the samples can be measured.

The TAGSAM robotic arm of Osiris Rex works very differently. As soon as the sampler touches the surface, nitrogen gas is blown through the arm and regolith will be collected, almost like a vacuum cleaner. Here is a nice animation of the process.

The TAGSAM procedure took place on 20 October 2020 and was very successful, it is estimated that about 60 gram was collected. (For physicists: how can they know that now already? By using a clever trick, rotating the spacecraft and unfolded robotic arm before and after collection, a difference in the moment of inertia will be observed)

The spacecraft will leave Bennu next year and will return to Earth on 24 September 2023, deploying the SRC capsule to land in the Utah desert.

These has been close cooperation between JAXA and NASA. They will share a percentage of the collected material with each other.

TRIVIA:

Brian May, the lead guitarist of Queen, is also an astrophysicist and quite interested in the Hayabusa2 project. During a Queen tour in Japan in January 2020, he met a few project people: Meeting Brian May.

Because of the Covid19 pandemic, the Japanese Sample Collection Team had to arrive early in Australia (with special permission) and first go into 14 days compulsory quarantine . Here a team member is standing at the heliport where the search for the capsule will start.

The Game of Life

Posted on May 30, 2020 by janstu

Last month the English mathematician John Conway passed away at the age of 80. His name may not be familiar to many of you, but he was the inventor of the Game of Life, in 1970. For several years I have been interested in this game. A suitable time to write a blog about it.

When Conway was still an undergraduate at Cambridge University in the sixties, he became interested in “recreational” mathematics and got in contact with Martin Gardner, who had a popular column “Mathematical Games” in the Scientific American. In October 1970 Gardner published in this column The fantastic combinations of John Conway’s new solitaire game “life” Read here and here interviews with Conway about how he invented the game and that for a long time he actually hated it.

The game is played on a grid of adjoining cells, which can be either alive (black) or dead (white). Each cell is surrounded by eight neighbouring cells and what happens to a cell depends on how many neighbours are alive. These are the rules:

1. When a living cell has 0 or 1 living neighbours, it will die.
2. A living cell with 2 or 3 living neighbours will stay alive.
3. A living cell with 4 or more living neighbours will die.
4. A dead cell with exactly 3 living neighbours will become alive.

With zero or one neighbours you will die from loneliness, with four or more neighbours you die from overcrowding. With two or three neighbours you survive and when there are three parents around, a new baby is born. It looks a bit like life 😉

Of course other rules are also possible and it took Conway considerable time to find rules that gave interesting results. As there were hardly any computers in those days, they used a go board to follow the development of (simple) patterns!

Here are a few simple examples to show how the rules work. I have indicated the number of living neighbours in each cell. Living cells that will survive have a yellow number, those that will die have a red one. An empty cells with three neighbours gets a blue number. After the start pattern I have only marked the cells with get a colored number.

Two patterns have died, two became stable (one of them oscillating).

Here is a pattern of 5 cells. Again I count the number of neighbours, using the same colours, blue, yellow and red for birth, life and death. After 4 generations the original pattern appears again, but diagonally shifted one cell! This pattern has got a name, it is called a glider, it will continue moving diagonally

This pattern of 5 cells is very similar, with only the leftmost cell shifted to the right, but the behaviour is very different! It “explodes” rather chaotically, grows to a maximum of more than 200 cells and finally becomes stable after 1103 generations with 116 living cells, including 6 gliders (notice that three of them are escaping at t = 150). This configuration is called the R-pentonimo .

Of course you can not follow the development of such a pattern with pen and paper or a go-board. You need a computer. In those days they were huge and expensive machines. Here is a PDP-7 computer similar to the one used by Conway. The right picture shows the display screen running a life pattern. Click here for a video. The computers were still so slow that Conway was only able to follow the development of the R-pentomino until t = 460, when the article was published.

Here are a few more interesting patterns. This one is called a Heavyweight spaceship. It moves, like the glider, but orthogonally, two cells in 4 steps.

