DART and Hera

Four years ago, on 23 November 2021, I published a post titled “The DART Mission,” about NASA’s attempt to crash a spacecraft into a small asteroid in an effort to divert its orbit. The launch would take place the next day, and the crash was planned on 23 September 2022. So I ended the post with: My next update about DART will probably be in October next year.

Here is finally that update ;-). Let me start with an image from that blog. Didymos is an asteroid, a Near Earth Object (NEO) and even a Potentially Hazardous Asteroid (PHA), although there is no risk of collision with Earth in the next hundred years. A tiny moonlet Dimorphos, orbits the asteroid and was the target for the mission.

After a successful launch on 24 November 2021, DART arrived at the asteroid on 26 September 2022, about 11 million km away from Earth. How to direct DART to hit the tiny moonlet (about 150 m in diameter)? DART must do that itself with the help of its built-in camera DRACO. Four hours before reaching Dimorphos, still about 90.000 km away, DART became autonomous, using DRACO for navigation. Here is a photo taken by DRACO, 2.5 minutes before impact, the last picture where Didymos is still fully visible.

NASA collected all the pictures taken by DRACO and combined them into a time-lapse video. It shows the final 5.5 minutes, ten times faster, except for the last 6 images, which are shown in real time, every second. The “shakiness: in the beginning is a result of minor course corrections. The last image could only be transmitted partly because of the crash. A fascinating video.

The collision of DART and Dimorphos was a frontal one, so it reduced the speed of the moonlet a little but. This would cause Dimorphos to move a bit closer to Didymos with a slightly shorter period (see the first image above). Before the impact, one orbit of Dimorphos took about 12 hours. I wrote in my 2021 blog that the impact was expected to shorten the period by about 10 minutes. So it was a surprise that after the crash, the period of Dimorphos became 34 minutes shorter! In the appendix I explain how they could measure this, from Earth!

The explanation for the large reduction, was that the speed reduction of Dimorphos was not only caused by the crash of DART, but also, and even more, by the material blown away from the moonlet, causing an additional recoil.

How do we know that there was a lot of debris ejected by the crash? Because there was an eyewitness!

DART had on board a tiny spa craft, called LICIACub, which it released two weeks before reaching Dimorphos. This LICIACub had two cameras on board to take pictures of the crash and its aftermath. Here are two of the pictures. The left picture was taken 156 s after the impact, the right one after 175 s. The crash caused a lot of moonlet material to be ejected, probably leaving a crater in Dimorphos.

DART was very successful . It demonstrated that impacting asteroid could divert its course, important if ever an asteroid would be on a collision course with Earth.

n. October 2019 I published a blog Will an asteroid hit Earth?, after frightening reports of an impending asteroid collision with Earth appeared in the tabloid press. in that post I explained that the reports were sensational and not true. But catastrophic collisions have occurred in the past and may happen again in the future, so Earth must be prepared. NASA has its Planetary Defense program and so do other Space Agencies.,

In the context of this Planetary Defense, an ambitious collaboration started around 2013, between NASA and ESA. the Asteroid Impact and Deflection Assessment (AIDA) project. Two missions, DART by NASA and AIM (Asteroid Impact Mission) by ESA. AIM was to become the eyewitness, launched earlier than DART and going into orbit around Didymos, from where it could observe the impact and its aftermath.

The AIDD mission is shown below. AIM (lower right) is already in orbit around Didymos and has released two CubeSats and a Mascot lander which is hovering at the moonlet, here still called Didy-moon.

A fascinating project. But already a few years later, in 2016, ESA had to cancel the AIM mission, because Germany was unable/unwilling to contribute its portion of the funding. NASA decided to proceed with DART anyway and managed to include inro the spacecraft a CubeSat, which could act as an eyewitness. In my blog about DART, I wrote: As an European, I feel rather ashamed.

Then, in 2018, ESA came up with an alternative for AIM, called Hera. Basically, with the same mission, only reaching the asteroid in 2026, four years after the impact of DART. Here is an artist’s impression. It shows Dimorphos, with a very pronounced crater, the result of the crash. Two CubeSats are shown. No lander, but one if the CubeSats may land on the moonlet at the end of the mission.

Hera was successfully launched on 7 October 2024 and is now on its way to Didymos, where it will arrive in late 2026. In 2022 The atseroid was 11 million km away from Earth, but Hera has to travel nuch farther, abou 190 miilion km. In the video you can follow the trajectory of Hera. On12 March 2025 the spacecraft has used a gravity assist from Mars to get the right course to Didymos. In the vidoe Hera is the orange dot and Didymos the red one.

During the flyby Hera took fascinating pictures of Mars and its small moon Deinos.

When Hera arrives at Didymos, it will go into orbit around the binary asteroid. Spacecraft has landed on asteroids and crashed into them, but never gone into orbit. It needs careful navigation, much of it autonomous. Hera will study the crater formed by the impact of DART and investigate the properties of Didimos and Dimorphos. A fuill programme for the planned 6 months of the mission.

Appendix

You may wonder how astronomers discovered that Didymos had a companion, the tiny moonlet Dimorphos. Even with large telescopes, the asteroid shows as a tiny speck of (reflected) sunlight. In 2003 scientists noticed that the brightness of the speck of light varied periodically, showing tiny dips. They concluded that there had to be a companion transiting the asteroid, passing in front and at the back! They could measure the period to be 11 hours and 55 minutes, before the impact, and 34 minutes shorter after the impact.+

This image shows the effect, in an exaggerated way. The big dips are when Dimorphos passes behind the asteroid, the smaller ones when it transits before the ateroid, blocking a bit of its light.

The actual effect is so small that the scientists need advanced techniques to filter the data.

Apophis and Ramses

Besides eight planets, our solar system has a huge number of smaller astronomical bodies, mainly asteroids, but also comets and dwarf planets. They are collectively called Minor Planets, and data about their properties are collected by the Minor Planet Center in a database. At the time of writing this blog, the monumental database contains 1,478,907 objects, with new discoveries added daily. Most objects are asteroids in the main belt between Mars and Jupiter, but there is an important subcategory, the Near-Earth Objects (NEO), that come close to Earth. Their number in the MPC database is now 40,146, also daily increasing. When asteroids in this category have orbits that cross the orbit of Earth, and are large enough to cause substantial damage in case of a collision, they are called Potentially Hazardous Asteroids (PHA). At the moment, their number is ~2500, with an estimated ~2000 not yet discovered.

