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 πŸ˜‰ . 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 πŸ˜‰ 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.

Me as a Student

A few weeks ago I published a blog post Me as a Physics Teacher. Searching my archive for photos, I came across several pictures taken during my “student” days. So here is a post about my life as a student.

Here is the only photo I have about the start of my “student” life πŸ˜‰ Taken when I was 5 year old, during my stay at the kindergarten school.

Some photos must have been taken during my primary school time, but I cannot find any in my archive. My results were good, I skipped a class and was only11 year old in 1955 when I went to the Christelijk Lyceum in my hometown Alphen a/d Rijn. In those days a Lyceum was a school type with two courses, a five year one (HBS) and a six year one (Gymnasium). The Gymnasium stream had Greek and Latin as additional languages (besides Dutch, English, German and French) and prepared for university.

I was admitted to the Gymnasium stream. Here is my 2 Gym class in 1956-57. I am standing, fourth from the right.

One year later, class 3 Gym. I am standing in the back row, third from left. Next to me my best school friend Bram and my physics teacher Smit, who played an important role in my decision to study physics.

Our Gymnasium class was already quite small, but in class 5 Gym it was split in two, Alpha and Beta. The alphas got more Greek and Latin, the betas more mathematics and science. Here is the small 5 Gym Beta class with our Greek language teacher Flink. He was a nice old-fashioned gentleman, and we accepted willingly the awful smell of his pipe tobacco (smoking in the classroom was still permitted in those days). Can you find me? Sitting in the center, next to my friend Bram.

The usual school photo, in class 5 Gym Beta. February 1960, I am still 15 year old, will be 16 in April.

The final examination for Gymnasium classes was quite special in those days. In addition to the written tests, there was also oral ones, taken by your teacher and a university professor. After an exciting day, the end result was discussed by teachers and visitors in the staff room. We had to wait in a classroom for the verdict. Luckily in our small group everyone passed.

Time to celebrate, here in front of my family house.

Many of us continued our studies at various universities. The famous Leiden University was close to my hometown and a logical choice, but I was the first in my (extended) family to go to university and my parents preferred the Christian Vrije Universiteit in Amsterdam. They managed to find lodgings for me with a nice (Christian) landlady. I was only seventeen year old, in retrospect too young.

I enrolled for physics and mathematics. and I also joined the student corporation of the VU. In those days the student corpora had severe initiation rituals. The aspirant members had their head shaven and were humiliated in many ways a couple of weeks, before they were accepted. Here is a picture I found on the Internet, taken in 1961. I still vividly remember the experience.

At the end of 1961 a few of my classmates had a kind of reunion. Our favorite teacher of Dutch language, Miss Dubbeldam, was also present. Notice that my hair is growing back already, pity that I don’t have a picture when my head was clean shaven.

My room in Amsterdam was actually a kind of garden house. Private, but to reach it, I had to pass through the house of my landlady. Here I am standing in front of my rooms, around 1963. I did not really enjoy those first years at university, as soon as the lectures finished (Saturday morning!) I took the bus back to my hometown and stayed there with my family until Monday morning.

After I was accepted in the student corporation, I became a member of the sorority (“dispuut”) Odysseus. Weekly we met for drinks and there were regular meetings, where you could train/show your oratorical skills. A nice “cultural” dispuut, but still too macho for the immature guy I was. After a few years I left the club.

I had a few good friends. One of them is Nellie, we first met when we were both freshmen, more than 60 year ago. Here I have joined Nellie at a party of her :”dispuut” Notice how formally dressed I am, in a three-piece suit..

I was a diligent student. On the wall of my room the certificate that I was a member of the student corporation.

In my room with some more friends. Jan, my best friend in those days, is trying to sing something from Bach. We were a serious bunch.

Pictures taken at the same time. I had bought an old piano and was still following piano lessons in my hometown. It must have been a party, with the bottles stored in the piano, but I don’t remember what we celebrated. .