And here are three oscillators. From left to right Figure Eight (period 8), Pulsar (period 3) and Fumarole (period 5)

The publication in the Scientific American aroused a frenzy of interest among professional mathematicians and amateurs alike. Conway thought himself that no pattern could grow indefinitely and offered a prize of 50 dollar to the first person who could prove or disprove this conjecture before the end of 1970.

It took only a couple of weeks before an MIT group constructed a pattern that generates a glider every 30 moves. therewith proving that patterns can grow indefinitely. It is called the Gosper Glider Gun. and one of the many guns that have been found since then. Keep in mind that all this is the result of 4 simple rules 😉 .

Fifty years have passed since Conway’s invention of the Game of Life, and there is still considerable interest, leading to new interesting patterns every year. There exists a comprehensive Life Wiki, similar to Wikipedia, containing at the moment more than 2100 articles. Here is the main page of the wiki.

Notice at the right a list of pattern categories. The Wiki contains at the moment more than 1350 pattern pages. Each page gives a description of the pattern and an option to watch the development of the pattern, by launching the so-called Lifeviewer at the right side of each page. I have linked the patterns described above to the corresponding Wiki page.

There is a yearly competition for the Pattern of the Year . Here are a few winners :

David Hilbert (2019) , 122 cells an oscillator with period 23
Sir Robin (2018) , 282 cells, a spaceship moving in an oblique direction
Lobster (2011), 83 cells, another spaceship, diagonally moving

Not always use the creators fancy names. Here is the p416 60P5H2V0 gun (left image) It has 26342 cells and fires gliders from four directions which collide in such a way that every 416 generations a 60P5H2V0 spaceship (right image) is produced. The center image shows a just completed spaceship, while gliders are already approaching to form a new one. Fascinating. When you click on the image, you can watch a YouTube video of the process.

You can play with the Lifeviewer , by clicking the image below. You start with a blank grid, where you can draw any pattern you like. The Lifeviewer is versatile and powerful, it may take some time to get to know all the options, just give it a try!

Let me finish this post with a few general remarks.

The Game of Life is deterministic but unpredictable. Simple rules lead to complex behavior. All my life that has been a topic of great interest to me.
When I got my first desktop computer, in the eighties, I wrote my own Game of Life program, in Pascal and partly in Assembler. I took part in a competition. No prize but a honourable mention that my program was very fast. Nowadays a lot of software exists, powerful and of course much faster. Golly is the most popular one, you can download it here.
The Game of Life is much more than a collection of beautiful patterns. It has been shown by Conway himself that the Game of Life is a Universal Turing Machine, it can perform any calculation that a computer can do. The Pi-calculator calculates the decimal digits of π , the Primer uses the Sieve of Eratosthenes to determine the prime numbers. AND and OR gates can be constructed, etc.
The Game of life is an example of what is called a Cellular Automaton.
Martin Gardner has written three columns about the Game of Life. Here is the pdf-file with all three articles.

Betelgeuse

Posted on March 12, 2020 by janstu

Most of you will know the constellation of Orion. Here is an image taken by the Hubble Space Telescope. The bright reddish star, forming the left shoulder of the Hunter, is called Betelgeuse. Recently this star has been in the news, because there were indications that it might explode in the (near) future.

With the present level of light pollution, it is often difficult to observe the colors of stars, and you will see only the brightest. Of course a star closer to the Sun will look brighter than a star many hundreds of lightyears away. Taking the distance into account, astronomers can determine the intrinsic brightness of a star, called the luminosity. When you plot the luminosity of stars against their color, you get the diagram below. It’s called the Hertzsprung–Russell diagram, named after the two astronomers who created it around 1910.

As you see, the diagram has a lot of structure and it has helped astronomers a lot to understand how stars evolve. The vertical axis gives the luminosity, in units of the Solar luminosity, while the horizontal axis gives the surface temperature of the star, which is directly related to its color. Notice that the temperature decreases from left to right.