This beautiful image, published by NASA in 2013, show the orbits of the ~1400 PHA’s, known at that time.

On 19 June 2004, the Pitt Peak National Observatory discovered a “new” asteroid. It got a provisional designation 2004MN4 in the MPC database. In a recent blog, I explained the coding used by MPC. The M stands for the 2nd half of June, the N for the number 13, and the 4 means 4×25. This asteroid was the 13 + 4 x 25 = 113th asteroid, discovered in the second half of June 2004.

But 2004MN4 was not an ordinary asteroid. After its orbit was calculated, it became clear that it was a NEO and even a PHA, with a small probability (2.7%) that it would hit Earth on 13 April 2029. More accurate calculations of its orbit showed that it would not hit Earth, although it would come very close, and there remained a possibility that it might hit Earth exactly 7 years later, on 13 April 2036.’ The asteroid got a permanent number in the MPC database (99942) and was given the name Apophis, the Egyptian god of the underworld, the enemy of the sun god Ra.

The possibility of a hit in 2036 remained a matter of concern, and in December 2009 I read in the Guardian about a Russian proposal to send a spacecraft to Apophis and modify its course away from Earth. The newspaper had this impressive artist’s impression of what could happen if Apophis were to hit Earth. Click on the image for a link to the Guardian article.

This was the first time I read about Apophis, and I was curious to know more. I had just started blogging, and in January 2010 I published my first post: Will the Earth be hit by Apophis in 2036? I got a few comments from readers and published a second post a few weeks later: Again Apophis, with more details and an explanation why in 2036 it would be again on 13 April.

In the following years, accurate calculations of Apophis’ orbit showed that also in 2036 the asteroid would not hit Earth, not even in the next 100 years. Actually, none of the known PHA’s will hit Earth in the next century!

But on 13 April 2029, less than 4 years from now, Apophis will pass Earth within about 30,000 km. That is closer than the orbits of the geostationary satellites. An asteroid crossing our own backyard, what a unique opportunity!

In July 2024, the European Space Agency (ESA) proposed a mission to Apophis. It got the name Ramses (Rapid Apophis Mission for Space Safety), to be launched between mid April and mid May 2028 and to arrive at Apophis in February 2029 . It would then measure properties of Apophis before, during and after the flyby. It would also deploy two so-called CubeSats, miniature spacecrafts. One of them might try to land on Apophis. Here is an artist’s impression of RAMSES, the two CubeSats and Apophis, about 30,000 km above the surface of Earth.

Preparations for the mission started in July 2024 with partial funding by ESA. In August 2025 JAXA, the Japanese Space Agency, decided to collaborate with ESA and received funding from the Japanese government. RAMSES will be launched on one of their rockets.

Would RAMSES receive full funding by the European Union? Those decisions are made by the ESA Council meeting at Ministerial level, this year held in Bremen, 27 November. The result:

The largest contributions in the history of the European Space Agency, €22.1 bn

Three missions have been approved. So It means green light for RAMSES, which now has to be built on a very tight schedule, within two and a half years! But it makes sense, because RAMSES is part of ESA’s Planetary Defense System. Apophis is not dangerous, but another asteroid might be in the future, and inthat case fast action is critical. It explains the “Rapid” in the name of the mission.

This will be the first post about RAMSES, just to celebrate that it has been funded.

Alien attack in November?

The Sun, a UK tabloid, published on 17 August an article titled: A MYSTERY++ object tearing towards Earth at break-neck speed has raised fears that ALIENS are on their way here with these two pictures

That sounds scary, right? What is happening?. Here are the facts.

The “Mystery object” was discovered on 1 July 2025 by ATLAS (Asteroid Terrestrial-impact Last Alert System). ATLAS is a cooperation of earth-based observatories that continuously watch the sky, looking for moving astronomical objects. ATLAS started in 2015 and currently five observatories are taking part. They specialise in looking for smaller asteroids that may impact Earth and can only be detected when they are close. a last alert. Until now they have found 1241 Near-Earth asteroids, of which 110 were potentially hazardous. But also other objects were found, 106 comets and 4847 supernovae (which don’t move but change brightness)

The object found on 1 July is a comet, but it is causing huge excitement in the scientific community because of its extremely high speed. That means it comes from outside our solar system, will be slightly deflected by the Sun, and will escape again. Here is its (hyperbolic) orbit. The (animated) image comes from Wikipedia: 3I/ATLAS

The Wikipedia article contains a massive amount of information about 3I/ATLAS, a proof of the excitement caused by its discovery. Two more pictures from Wikipedia, the original discovery photo (animated gif) and a detailed photo taken by the Hubble telescope on 21 July.

The fuzziness of 3I/ATLAS in the Hubble picture is characteristic of a comet. The icy nucleus is hidden in a coma, water and dust evaporated by the solar radiation. That’s why the present estimate of its size is very inaccurate ( between 0.32 and 5.6 km). The comet will reach its perihelion (closest distance to the Sun) on 29 October and will never come closer to Earth than 209 million km (on 19 December).

Until now, three interstellar visitors have been detected: 1I/’/Oumuamua in 2017, the interstellar comet 2I/Borisov in 2019, and now 3I/ATLAS. In my blog post of February 2018, Oumuamua, I discussed in detail the first interstellar visitor. Now we have another one.

So, why the consternation in the popular press and the social media, like here or here or here. Google for 3I/ATLAS alien and you will find more links.

In my Oumuamua post, I wrote: “Of course, there are people who are wondering if it could be a spaceship”. Basically, it was one man who suggested this, Avi Loeb, an astrophysicist at Harvard University. He was widely criticised by the scientific community. He even wrote a popular science book about it: Extraterrestrial. The consensus is now that Oumuamua is just a physical object.

Avi Laub must have an obsession with alien life. Within weeks of 31/ATLAS’ discovery, he published an article, Is the Interstellar Object 3I/ATLAS Alien Technology? Here is a quote (bold by me):.