In those days university studies were split in two parts , the “kandidaatsexamen” and the “doctoraalexamen”, more or less equivalent to present day Bachelor and Master degrees.

I passed my “kandidaats” in 1965. In those days taking four years for this degree was quite normal. For the second phase, we had to follow lectures, pass tests, but also .work in the physics laboratory, taking part in excursions to other universities etc. I chose nuclear physics as a specialism and worked in a group, led by Anne de Beer, who was doing research for his PhD thesis. A very enjoyable few years

In 1967 I took part in a trip to the UK where we visited several laboratories

At the end of the trip we enjoyed a nice dinner. Notice that we are smoking cigars.

At the end of 1967 an important event took place in my life, resulting in a big change in my outward appearance. It was hippie time, my hair grew longer, my clothing became informal and I got interested in popmusic. See my blog Musical Nostalgia.

In those days military service was still compulsory, but you got a deferment if you studied. In 1968 I was given a test to determine whether I had leadership qualities. It was fun, here I am (no 26), I didn’t try to qualify because I had already decided to become a conscientious objector in case I had to go into military service.

Anne, the leader of my group defended his dissertation on 20 December 1968. He asked me and another student to be his paranymph, an old tradition. Formally dressed in white tie, but with long hair, I was of course subject to funny remarks.

A few months later I obtained my doctoraalexamen (Master of Science degree), I became a doctorandus .My university asked me if I would like, to stay , get a part-time job as scientific assistant and do research for a Ph.D. .I was honored and accepted. As my interest was more in theory than in experiments, it was decided that I would do research in theoretical nuclear physics.

Although I was no longer a student, I was still entitled to a student identity card

For various reasons it took me a rather long time to do my research and write my thesis. Here are a few pages of my thesis.

Here I am defending my thesis, 2 September 1976. Paranymphs were no longer needed.

It was a public ceremony, colleagues from the physics faculty were present, my proud family on the first row. My physics teacher from the Lyceum was there (second row, second from right), I had already accepted a job as physics teacher and started a few weeks earlier. The principal of my new school was there and a teacher colleague with a few young pupils from one of my classes (one row below the top row, in the middle).

That was the end of my academic career, although I still published an article about my research in 1978

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.

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 (ΞΌm) where 1 ΞΌm = 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 ΞΌm -28 ΞΌm).

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.

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.

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.


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.

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.

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.

The Paleomap Project


Twenty years ago I started my own website. Although now in hibernation, this Stuif Site is still online. It has a Science -> Earth category, here is a screenshot of that page. I was quite interested in plate tectonics and continental drift and was planning to write more webpages about it. This never happened, the Earth page remained a “stub”.

But finally I have now decided to write a blog.

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

Apparently some Tamil revivalists still think that this continent really existed and actually was the cradle of civilisation, not Mesopotamia . The continent was submerged after the last Ice Age, when sea levels rose, forcing the Tamil people to migrate to other parts of the world. And yes, the sea levels rose after the last Ice Age, more than 120 meters. But have a look at the Google Earth nap of the Indian Ocean, where I have outlined Kumari Kandam. Mean sea depth is ~ 4 km!

So the Kumari Kandam continent never existed. A few months ago I have written a separate blog about this myth: Kumari Kandam & Lemuria .In that post I announced a post about continental drift and plate tectonics. Here it is.


When Earth was formed, 4.55 billion year ago, it was in a completely molten state. The heavier elements sank to the center, the lighter elements rose to the surface. Because of cooling soon a crust developed. Here are two images of present Earth , showing its structure. Basically there are three main layers, the Crust, the Mantle and the Core.

The Core consists mainly of iron and nickel. In the Outer Core they are liquid (high temperature) and are the source of Earth’s magnetic field. The Inner Core is solid, the temperature is even higher, (about 6000 Β°C) but the pressure is gigantic.

The mantle is basically solid, but the upper mantle is already so hot, that it behaves as a fluid on a timescale of many millions of years. This upper part is called the Asthenosphere. .

