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Kepler’s other achievements

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As mentioned in my previous post, Kepler’s enchancment of Copernicus’s heliocentric system led to its extra basic acceptance, and his three legal guidelines describing the best way planets transfer are elementary legal guidelines of astronomy. Nevertheless, this wasn’t his solely contribution to science. He was one of many biggest thinkers of the seventeenth century scientific revolution and on this put up I’ll define a few of his different main achievements.

Statue of Kepler in Linz, Austria – picture from Wikimedia Commons

The Keplerian telescope

The Italian astronomer Galileo Galilei (1564-1642) was the primary particular person to take observations of celestial objects with a telescope . Nevertheless, Galileo’s telescope may solely enlarge objects 30 occasions earlier than the picture turned distorted. It additionally had a slender subject of view

In 1610 Kepler started theoretical and experimental investigations of the best way that totally different combos of lenses may work collectively to provide a magnified picture. He revealed his discovering in a e-book referred to as Dioptrice, which laid the inspiration of contemporary optics.  Utilizing the outcomes of his investigations, he invented a brand new sort of telescope with a special mixture of lenses than that which Galileo had used. This new design turned often known as the Keplerian telescope.  It’s nonetheless in use immediately and permits the next magnification to be achieved with much less distortion than a Galilean telescope.

Keplerian telescope – picture from Wikimedia Commons

For extra particulars on the variations between the 2 varieties of telescope see the notes on the backside of this put up.

The supernova of 1604

In October 1604 Kepler took observations of a brand new object which had appeared within the constellation Ophiuchus. Though Kepler was not the primary to see it, he took correct measurements of its place and brightness over a interval of yr.

He noticed that the brand new object didn’t transfer with respect to background stars, so wasn’t an object revolving across the Solar like a planet or a comet. Additionally, the truth that it didn’t present any parallax meant that it have to be an awesome distance away and wasn’t a close-by object in entrance of the celebrities. That is proven within the diagram under

It it have been nearer than the background of fastened stars then, at  totally different occasions of yr, the brand new star would seem like in a special positions with respect to the extra distant background of fastened stars. As this shift in place was not seen,  the brand new star have to be the identical distance because the fastened stars.

The looks of a brand new star which elevated in brightness after which step by step pale over time contradicted an essential perception, which had been held since historic occasions, that every one the celebrities have been fastened in place respect to every and have been unchanging. In 1606 he revealed his ends in a e-book referred to as ‘De Stella nova in pede Serpentarii’, which like most scientific literature of the time was written in Latin.

Its title translated into English is ‘On the brand new star in Ophiuchus’s foot’. For these of my readers in a position to learn Latin, it may be downloaded at no cost from the next web site: http://www.univie.ac.at/hwastro/rare/1606_kepler.htm

Right now this object, reasonably than being a brand new star, is thought to be a supernova, a large star which exploded on the finish of its life. The explosion fully destroyed the star, blowing the outer layers into house in a large glowing gasoline cloud, which is what Kepler noticed. The remnant of the supernova is formally often known as SN 1604 however is  extra generally referred to as Kepler’s supernova and is 20,000 gentle years away, which is properly inside our Milky Method galaxy.  It’s the final time supernova exploded shut sufficient to be seen to the bare eye.

Remnants of Kepler’s supernova – picture from NASA

Kepler’s contribution to arithmetic

Kepler’s contributions weren’t restricted to astronomy both. In 1611 he produced  a pamphlet entitled Strena Seu de Nive Sexangula (A New Yr’s Reward of Hexagonal Snow). On this he revealed the primary description of the hexagonal symmetry of snowflakes.

All snowflakes when freshly shaped have a hexagonal symmetry such that proven above.

Kepler found a sequence of standard strong shapes, that are often known as ‘the Kepler solids’.  The time period ‘common’ signifies that all of the faces are the identical.