As largely a pedagogical exercise, in this paper we present additional analysis into the astrodynamics of 3I/ATLAS, and hypothesize that this object could be technological, and possibly hostile as would be expected from the ‘Dark Forest’ resolution to the ‘Fermi Paradox’

He also has a blog and wrote two posts about 3I/ATLAS, on 17 July and 5 August . And two weeks ago, he was interviewed by FOX 10 Talks. Click on the screenshot to watch the video. The interviewers are in awe that, for the first time, they have a Harvard professor in their program.

When Loeb is right about 3I/ATLAS, that it might be an alien, hostile spacecraft, what about November? Here is a possible scenario.

The spacecraft, disguised as a comet (!), reaches perihelium on 29 October. If you look at the animated GIF above, you will see that Earth is then on the other side of the Sun, so 3i/ATLAS will not be visible to us. During that period, the spacecraft will change its course and when it is visible again, it will come to attack and destroy us!

Just when I was ready to publish this post, I came across this website: Elon Musk: “It’s Confirmed, The 3I ATLAS is an Alien Space Craft!”. I am sure the mention of Musk is fake, only meant to attract more viewers. But the YouTube video on the website is fascinating, a mixture of science and sc-ifi. Click on the screenshot to watch the video.

Don’t worry. It’s a comet, not a disguised alien spacecraft.

Here is a promise. If humanity is still alive after November, I will write a post about the Fermi Paradox and the Dark Forest. And about my solution, the Rare Earth hypothesis.

Dwarf Planet 2017 OF201 and Planet 9

In April 2016 I published a post Our Solar System, an update. At the end of this post I wrote about the New Horizons mission, that it was on its way to the Kuiper Belt, after a successful flyby of {luto.

Here is the Kuiper Belt, a ring of (mainly) small icy bodies orbiting the sun beyond the orbit of Neptune. The distance scales are in Astronomical Units (AU), where 1 AU is 150 million km. the average distance between Earth and the Sun. The locations of Jupiter, Saturn, Uranus, and Neptune are given. Earth and the other planets are inside the yellow blob in the center. The grey cloud between this blob and Jupiter represents the asteroid belt.

More than 3000 Kuiper Belt Objects (KBOs) have been found and that number is increasing yearly. Many of them are (relatively) small, like, for instance, the 2014 MU69, mentioned in my 2016 post as the next destination for New Horizons. Another flyby on 1 January 2019 was very successful. Here is an image of 2014 MU69, taken by New Horizons. It is a contact binary, dimensions ~40x20x10 km, now renamed Arrokoth. See the appendix about naming (and renaming) objects in the Solar System.

The official name for any object orbiting the Sun beyond Neptune is Trans-Neptunian Object (TNO). Some of them can be quite large. In 2005 Eris was discovered, with a diameter of ~2300 km, about 1/5th of Earth’s diameter, similar in size to Pluto. A heated discussion among astronomers led in 2006 to the demotion of Pluto as a planet and the introduction of a new concept: dwarf planet. Pluto was always an odd one out with its elliptical orbit. It is now a dwarf planet, like Eris. Here is the Outer Solar System.

More dwarf planets have been discovered in the region beyond Neptune. A fascinating one is Sedna, discovered in 2003. Its orbit is extremely elliptical, its distance to the Sun varying between 76 and 937 AU, far outside the Kuiper Belt. One orbit takes 11.400 years, Various estimates for its diameter, Wikipedia gives >1000 km. Here is the orbit of Sedna in orange. The Outer Solar System is now so tiny, the Kuiper belt is marked in blue.

Also shown is the orbit of 2012VP113, in red. Discovered in 2012, diameter ~600 km. Again very elliptical, distance to the Sun between 80 and 460 AU. One orbit takes ~4500 years. You may wonder how astronomers discover such a remote object and even determine some of its properties. In the picture you can see how. Three images, taken by a powerful telescope, with a 30-minute interval, have been superimposed. Look at the small dot in the center. That is 2012VP113, moving against the background of stars

One more extreme TNO, 2015TG387, was discovered in 2015. Its aphelion (the farthest distance from the SUn) is a staggering 2114 AU. The orbital period is about 40.000 years.

More of these extremely elliptical TNOs have been found. What can have been the cause? . Not the giant planets or the Kuiper Belt, they never come close enough to feel their gravitation.

In 2016, two astronomers, Batygin and Brown, came up with an interesting hypothesis. A planet with a mass of about ten times that of Earth, orbiting the Sun in an elliptical orbit between 280 and 1120 AU, orbital period of 5000 years, could explain the orbits. In the diagram, the orbit of this hypothetical Planet Nine is shown.

P[anet Nine has not yet been found and it will not be easy. Not all astronomers are convinced that it exists, but it generated a lot of interest in extreme TNOs.

Recently, a new one has been found 2017 OF201. First observed in 2017. Distance to Sun between  45 and 1630 AU. Orbital period 24.000 years. Here are again three superimposed pictures, this time taken with an interval of 1 hour. Estimated diameter ≈ 550 to 850 km.

In an appendix I will tell more about the interesting way this extreme TNO was discovered and how an estimate could be made about its size. The evidence presented was so convincing that on 21 May TNO 2017 OF201 was accepted by the authoritative International Astronomical Union (IAU) as a new dwarf planet. I flurry of articles in magazines and newspapers followed. Some are accurate, like the EarthSky one, others contain errors, like the Yahoo!News one.

Here the orbit of 2017PF201 is added in red to the other TNOs. The supposed orbit of PLanet 9, here called Planer X, is shown in black.

As you see, the orientation of this new TNO is completely different from the others! And that is a serious challenge for the Planet 9 theory. Model calculations show that Planet 9 would strongly disturb the orbit of 2017 OF201 and, in the future, would kick it out of the solar system. So, does Planet 9 really exist?

That was the ending I had in mind for this post.

But, very recently another interesting article was published, claiming that PLanet 9 may have been found! Click here for the original publication (quite technical). The idea is “simple”. Planet 9 will be cold, but still it emits (thermal) infrared radiation. The authors use data from two infrared missions, IRAS (1983) and Akari (2006), comparing them, filtering out all known infrared sources and looking for an area, that doesn’t move within a few months, the operating time of both missions, but is found in a different location after 23 years. They find one suitable candidate, which fits with the theoretical orbit of Planet 9. Amazing.

I am sure that this is not the end of the story 🙂 .