The right image gives more details about the size of the various layers. The crust of Earth is very thin, especially under the oceans (~6-7 km). The continental crust is much thicker , 30-70 km and less dense than the oceanic crust. Compare the Earth crust with the shell of a chicken egg, or the skin of an apple

The crust of Earth is not one whole, it is broken in many separate parts, called tectonic plates. Below you see the main tectonic plates at present. They “float” on the mantle, very slowly, about a few cm/year. Red arrows indicate the direction in which they move.

A few comments on this map

  • In the Atlantic Ocean the Eurasian plate and the North America plate move in opposite directions, creating a gap, that is filled by magma from the underlying mantle. They are called Mid-ocean ridges.
  • The Eurasian plate and the Indian plate collide, resulting in the Himalayas.
  • The Australian plate and the Pacific plate also collide, but here they create a Subduction zone. Because oceanic crust is denser than continental crust. the oceanic crust will go down under the continental crust and merge again with the mantel.

Two images as an illustration: a mid-ocean ridge (left) and a subduction zone (right)

These examples show that plates can change in time, they can also merge or split. In the past Earth has looked different, and in the future it will also look different.


A paleomap is a map of Earth in the past, using information about tectonic plates. The American geologist Christopher Scotese started the Paleomap Project in the 1990s and is still actively working on it. Here are a few of his maps

This is a map of Earth, about 200 million year ago. In that period most of of the landmasses were connected and formed a supercontinent, named Pangaea. In the lower part, called Gondwana, you can already see the shapes of present-day Africa, South-America, Antarctica and Australia

Millions of years later, Pangaea has broken apart. Dinosaurs are roaming the earth

Earth starts to look a bit more familiar South-America and Africa have split, with the southern Atlantic Ocean separating them. Eurasia begins to take shape. Australia is still connected to Antarctica. Note that India has split from Africa.

Earth 66 million year ago. The impact of the Chicxulub meteor in Mexico causes the extinction of the dinosaurs and the rise of mammals. India is on a collision course with Asia and Australia has split from Antarctica.

Present Earth..

More maps can be found here. The oldest map shows Earth 513 million years ago

These are static images, it would be nice to follow the development in time through animations The Paleomap Project homepage has many animations , but they do not work anymore, because they are using Java applets, which most browsers don’t accept nowadays. The site has not been updated since 2003 and I assumed that the project had been stopped. But searching information for this blog, I discovered that I was wrong, Scotese is still very active! But nowadays he and his coworkers create YouTube videos. Here is one of them. Time runs backwards, the video starts with the modern Earth and goes back to 750 million year ago.

It is also possible to predict how Earth will look like in the future. Of course such a prediction is less accurate because you have to extrapolate , using current plate movements.. Scotese’s prediction is that in the future another supercontinent will form, which he has called Pangaea Proxima. Here is the video. Notice that Australia will merge with Asia and l Antarctica.with India. The Mediterranean Sea will disappear.

Scotese’s YouTube Video Channel contains more than 70 videos about aspects of plate tectonics and continental drift. I will mention one more here, about the Story of the Malay Peninsula. (There doesn’t exist a Story of the Netherlands because God created the world, but the Dutch created The Netherlands πŸ˜‰ )Notice how during the Ive Ages the sea-level was so low that the islands of the Malay archipelago were connected. This was called Sundaland. Topic for another post.

A few concluding remarks

  • Before Pangaea there have been several more supercontinents. Click here for a list.
  • When plate tectonics started on Earth, is still a matter of dispute. Possibly 3 billion year ago.
  • It can be argued that plate tectonics has been essential for the development of life. Watch this fascinating video The World before Plate Tectonics.

Beautiful Shapes

I could have named this blog Uniform Polyhedrons, but I think in that case not many would have read it πŸ˜‰ A polyhedron is a 3D object, bounded by polygons and a polygon is a flat surface, boudned by straight lines. A cube is a simple polyhedron and a triangle is a simple polygon.MOre terminology in the appendix.