The Kepler solids

In 1611 he posed a mathematical downside, which turned often known as the Kepler Conjecture. It offers with essentially the most environment friendly approach to pack spheres collectively in a big container, so there may be as little empty house as attainable. It may be summarised as follows:

Think about filling a big container with small equal-sized spheres. The packing density is the same as the overall quantity of the spheres divided by the amount of the container. So a packing density of 1 would imply that there was no free house in any respect.

The Kepler conjecture states that the utmost packing attainable density is:

∏ /(three√2), (which is roughly  equal to zero.7405).

∏ /(three√2)  is the packing density we get if we pack collectively spheres in layers, as proven within the image under.

So what the Kepler conjecture in saying is that there is no such thing as a different association out of the very giant variety of attainable methods to pack spheres collectively which supplies the next packing density than that proven within the image. Though Kepler and different subsequent mathematicians believed this assertion to be true, they have been unable discover a approach to show it. For over 400 years, it remained as one of many biggest unsolved issues in arithmetic. It wasn’t till 2017 workforce led by the American mathematician Thomas Hales proved it to be true (phys.org 2017).

Thomas Hales – picture from Wikimedia Commons


Curiously, Kepler additionally has the excellence of writing what the astronomer and science educator Carl Sagan referred to as the primary ever work of science fiction. It was written in 1608 in Latin and known as Somnium (The Dream) and is a couple of man who travels to the Moon. On this e-book he describes how the Solar, Planets and the Earth would seem to an observer on from the point of view of the Moon. In Kepler’s time is was not identified how harsh and barren the Moon was as an atmosphere and a few writers had speculated that there could be creatures on the Moon much like these discovered on the Earth and even lunar civilisation.

To Kepler it was clear that the twin results of the lunar local weather and the irregular, hostile terrain would produce vegetation and animals far totally different from those who inhabit the Earth. in Kepler’s Lavania  (which was the title he gave the Moon in Somnium) there aren’t any women and men, no civilizations.

And at last…

I hope you’ve gotten loved studying this put up. I’ve tried to stipulate a few of Kepler’s achievements, however in a 35 years scientific profession he made many further contributions, which I’ve not had time to say, together with discovering how the human eye works. What is evident to me is that he’s one among most essential thinkers of the scientific revolution which passed off in Europe through the seventeenth century.

The Science Geek


These further notes give a quick overview of the variations between the Galilean and Keplerian telescopes. I’ll focus on them in additional element in a subsequent put up on how telescope work.

To grasp how these telescopes are constructed it’s needed to grasp a little bit about lenses.

There are two varieties of lens:

  • A converging lens, proven within the high of the diagram above, causes parallel gentle rays from a distant object, proven in pink, to converge at level often known as the main target. The focal size of the lens is the gap between its centre and the main target.
  • A diverging lens, proven within the backside of the diagram, causes parallel gentle rays from a distant object to unfold out so they seem to come back from the main target. Like a converging lens the focal size of the lens is the gap between its centre and the main target. By conference the focal size of a a diverging lens is adverse.

A Galilean telescope consists of a converging lens of lengthy focal size (often known as the target) and an eyepiece which is a diverging lens of a shorter focal size.

If FO is the focal size of the target and FE the focal size of the eyepiece, then  the magnification is given by FO/FE. So a Gallilean telescope with an goal with focal size of 50 cm and and eyepiece of focal size of -10 cm, would have an magnification of -5.  The minus signal simply means the target is the fitting means up.

A Keplerian telescope consists of a converging lens of lengthy focal size (often known as the target) and an eyepiece which is a converging lens of a shorter focal size. It may possibly obtain greater magnifications than the Galilean telescope and has a bigger subject of view.

As with the Galilean telescope, if FO is the focal size of the target and FE the focal size of the eyepiece, then the magnification is given by FO/FE. So a Keplerian telescope with an goal with focal of size 300 cm and and eyepiece of focal size of 5 cm would have an magnification of 60.


phys.org (2017) Mathematicians ship formal proof of Kepler Conjecture, Out there at: https://phys.org/news/2017-06-mathematicians-formal-proof-kepler-conjecture.html(Accessed: 25 January 2018).

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