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Appendix 1 Naming/renaming of astronomical objects in the solar system

All astronomical solar system objects (except comets), smaller than planets, are called minor planets (planetoids). Asteroids, KBOs, TNOs, and dwarf planets. The Minor Planet Center keeps track of them. When a new minor planet has been discovered, it gets a name. For the new dwarf planet, this (provisional) name is 2017 OF201. Here is the explanation. 2017 was the year it was first observed. Followed by two letters.

The first letter, O, tells in which half-month of that year it was discovered, in the second half pf JUly 2017. The second letter gives the order of discovery for that half-month. The F would naan that it was the sixth minor planet discovered in that half-month. But wait. When this coding was designed ( in 1925), it could handle 25 discoveries in a half-month, but nowadays, with modern technology, there are many more. That’s why the subscript is added. 201 x 25 = 5025 +8 = 5033. This dwarf planet was the 5033th discovery in the second half of July 2017!

When the orbit is determined accurately enough, this provisional designation is replaced by a (sequential) number. The team that discovered the minor planet can then suggest a name. The minor planet 2014 MU69, visited by New Horizons, is now named 486958 Arrokoth. Using the coding given above, you should be able to check that Arrokoth was the 745th discovery in the second half of June 2014.

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Appendix 2 T The discovery of dwarf planet 2017 OF201.

The original article can be found here. The authors use data from the Dark Energy Survey project, which itself is not related to the solar system. To find objects in the solar system, you must look for objects that move. Using the survey data, already ~800 TNOs have been found. The next step is to find the distance of the object. For that we use the apparent motion of the object against the background of the stars. It is called parallax. Due to Earth’s orbit around the Sun, the position of the object changes. From how much it changes, the distance can be calculated. For 2017 OF201 this distance is at the moment about 90 AU.

The combined effect of parallax and real motion for 2017 OF201 is shown in this diagram

The oval (due to parallax) is moving throughout the years. Observation dates are indicated.

From the amount of light, combined with the distance, a rough estimate can be made of the size. For 2017 OF201 this results in a diameter of 550 to 850 km . Big enough to call the object a dwarf planet.

2025 is a leap year!

Before you start protesting, we are not talking about the Western (Gregorian) calendar but about the Chinese one 😉 .

In the Western calendar, a year has 365 days, but one orbit of Earth around the Sun takes 365.25 days, 6 hours more! To compensate for this shortage, an extra day is added (29 February), when the year is divisible by 4. As 2025 is not divisible by 4, it is NOT a leap year. Have a look at Appendix* f for more details.

MoonThe Chinese calendar is a lunar calendar, based on the orbit of the Moon around the Earth. One orbit takes on average 29.53 days. Therefore, a lunar year is 12 x 29.53 = 354.36 days, 11-12 days shorter than the solar year.

As a result the lunar year moves forward 11-12 days yearly with respect to the solar year. The Islamic calendar is doing that.

Does that matter? It depends, for an agricultural society it does, because a lunar calendar has no relation with the seasons.

The solar year has seasons because the Earth’s axis is tilted. Here is a diagram. There are two times when the Sun is right above the equator. Day and night are of equal length all over the world. They are called the Spring equinox (~ 21 March) and the Autumnal equinox (~21 September). Around 21 June, the Sun reaches its northernmost position, the Summer Solstice, when daylight is at its maximum in the Northern hemisphere. Half a year later, the daylight is minimal. around 21 December, the Winter Solstice. (Of course in the Southern hemisphere it is just the other way around).

I wrote “around” and in the diagram a few dates are mentioned. In Appendix 2 I will explain why the dates vary, although the events are fixed.

Another way to describe the location of the Sun, is by using degrees (ecliptic longitude is the technical term).. We start at the Spring equinox (0°), and go counterclockwise. Then the Summer solstice is at 90°, the Autumnal equinox at 180°, and the Winter solstice at 270°.

Can we also divide the solar year in months? Sure, by dividing the Sun’s orbit in 12 sectors, each of 30 degrees. Each sector corresponds to a solar month. It is what the Chinese solar calendar does. It introduces 24 Solar Terms, two for each month, one for the start and one for the center. It is called the Center Point of that month. (similar to a Full Moon day in the lunar calendar). Here is a diagram of the 24 Solar Terms.

The diagram contains lots of information, the names of the solar terms (in English and Chinese) and the approximate dates. When you are Chinese, you may find a few familiar names: Qing Ming (15°), Dhong Zhi (270°) and Li Chun (315°). More about this in Appendix 3.

To explain the lunisolar calendar, we need the dates for the lunar and the solar months. Lunar data( for the years 2005-2045) can be found here and the Solar Terms (for the years 1900-2049) are here.

Here is the info for the first lunar month in 2025. The link above gives 29 January at 20:35 for the New Moon. So, the first month of CNY starts at 29 Januarty. The next New Moon is at 28 February, so the last day of the first month is 27 February.

The Solar calendar starts with Li Chun (the beginning of Spring). Using the Solar Terms link above, we find the date for that solar term: 3 February at 22:10, so the first solar month starts on 3 February. The next solar term (Rain Water) is at 18 February 18:-0, so tne Center Point is on 18 February. I have collected the results in the table below. The first lunar month contains the first solar center point.

I have done the same for the next two lunar months.More or less the same but the Solar Center Point shifts to more the end of the lunar month (8 resp. 7 days). That makes sense because a solar month is slightly longer than a lunar month.

Here are the other months for 2025. Notice the month I have given a blue color.

As you see there is a lunar month that doesn’t contain a solar center point!. When that happens, that month is considered a leap month. It just duplicates the earlier month. The result is that a lunisolar leap year contains 13 lunar months.

Notice how after the leap month the solar center point is at the beginning of the lunar month. Each lunar month it will advance 1-2 days, so after 2-3 years there will be another leap month. Not necessarily the sixth month, like this year. See Appendix 4.

In the Chinese lunisolar calendar, a lunar month is a leap month when it does NOT contain a solar center point.

Appendix 1 About a leap year in the Gregorian Calendar

A leap day is added when the year is divisible by 4. This makes the length of a year 365 + 1/4 = 365.25 days. But the solar year is actually 365.2422 days, slightly less. Therefore, the Gregorian calendar has a second rule: when the year is divisible by 100, it is NOT a leap year; This makes the average year length 365 +1/4 -1/100 = 365.244 days. A better approximation, but it can be made even better by a third rule: when the year is divisible by 400, it IS a leap year; making the average year length 365 + 14 − 1100 + 1400 = 365.2425 days. More information about leap years can be found here.