When I was a kid, I was fond of making cardboard models of buildings, ships etc. I bought the “bouwplaten” in the local bookstore. It was quite a popular pastime in those days, now no more. Here are two simple examples, found on the Internet.

It was during the 1970s , on a trip to London, that I came across the book Polyhedron models by Magnus Wenninger. It contained descriptions of 119 polyhedrons with detailed instructions how to make cardboard models of them. With my youthly love of bouwplaten and my interest in mathematics I immediately bought the book. Left my copy, right Magnus Wenninger (1919-2017) with a complicated polyhedron in his hands.

Back home, I bought sheets of colored cardboard and started building polyhedrons. Compared with the commercial “bouwplaten” as shown above, where you just have to cut out he various pieces, you have to draw the pieces first on the cardboard sheet, add tabs and then only cut them out. Here are two examples. The numbers are from Wenninger’s book, which can be found online.

The tetrahedron (left)is the most simple polyhedron, it consists of just four triangles. I have marked how many pieces you have to cut with a colored number. The football like polyhedron with the unspeakable name (right) consists of 30 squares, 20 hexagons and 12 decagons. 62 pieces in total.

Here are a few of the polyhedrons I have built. That was more than 40 years ago, the colors have faded. The polyhedron in the center of the top row is still “simple”, consisting of squares and triangles. The one left on the top row looks more complicated, but when you look carefully, you will see that it only consists of triangles! But only parts of a triangle are visible from the outside. In the right polyhedron, on the bottom row it is easy to see that there are pentagons (five-sided polygon), but there are also hexagons (six-sided polygons), which are hardly visible in this model. In total 12 pentagons and 10 hexagons!.

The polyhedrons where all faces are completely visible, are called convex, the others where you can only see parts of the faces are called nonconvex. See the appendix for more terminology and mathematical details.

Nonconvex polyhedrons are more difficult to build, because you have to be careful that the pieces of one polygon have the same color. But they are worth building, because they are beautiful. Here are a few examples. The left polyhedron consists of 12 pentagons and 12 pentagrams, 24 faces in total. The one at the right is more complicated , 20 triangles, 12 pentagrams and 12 decagons (10-sided polygon), total 44 faces.

Two more. The polyhedron left has 30 squares, 12 pentagons and 12 decagons, total 54 faces. And the beautiful polyhedron to the right has 20 triangles, 30 squares and 12 pentagrams, total 62 faces. The complexity of this polyhedron is difficult to see in a picture. On Wikipedia I found a 3D version which you can rotate with your mouse. Amazing, try it out and see if you can find the triangles (easy) and the squares (difficult).

The polyhedrons at the end of Wenninger’s book are even more complex, Here is a description with templates for the “Great Inverted Retrosnub Icosidodecahedron“. Yes, they all have names, see the appendix. It contains 80 triangles and 12 pentagrams, 92 faces in total .His description starts with “This polyhedron is truly remarkable in its complexity” and at the end he writes “Your patience and perseverance will have to hold out for more than 100 hours if you want a complete model of your own

At first I decided that “more than 100 hours” was too much for me. But I was curious about this polyhedron, and I used the templates to build a small part of it.. Soon I found out that there was something wrong with the templates for this model. Parts that had to be glued together, had different lengths! I tried to check and correct the size of the pieces (see right image with my comments) but that did not work..

I decided to contact Wenninger, but didn’t have his address, so I wrote to the Cambridge University press ( the publisher), asking them to forward my letter to Wenninger. I didn’t really expect a reply, so I was pleasantly surprised when after a couple of months I got a letter from Wenninger. He explained that in the printing process of the book one or two templates had been incorrectly represented. A few more buyers of the book had noticed the error. His letter contained the correct templates!.

After his kind gesture I felt “morally” obliged to build the polyhedron. I spent many evenings cutting and gluing the 1290(!) pieces. I did not keep track of the hours, but it must have been more than 100. Here is the final result. Of course I took a picture and sent it to Wenninger.