The position of some well-known stars is indicated. Of course our Sun, a yellowish star. Betelgeuse can be found in the upper right corner. it has a luminosity of ~ 100.000 times the Sun ! It is a so-called Red Supergiant Star. A giant star, it’s size is about 900 times the size of the Sun. If it would replace the Sun, we would be swallowed, it would extend to the orbit of Jupiter. The reddish color means that its surface temperature is about 3000K

There are also Blue Supergiant Stars. An example is Rigel, also in Orion (his right leg) with a surface temperature of 11000 K. And there exist White Dwarf Stars, with a size 0.1-0.01 times the Sun, and Giant Stars.

Along the diagonal in the HR diagram you will find the Main Sequence Stars. Most stars are located in this band. Here is a plot of 23000 individual stars in the HR diagram

To understand what will happen in the (near) future to Betelgeuse, I must explain a bit about how stars are formed and how they evolve. Stars are born when clouds of interstellar matter (mainly hydrogen and helium) contract as a result of their own gravity. This contraction increases the temperature in the interior of the cloud until the core becomes so hot ( about 15 million Kelvin) that fusion of hydrogen becomes possible. The energy and radiation from this fusion stops the gravitational contraction, a star is born! Here is a very simplified picture of the fusion process.

Let’s look at the star nearest to us, our Sun, It was born about 4.6 billion years ago, and its total lifetime is estimated to be around 10 billion year, so at the moment it is about halfway its life. Here is a sketch, the fusion takes place in the core, the radiation is transported to the surface (photosphere), resulting for the Sun in a surface temperature of about 5800 K and an orange color.

For a heavier star than the Sun, the inward pressure due to its gravity is stronger, so the counter pressure of the fusion in the core must also be stronger to create a balance. Here are some of the effects:

The star is bigger and brighter
Its core temperature is higher, the “burning” of hydrogen faster
The surface temperature is higher, the color more blueish/whitish
The lifetime of the star will be shorter

Here is an example: Sirius, the brightest star in the sky. Its mass is two times the mass of the Sun. Compared to the Sun, its radius is 1.7 times larger, its luminosity 25 times larger, its surface temperature is almost 10.000 Kelvin and its lifetime is only about 240 million years. Heavier stars will live even shorter.

We can now explain the Main Sequence in the HR diagram. It is the location of all “normal” stars, who are burning hydrogen in their core. At the lower right we find the low-mass stars, sometimes called red dwarfs , who burn their hydrogen so slowly that their lifetime is many hundred billions of years, longer than the current age of the Universe! At the top left, high-mass stars burn their hydrogen so fast, that in spite of their large mass they have lifetimes of only a few million(!) years.

What happens after the hydrogen fuel in the stellar core is exhausted? That depends on the mass of the star. We will concentrate in this post on the high mass stars (more than 8-10 solar masses), because Betelgeuse is one of them.

In these massive stars, after all hydrogen in the core has been fused into helium, gravitation will contract the core further, raising its temperature, until helium starts fusing into carbon. At the same time the outer layers of the star expand dramatically, while cooling. The star enters its (red) supergiant phase.

The triple-alpha process, as it is called, generates less energy than the hydrogen fusion. Three helium nuclei fuse into on carbon nucleus. Another simplified image.

When the core has fused into carbon, the process repeats. Gravitation contracts the core, its temperature increases , and another fusion process starts, leading to a neon core. Next an oxygen core, a silicon core and finally an iron core. Here is a sketch. A few comments. Notice the difference in scale. The outer layers of the red giant extend to the orbit of Jupiter, whereas the core has about the size of Earth! As you see, the central core is surrounded by layers of lower temperature where still fusion of hydrogen helium, etcetera is going on. It’s like the layers of an onion.

The red supergiant phase doesn’t last long, astronomically speaking, the energy of these fusion processes is much less than the hydrogen fusion. Here is an estimate of the time spent in each of the phases for a star of 25 solar masses. Notice the columns for temperature and density.