Appendix 2: Why do the dates for solar terms vary, while the events are fixed.

Because a normal year is 6 hours short of a solar year, the solar terms will shift 6 hours! Take for example Li Chun. In 2025 it falls on 3 Fberuary at 22:10, but in 2026 on 4 February at 4:02. Six hours later, so next year Li Chun will fall on 4 February. Another cause of variability is the time zone system we are using on Earth. All dates and times in this post are in China/Malaysia time (UTC + 8). in that timezone the Summer Solstice falls in 2025 on 21 June at 2:42. New York is using Eastern Time (UTC-4), the Summer Solstice in that timezone is 12 hours earlier and falls on 20 June 22:42, one day earlier.

Appendix 3 About Dong Zi, Qing Ming and Li Chun

The Chinese festivalls follow the Lunar calendar , with three exceptions. Around Qing Ming (Cheng Beng) Chinese families visite the graves of their ancestors. `And around Dong Zhi, Chinese celebrate the harmony in the family. Li Chun is of special imporatnce for the believers in Feng shui. All three belong to the solar calendar, they don’t move around.

Appendix 4: How to find a leap month

You don’t need mathematics to find a leap month, just the tables for moon phases and solar terms as given above. Solar Center Points advance relative to lunar months, so we must find a lunar month where the Solar Center point falls on the first day of that month. We have to continue until 2028 before we find a month that fits that condition. Here is the relevant part of the table for 2028

I2028 will be a leap year, the 5th month will be duplicated.

Life on Europa & Enceladus?

It is generally assumed that you need liquid water for life to develop. The planet Mars is now dry and arid, but had lots of water in its far past.. The Perseverance rover (see my blog) is at the moment collecting samples of Martian soil, hoping to find fossil remains of (microbial) life, until now without results. Disappointing for those who are convinced that “simple” life must be ubiquitous in the universe.

When you have been following my blog, you will know that I am not really surprised. Personally I think that (simple) life will NOT develop easily, even in a suitable environment. See my recent post about the Drake Equation.

Are there other places in our solar system with (abundant) liquid water? Yes, there are, here are two, Europa and Enceladus. Europa is a moon of Jupiter and Enceladus a moon of Saturn. Europa is large with a diameter of 3122 km, only slightly smaller then Earth’s Moon (3475 km). Enceladus is much smaller, with a diameter of 504 km. In this image you see the relative sizes of Earth, Moon and Enceladus,

Here are the two moons, Europa left and Enceladus right.. Both moons are covered with a thick crust of water ice. This ice surface has a temperature of about -200 degree Celsius. But underneath this crust both moons have oceans of liquid water!

We think that the interior of the two moons look like this. Europa has a metallic core (iron and nickel),a rocky mantle and a (salty) ocean with an estimated depth of 60-150 km.. A thick ice crust ( 15-25 km) covers the ocean. The model shows the layers to scale.

Enceladus has a rocky core with radius of ~ 180 km , covered by a 30 km deep ocean. and a 20 km thick crust. The ice crust is thinner at the south pole.

How is it possible that these moons have liquid water under their ice crust? Where does the energy come from, the Sun is far way. The answer is: because of the tidal forces exerted by the giants Jupiter and Saturn on their moons.

Newton’s gravitation between two objects depends on the distance between them. For example the gravitational force exerted by the Moon on Earth is stronger on the side facing the Moon than on the other side. This difference is responsible for the tides. The tidal friction will slow down the rotation of Earth , so the length of a day will increase a little bit, about 1,8 millisecond per century. In the far past when the moon was born, the day length may have been about 4 hours only!, For the moon the story is similar: tidal friction has slowed it down, even a lot more, the Moon shows always the same face to Earth, it is “tidally locked”. Actually all the major moons in the Solar System are tidally locked to their planet.

Even tidally locked moons still can undergo tidal flexing, if the orbit is elliptical, a kind of kneading. Model calculations for Europa and Enceladus indicate that this .can generate enough energy to keep the oceans liquid. More (technical) details here.

So both moons have liquid water and a source of energy , two of the essential ingredients for life as we know it. The third ingredient (chemicals like carbon, hydrogen, nitrogen, oxygen, sulfur, and phosphorus) should be available in the rocky core.

The information about the two moons comes basically from two successful space missions. The Galileo spacecraft arrived at Jupiter in 1995 and stayed in orbit until 2003. It’s main mission was to study the planet, but it managed to have numerous flybys’ of Europa. The Cassini entered Saturn’s orbit in 2004 and stayed there until 2017.

The Cassini mission was very successful, click here for an overview. One of the most spectacular discoveries was that Enceladus is an active moon. There are geysers in the south polar region of the moon! This picture was taken by Cassini in February 2010.

The geysers consist of water vapor and ice particles. The explanation is that water seeps from the ocean floor into the rocky core where it is heated. The heated water rises and erupts though fissures in the icy crust.. It is a bit similar to the hydrothermal vents in Earth’s oceans.

There are indications that Europa also has this kind of geyser activity, although less intense Here is a recent (2021) NASA report, Are Water Plumes Spraying from Europa?

In the search for extraterrestrial life these two moons have top priority. Many proposals for missions to Europa have been formulated and later discarded, here is a list. At the moment the Europa Clipper is being prepared for a launch in October 2024. It will arrive at Jupiter in April 2030. Here is an artist’s concept, of Clipper, Europa and Jupiter. The solar panels of Clipper span 30 meter!

The artist impression might suggest that the Clipper will orbit Europa, but that is not the case, it will orbit Jupiter in an elliptical orbit and make 44 flybys of Europa. It will study Europa’s icy crust, find confirmation for the ocean underneath and try to make flybys through the geysers (if they exist).

A proposed follow-up mission is the Europa Lander. It would land on Europa, collect some material from the icy crust and search for biomarkers, signs of life. Here is another artist impression. Notice the geyser at the horizon 😉 .