Here is a digital 3D version of the polyhedron. Rotate it with your mouse, to see the complexity.

I assume that in a reprint of the book the mistakes will have been corrected, but when I built the model, it must have been one of the few in the world ;-). Years later I visited the Science Museum in London, where they have the whole collection.

Polyhedrons have fascinated artists, philosophers and mathematicians throughout the ages. Here are Durer;s famous Melencolia I (1514) and John Cornu’s Melencolia (2011)


First some terminology.

  • A polygon is a 2D figure with straight sides, for example a triangle. When all sides are equal it is called a regular polygon
  • A polyhedron is a 3D form bounded by polygons, for example a cube. A polyhedron has faces, edges and vertices (plural of vertex) When the polygons are regular and all vertices similar, the polyhedron is called uniform.

The left polyhedron has 6 faces (F=6), 12 edges (E=12) and 8 vertices (V=8). The right polyhedron has F=4, E=6 and V=4.

The most simple polyhedrons were already known in antiquity and are called Platonic solids. These polyhedrons have only one regular polygon as face. , a triangle, square or pentagon. Here they are

There are 13 polyhedrons that have more than more than one regular polygon as face.. They are called Archimedean solids, because they were first enumerated by Archimedes, later rediscovered by Kepler who gave them their names. Here they are. Notice that they all have one single edge.

The names give information about the composition of the polyhedron. For example the icosidodecahedron has 20 (icosi) triangles and 12 (dodeca) pentagons.

The polyhedrons often contain pentagrams. A pentagram is related to a pentagon by a process called stellation, extending the sides of a polygon. Polyhedrons can also be stellated by extending their faces. Left the pentagram and right one of the stellated dodecahedrons.(there are three more)

In the Platonic and Archimedean polyhedrons all faces are completely visible, The mathematical term is that these polyhedrons are convex. The stellated dodecahedron, shown above, has pentagrams as faces, but the center part of the pentagram is not visible, it is inside the polyhedron. The mathematical term is that this polyhedron is nonconvex. In total 53 nonconvex polyhedrons exist. This has been proven only in 1970.

Wenninger’s book describes 119 uniform polyhedrons, the 5 platonic solids, the 13 Archimedean ones, 48 polyhedron stellations and the 53 nonconvex polyhedrons. A List of Wenninger polyhedron models can be found on Wikipedia. The list contains images of all polyhedrons and lots of details

Here are the numbers of the polyhedrons shown in this blog (I have built more). 17, 24, 39, 76. 80, 99, 102, 105, 107 and 117.Except 39, a stellation of the icosahedron, they all have a Wikipedia page.

When I built my models, PC’s were still in an infant stage and the World Wide Web did not yet exist. Nowadays there is wealth of information available, there even exists software to create the polyhedrons digitally. Great Stella looks promising. I feel tempted πŸ˜‰

Why did I write this blog, more than forty year later? Recently I visited the Bellevue Hotel in Penang. The owner of the hotel is a friend of mine. In the garden of the hotel he has built a geodesic dome. He was a close friend of the American architect and philosopher Buckminster Fuller (1895-1983), who was the “inventor” of the geodesic dome.

You will not be surprised that there is a close relation with the polyhedron models of Magnus Wenninger. Have a look at the Wikipedia article Geodesic polyhedron, where both Buckminster Fuller and Wenninger are mentioned. Enjoying the view and admiring the dome, the thought arose to write a blog about my “hobby” from the past πŸ˜‰


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 πŸ˜‰

Kumari Kandam & Lemuria

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

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 πŸ˜‰

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.

We are Star Children

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 3.0Γ—10βˆ’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 Β± 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.

  1. The strong nuclear force between nucleons, only active when the nucleons are very close together,”short-range”
  2. The electromagnetic force, ~100 times weaker, but “long range”, holds atoms together.
  3. The weak nuclear force, ~ 1 million times weaker, “short-range”, responsible for radioactivity.
  4. 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 8Γ—10βˆ’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


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 πŸ˜‰