When the core has become iron , no more energy can be obtained from fusion and the end of the star is near. Gravity will finally win, the core implodes into a neutron star or a black hole while the outer layers are blown away in a cataclysmic explosion. It is called a (Type II) supernova. During a couple of weeks, the supernova may outshine the galaxy it belongs to and release more energy than the Sun during its whole lifetime. If the supernova is not too far away from us, it may become the brightest star in the sky, even visible during daylight. It looks like a new star (nova = new in Latin), but actually we are watching the last throes of a dying star.

Supernovas are extremely rare, they occur about once every 50 years in a galaxy the size of the Milky Way. A few have been recorded in human history, nowadays many more have been observed in other galaxies. In 1054, Chinese astronomers observed a new star, so bright that during a few weeks it was visible during daylight. Their accurate description made it possible for modern astronomers to conclude that it was a supernova (SN1054) and to identify the Crab Nebula as the remnant of this supernova. Here is the Crab Nebula. At its center a neutron star has been found, the Crab Pulsar.

Click here for a list of supernovae that are of historical significance. The most recent one in our own Milky Way galaxy was Kepler’s Star, observed in 1604, more than 400 years ago!

Time to go back to Betelgeuse. As mentioned in the beginning of this post, it is a red supergiant star at a distance of about 640 lightyear from us. Its mass is about 12 solar masses and its estimated lifetime about 8 million year. It has fused all the hydrogen in its core and is now burning helium in its core. Here is a computer animation of how Betelgeuse might look like.

The gigantic (convection) bubbles are characteristics for this kind of stars. Our Sun has them too, but on a much smaller scale.

Betelgeuse is a variable star, it changes its brightness in a rather irregular way. Here is a graph showing the brightness of Betelgeuse between 1990 and now..

From the right part of this graph you may understand why first astronomers and later the media and the general public became so excited about Betelgeuse. Starting October 2019, the star began to fade more than usual, and by the end of January 2020 it had dropped almost a factor 3 in brightness. A very noticeable difference, here are two photos.

Could it be that this dimming was a signal that Betelgeuse was on its way to become a supernova? It would be a spectacular event, the star might become as bright as the moon and be visible in daylight for many weeks. A harmless event too, the distance of 640 lightyear is too far away. By the way, light from Betelgeuse takes 640 year to reach us, so it could have been exploded already, without us knowing it yet 😉 .

Here is an example of a newspaper headline, in this case the Daily Mail , 23 December last year.

Not surprisingly observers from all over the world have been looking at Betelgeuse the last few months, as you can see in the graph below, notice the density of observations in the last three months :-).

I am sure it must have been a disappointment for many that the last month, the fading stopped and Betelgeuse started to become brighter again.

The last few weeks scientific papers are appearing with possible explanations for the unusual dimming. Probably it has been caused by dust. Supergiant stars regularly spew out some of their material into space, where it may condense into grainy particles, temporarily blocking the light of the star.

So, no supernova? Well, on the long term, it will. Betelgeuse is dying and will go supernova. That can happen in our lifetime, but it can also take 100.000 years or even more (see the table above with lifetimes of the various fusing phase).

I will end this post with two short paragraphs about related topics.

This blog is about massive stars. Our Sun, a dwarf star, has not enough mass to become a supernova. After exhausting the hydrogen in its core (in about 5-6 billion year) , it will start fusing helium into carbon and oxygen and become a red giant star, swallowing the inner planets, Earth included. But there the fusion stops. Gravity takes over, and the Sun will end as a white dwarf.
In massive stars, fusion ends when the core has become iron & nickel, because further fusion would need energy instead of releasing it. However, during the supernova explosion so much energy is released that elements heavier than iron can be created. Our Sun is a second-generation star, it was formed from an interstellar cloud that contained, besides hydrogen and helium, already material from earlier supernovae. Earth and everything in it, consists of atoms that have been formed in the interior of stars. We are Star Children, each atom in our body (except hydrogen), has been created inside a star!

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