Probably the Europa Lander mission will be cancelled. Why? Because Enceladus offers better options than Europa. The main difference is that Enceladus is continuously spewing water and ice crystals, whereas the geysers of Europa are sporadic and still have to be confirmed.

The reason that there is so much interest in the geysers is obvious. To find out if there is life in these oceans, we have to drill through a 15-25 km thick ice crust first. Actually there are studies how to do that, they read like science fiction. Here is the final report (pdf file, 70 pages, 2019) about the Europa Tunnelbot. The basic idea is that this tunnelbot would melt itself down through the ice crust of 20 km in 3 years time, to reach the ocean. Here is a artist impression from the report, I have rotated it 90 degrees, to fit better in this post. Left is the icy surface of Europa, the inset shows three “repeaters” because even when the bot reaches the ocean it still must transmit date to the lander.

Science fiction and I think it will never happen, because the geysers on Enceladus and possibly on Europa may already give information about life in the oceans below the crust!

After Cassini observed the geysers on Enceladus, the scientific program was adapted and the spacecraft went a few times through the plumes. It found water, ice crystals and organic compounds!

So that will be the program for the next decades, explore Enceladus and find out whether the geysers will have convincing biomarkers.. .

Of course it will take time to design Enceladus missions. Here is one, the Enceladus Orbilander. Approved as a so-called Flagship Mission. Still in the design phase. possible launch in the late 2030s Arriving at Enceladus in the early 2050s.

First it will fly numerous times through the geysers, collect material and analyse it. Then it will land at the South polar region.

This is the South polar region of Enceladus. The “tiger stripes” are fissures in the ice crust where geysers erupt.

And here is an artist impression of the Orbilander on the surface of Enceladus.

Until now life has only be found on Earth. Discovery of (primitive) life elsewhere in our solar system would be dramatic, because in that case we would know that (intelligent) life is ubiquitous in the universe.

At the moment Perseverance is collecting soil samples on Mars which will be brought back to Earth by the Mars Sample Return Mission around 2033. At about the same time Clipper will explore Europa. So we will have to wait for 10 years and for results from Enceladus about 30 years.

Perseverance perseveres

On 18 February 2021 the Perseverance rover landed successfuly in the Jezero crater on planet Mars. A few weeks later I wrote a detailed blog about the landing and the mission of the Perseverance: to determine whether Mars ever was, or is, habitable to microbial life. We are now more than two years later, time to give an update. I assume that you have read the first post ;-).

First about the Ingenuity helicopter. There has been a lot of opposition to include the helicopter in the project, many people were worried that it might compromise the main goal of Perseverance. Here are two pictures taken by the WATSON camera (mounted on the robotic arm). Left the Ingenuity still under Perseverance’s belly with its legs unfolded, right next the the rover, ready to fly. Photos taken 1 and 7 April 2021, respectively

Here is a selfie of Perseverance, taken on 6 April 2021 again by the WATSON camera. Notice how small the helicopter is. Do you wonder why you don’t see the robotic arm in this picture? Actually WATSON took 62 pictures, resulting in this composite image, click here for details.

Originally only 5 flights of Ingenuity were planned, just to test if the helicopter could fly in the very thin Martian atmosphere. Because contact with Earth takes about 11 minutes, those flights have to be autonomous. They were so successful that the Ingenuity is still operating now, on 23 April it had its 51th flight. It is actually scouting for Perseverance to find suitable locations to explore. Click here for a list of all flights, full of interesting details. During flight 51 Ingenuity took a picture of Perseverance (upper left corner). Not easy to spot, the right picture shows an enlargement

In my Perseverance blog, I could only be rather vague about details of the mission. The rover was supposed to collect samples of Martian rocks and soil (regolith), using the drill on its robotic arm. Then put these samples in sample tubes and store them in a container. Here is an example of a sample tube, the container can hold 43 of them.

Here is the proposed route at the time when I wrote my blog.. The x marks the landing of Perseverance in the Jezero crater, which was a lake, billions of year ago. In those days a river was flowing into the lake (from the left), creating a delta of sediment. If ever life developed on Mars, this region might be suitable to find proof of it.

And here you see the actual route of the rover during the last two years. It is a screenshot from the NASA website Where is Perseverance? Really worthwhile to visit the site, you can zoom in on the map which is updated regularly. The red markers give the locations where samples have been collected. The blue markers show where the Perseverance and the Ingenuity are.

When you visit the website and zoom in, you will get this. Clicking on a white circle will tell you when the rover was there, clicking on a line segment gives the distance, clicking on a red marker will tell you the number of the sample collected

During the two years that Perseverance has been exploring, it has collected 19 samples, here is the list, with lots of details for each sample.

The first sample was actually a failure, it must have been a shock for the team! Here is a screenshot. Sample Type: Atmosopheric. The core must have been too powdery/brittle, broken into pieces, and the capsule is empty. More about it here .

Fortunately all other sampling attempts until now were successful. Here is an example. The rocky outcrop has been named Wildcat Ridge. Two samples (no 12 &13 in the list) have been drilled and a circular patch of the rock has been abraded to investigate the rock’s composition.

Why two samples from the same location? When you look at the list, you will find that this is the usual procedure. All samples have been collected twice from each location (except the first, failed, one).

In the period between 21 December 2022 and 28 January 2023, one sample of each location has been dropped in what has been called a depot, named Three Forks. I have indicated the location with a red oval in the detailed map above. Here is a picture of the second sample being dropped.

And here is a collage of all 10 samples dropped. THe Atmospheric sample, 8 samples with rock or regolith and one witness sample. A witness tube will follow the same procedure, but not collect any rock or regolith. Back on earth it will be inspected to check for any contamination with material from Earth. Click here for more details.

,The sample tubes tubes are not dropped at the same spot, but about 5-15 meter apart. The center of each circle is the location where that sample was deployed, with in red the name given to the sample (see the list).

Why all this? Basically for safety reasons. The ultimate goal of the mission is to bring the sample capsules back to earth, where they can be studied in much more detail than is possible by Perseverance. In my first blog I wrote that this so-called Mars Sample Return porject at first sight looks like science fiction. And I still think it does 😉 . Here is an outline of the project in its present form.

  • In 2027 the Earth Return Orbiter (ERO) will be launched and reach Mars in 2029 where it will go in orbit and wait for the container with the samples.
  • In 2028 the Sample Retrieval Lander (SRL) will be launched. It will land on Mars in 2029, probably close to the Three Forks depot. It will bring two helicopters and the Mars Ascent Vehicle (MAV), a rocket.
  • If Perseverance is still working properly, it will also travel back to the Three Forks depot. In that case it can transfer its samples to the MAV
  • If not, the two helicopters will transfer the ten dropped samples to the MAV
  • After the samples have been stored in the MAV, it will leave Mars, go in orbit around the planet and release the container with the samples.
  • The ERO will pick up the container with the samples and place them in the Earth Entry Vehicle (EEV). Then it will leave its orbit and travel back to Earth
  • Near Earth the ERO will release the EEV which will “fall” back to Earth. No navigation, no parachute. It is scheduled to land in 2033 in the desert sand of the Utah Test and Training Range.

In this artist impression the Sample Retrieval Lander is at the right, left the Perseverance. The Mars Ascent Vehicle has just been launched, it will bring the container with the precious samples to the Earth Return Orbiter. One of the Sample Recovery Helicopters is hovering in the thin Martian atmosphere.

In the original design, the Sample Retrieval Lander carried another rover which transported the sample tubes from Perseverance to Mars Ascent Vehicle. . It has been skipped because of the success of the Ingenuity helicopter. The Sample Recovery Helicopter has basically the same design, but is stronger, can carry a small load and has wheels. Here is an artist imprssion. It can transport a dropped sample tube, one at a time, from the depot to the Lander.

.Another design change is that the Sample Retrieval Lander has a powerful robotic arm to put the samples in the sample container. Have a look at this fascinating video. The robotic arm picks up a sample tube from the ground, and puts it inside the rocket. But it can do the same with samples stored inside the Perseverance.

Have a look at this animation. You see the Sample Retrieval Lander land near the Perseverance. The robotic arm transfers the sample capsules to the Mars Ascent Vehicle, which is then launched. When in orbit it releases the container with the samples. This container is then collected by the Earth Return Orbiter. There the container will be placed in the Earth Entry Vehicle. All this will take place after the landing of the Sample Retriever Lander in 2029.

At the moment the whole whole retrieval mission is still in the design phase. Here are prototypes of the sample container and the Earth Entry Vehicle. To give you an impression of the size, a sample tube is about 15 cm long. The container is roughly the sise of a basketball. The diameter of the EEV will be about 1.5 meter.

The retrieval operation will take place in 2029, six years from now. The Perseverance is working beyond expectation, but will it still work properly in 2029? In the first phase of the exploration Perseverance has collected dupilcate samples and dropped one of each at the Three Forks depot. In one of the NASA reports I read that in the second phase the Perseverance will no longer collect duplicates.

So, when everything goes well, in 2029 Pereverance will return to the Three Forks Depot with in its belly around 30 collected samples. In that case The Robotic Arm will transfer the samples to the sample container. It will leave the depot untouched! Why? Because the retrieval will be a risky process. The container after launch will be floating in orbit and hopefully collected by the Earth Retrun Orbiter. And near earth the container, now inside the EEV, will be dropped near Earth and hopefully fall down in the Utah desert. I still think it’s science fiction 😉 So, in case something goes wrong, at least there are still 10 samples in the depot, waiting for another mission.

The paragraph above is my own interpretation.

And this is my personal comment, before I finish this blog.

The whole mission until now has been presented as a huge success. And techologically speaking, I agree. But still I think the scientists will be a bit disappointed, because a “smoking gun” has not been found until now.

When (microbial) life developed on earth, 3.5 billion year ago, it left fossil traces behind, called stromatolites, like this one, found in Australia..

If this kind of sediment would be found in the Jezero crater om Mars, it would be frontpage news all over the world: Life has existed on Mars.

In 2019 a team of NASA/ESA scientists went to Australia to study the stromatolites. In the video they call them the Holy Grail.

But until now no sign. The collected samples contain organic molecules, but that is nothing new, Curioisity, the predecessor of Perseverance already found them.

Of course Perseverance will persevere exploring the sediments in the Jezero delta and collect more samples. Hopefully it will one day be able to take pictures of stromatolite. If not then we will have to wait until 2033 when the samples are returned to Earth and can be investigated in specialised laboratories.

Yes, I think the scientists are a bit disappointed.

The Pillars of Creation

In 1995 NASA published this picture, taken by the Hubble Space Telescope. It shows a small part of the Eagle Nebula and became instantly famous. Because in the “pillars” stars are born, the picture got the name “Pillars of Creation”.

The Hubble Space Telescope was launched in 1990 and is still operating, with quite a few Space Shuttle service missions. To celebrate its 25th anniversary, a new picture of the Pillars of Creation was published in 2015. With a new camera installed, more details are visible,

At the same time this picture was published, an infrared picture of the Pillars. Infrared light can travel more easily through dust and clouds and that is why now you see stars in the pillars, where young stars are still being formed. But I hope you wonder how this can be an infrared picture as infrared light is invisible light. The explanation will be the main part of this post.

But first here are two pictures, recently taken by the James Webb Space Telescope. The JWST is an infrared telescope has and has two cameras on board to take pictures. The NIRCAM for near infrared light and the MIRI for medium infrared light. Here is the NIRCAM photo

And here is the image from MIRI, Amazingly different. And again, how can these be infrared pictures’?

Time to give some explanation about the pictures and also about the Eagle Nebula, where the Pillars of Creation are located.

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About visible and invisible light

Light is an electromagnetic wave, as are microwaves, radio waves, X-rays etc, They all have different wavelengths. The wavelengths of visible light are often given in nanometers (nm), where 1 nm is 1/billionth meter. Or in micrometer (μm) where 1 μm = 1000 nm. The human eye is sensitive to wavelengths between ~380 and ~750 nanometer and sees the various wavelengths as different colors! The longest wavelengths are seen as red, the shortest as purple/blue with all the “rainbow” colors in between.. In this diagram the electromagnetic spectrum is shown. The infrared part can be subdivided in near infrared, mid infrared and far infrared

The Hubble telescope has two cameras onboard. Most of the iconic Hubble pictures have been taken by the Wide Field Camera. The present wide field camera (WFC3) can take photos in two channels, one for ultraviolet and visible light (UVIS) and the other one for near infrared (NIR), The range of UVIS is 200-1000 nm and of the NIR 800-1700 nm

The James Webb has two cameras, the NIRCAM for the near Infrared, range 600-5000 nm and the MIRI for the mid Iinfrared, range 5000-28000 nm (5 μm -28 μm).

Before we describe in some detail how digital cameras record images, it is useful to have a look at the way the human eye sees colors.

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How does the human eye see colors?

The retina of the human eye contains about 6 million nerve cells, called cones. These cones come in three different types, S, M and L, sensitive to various parts of the spectrum. The S type cones are sensitive to the blue part of the spectrum and are also often called Blue cones, In the same way the other two are often called Green and Red.

The brain is able to combine the response of these RGB- cells. For some people the M and/or L cone cells are not working properly. As a result they are colorblind.

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How does a digital camera record colors?

Digital cameras have sensors consisting of millions of individual pixels that record the intensity of the incoming light, basically in a gray scale (black and white). That these cameras can take color pictures is because in front of the sensor there is a color filter, consisting of a mosaic of millions of red, green and blue “pixels”. A so-called Bayer filter. See the diagram below. Taking a picture, means actually taking a red, green and blue picture at the same time, but these pictures are “incomplete”. By mathematical techniques (interpolation) the full color pictures are constructed.

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Here is an example, where three images, in red, green and blue, when combined, give the full image in natural colors.

The sensors in space telescopes do not have these Bayer filters, they just record the image in gray scales. However, various filters can be placed in front of the sensor and multiple images can be taken of the same object. For example, the Hubble WFC3 camera has a huge choice of filters, 47 for the UVIS channel and 14 for the IR channel.

Why so many? Some filters are broadband, they pass a wide range of wavelengths. From a scientific point of vew the narrowband filters are interesting because they pass only the light emitted by specific elements. Here is one example, hydrogen (H) emits red light with a very specific wavelength of 656 nm. So one of the filters only passes wavelengths around that value and a picture taken with this filter shows the presence of hydrogen. Similar filters can be used to check the presence of oxygen (O), sulphur (S) etc.

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The Pillars of Creation pictures are “false-color” pictures!

On 1 April 1995, astrophysicists Jeff Hester and Paul Scowen published an article The Eagle Nebula, in which they showed a picture of the Pillars of Creation. If you think that was “just” a picture taken by the Hubble telescope, you are seriously mistaken. The PBS/NOVA website More than just a pretty picture explains in 19(!) webpages how the iconic photo was created. Very readable,

The WFC2 consisted actually of four cameras, each recording a quadrant. The top-right quadrant camera was slightly different, zooming to show more details. Resizing it to the format of the other three, causes the characteristic Hubble image with the “steps” in one corner. Here is the original image of this top right quadrant, in gray scales. What a mess. For an explanation how to clean this image, see the website. The second image shows the result of the various cleaning operations. What a difference !

We can do the same for the other quadrants.

Now we can “glue” the four parts together. You can still see a bit the seams between the four images.

For this mage a filter was used that only let blue-green light through from (doubly ionised) Oxygen atoms (OIII). Two more filters were used to create images in the same way. One filter let only the reddish light from Hydrogen atoms through (Ha), the other one selected reddish(!) light from ionised Sulphur atoms SII). Three narrowband filters, two of them in the same color range.

Here are the three filtered images

You might expect that the next step would be to give these image’s color corresponding to the filter used for each of them. The Ha and SII reddish and the OIII one greenish. But that is NOT what Hester and Scowen did. They assigned the RGB colors to the three images. Blue to the OIII image, Green tot the Ha image and Red to the SII image.

Final step is to combine them: the Pillars of Creation.

The main reason to assign “false colors” to the pictures is to enhance the contrast and to see how the various elements are distributed. Almost all Hubble photos are false color (also called pseudo color). Using the three narrowband filters for S, H and O and assigning them to RGB is so common that it is often called the Hubble Palette. Doing a Google image search for Hubble Palette gives a huge number of hits. Here is a part.

Other combinations of narrowband filters are also used. Here is an example where 6 filters have been used for the Butterfly Nebula. Besides SII, Ha and OIII, also ionised nitrogen, helium and oxygen. In the table the natural colors are given and also the colors assigned in the Hubble palette.

An American astrophotographer got curious how this nebula would look in the natural colors. Here are two images’, left the false color one and right the picture in natural colors. It is clear that the artificial image reveals many more details

It must be clear now that while with the Hubble telescope you have a choice to use false colors, with the JWST there is no other option, as infrared light is not visible. Here are the filters used for the MIRI camera. The colors suggested for the various infrared ranges are not significant, just to guide the eye.

For the MIRI picture three filters were used, F770W, F1130W and F1500W. In the above diagram I have marked them. For this picture they are assigned Blue, Green and Red respectively.

The NIRCam camera has many more filters, broadband, narrowband etc.

For the NIRCam picture 6 filters have been used, marked in the diagram above.

I have read somewhere that creating these images should be considered as art and I agree.

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The Eagle Nebula

Finally a few remarks about the Eagle Nebula. When massive stars die, they can “explode” as a supernova, erupting their remnants into space. In these clouds of dust and various elements, new stars can be formed. The Eagle Nebula is such a cloud, here is a picture taken by an astrophotographer, using a telescope and a DSLR camera! Many of the bright spots in this picture are young stars already formed in the cloud. These stars are so hot that they emit UV light and even X-rays. This radiation can has enough energy to ionize the cloud. Such a cloud is called an emission nebula. The dominant reddish color is caused by hydrogen

The Eagle nebula is located about 7000 lightyear away and is huge, roughly 70 x 55 lightyear. It is a young nebula, estimated age is 5.5 million year. It is also a temporary event, the forming of new stars still continues and the radiation those stars will erode the nebula.

In the center of the above image, you can see the pillars of creation.Here is a dteail. Comapre it with the images of Hubble and Webb. Even these pillars are huge, the logext one is about 4 lightyear long.

A final remark. From the Hubble and Webb picture you might think that the pillars are almost like rock, impenetrable. But this is not true at all. The density of nebulas varies between 100 – 1 million particles per cubic cm. A high vacuum on earth still has considerably more particles per cubic cm. It is just the huge size that makes the pillars look like solid.

Lagrange points

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

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.