Johannes Kepler - the "crazy" initiator of spaceflight

a lesson within a Comenius project for students in Getxo, Spain
Gerhard Rath
corrections: R. Geretschläger

in German

What do we think about a man who talks about planets as musicians, who believe in living beings on the Sun and Moon or who writes about Earth as a living object similar to animals like cows or elephants?
About himself this man wrote:
"He is like a pampered little dog. The body is lean and flexible. He likes to nibble at bones and old bread, he's greedy. He sniffs around in science and politics, is impatient in conversation and welcomes guests like a dog. If someone snatches away the merest trifle he snarls. Also he's snappish, for example in biting jokes. Most of the people hate and avoid him because of these properties, but his superiors are keen on him like holders on their dogs. He hates to wash and to bathe like a puppy." Die lebendige Erde - Karikatur (Gollowitsch)

How could just this man find out the basic laws of astronomy and spaceflight?
Kepler in Graz (original: Medaillon) He was born as one of seven children in the south of todays Germany in poor circumstances (Weil der Stadt, 1571). Nevertheless the talented young man could absolve a study of theology, mathematics and astronomy in Tübingen. He got his first job in Graz as "Landschaftsmathematikus" (responsible for calendars and all kinds of measurements and calculations) and as a teacher. At this time he starts to occupy his mind with astronomy.  

What about the astronomical picture of the world at this time?

We can see a closed, ordered universe - the world picture of belief and truth. Strong influences between man and cosmos let us understand better the importance of religion and astrology. The universe was seen as a kind of sphere centered by the Earth. Above Earth the spheres of the seven planets Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn are arranged; further outward, the sphere of the stars (and the zodiac). In the interior of the Earth we find hell, on Earth is the region of "normal" life, imperfect, with permanent combinations of the four elements earth, water, air and fire. The celestial spheres consist of the fifth element and are populated by angels. Above the stars reigns God.

Das Weltbild des Glaubens
This beautiful picture was not efficient for calculations with celestial objects (for navigation, calendars or horoscopes). For purposes like these, two systems were used: 
  • mainly the more than 1500 year old system of Ptolemy: It used combinations of circles around the Earth.
  •  the rather new system of Nicolaus Copernicus (published in 1543): here the Sun was the centre of combinations of circles. The heliocentric system was not exacter in its predictions than the geocentric.
Both systems were used only for calculations and were not seen as truth - religion and belief were represented by the picture above.
Nikolaus Kopernikus

The young Kepler was enthusiastic about the system of Copernicus and wanted to improve it, because he was convinced that this system represents the truth! He thought: why should the imperfect Earth with hell inside occupy the centre of the universe and not the glorious Sun?

He asked "crazy" questions:

Der kosmische Becher In Graz he found first answers and published them as the "Mysterium Cosmographicum" - secret of the cosmos
He was able to fit in the 5 platonic bodies (tetrahedron, cube, octahedron, dodecahedron and icosahedron) between the 6 planetary spheres. 

A beautiful harmonic picture - but not better for predictions than the other systems.

Die 5 platonischen Körper

Expelled from Graz in 1600 because of his confession, Kepler went to Prague - a stroke of luck from the point of view of astronomy. In the city of the emperor lived Tycho Brahe, one of the greatest astronomers of that time. Kepler became his assistant and successor.
Brahe had collected a lot of accurate data of planetary observations and Kepler started to calculate with the aim of improving his own system. Working for years, he recognized that his idea of using the platonic bodies couldn't be right - circles and spheres did not fit to the data! With reluctance he had to accept elliptical orbits, they described the observational data best:

So he had the content of the first and second law of planetary movement, for Kepler himself only assisting rules for calculations.

But with these rules he installed a system with exacter predictions than those made by any system before!

So the researching astronomer was content, but not the "crazy", dreaming Kepler:
that couldn't be the whole story, not beautiful enough to represent Gods universe!

With grimness he went on searching. If not the platonic bodies, what was Gods leading idea for the harmony of the cosmos? Maybe it was music?
Here Kepler was successful: he compared velocities of the planets in the extreme orbital locations perigee (nearest point to the Sun) and apogee (farest point) and he found proportions like 2:3 or 3:5. 

These proportions correspond with intervals like quint and quarte in music - that was the secret! 
The planets made a kind of music, harmonies not for the ears but to effect on our souls. ! 

Die singenden Planeten (Karikatur, Gollowitsch)
He combined this idea with geometrical figures (like the triangle and the pentagon) and with astrological influences to a great crazy system published in his book "Harmonice mundi" - harmony of the world.

But only one result of Kepler's pride remained until today: the third law of planetary movement.

Also this "law" was a rule to assist in calculations in Keplers eyes.
More important to him were the sounds of spheres - they were the reason for astrological influences, too. 

Kepler provided horoscopes and calendars with predictions and tried to give astrology scientific foundation. 

The strongest influences should work in the centre of the orbits - therefore Kepler concluded that the noblest living beings must exist on the Sun. Not enough - the celestical bodies themselves should have souls, they are alive. 

For example we notice the breath and sweat of Earth as weather phenomena.

After his death (1630, Regensburg, today Germany) Keplers "crazy" ideas became forgotten - except his "assistant rules", later named "Kepler's laws". 

These laws are not only applicable to planets but to every kind of object moving in gravitational fields like double stars or spacecraft

To bring a TV satellite in a geostationary orbit (36.000 km above the earth), the orbit is calculated with Kepler's laws. 

Der alte Kepler
What do these orbits look like?

If an object is launched from the earth with a minimum of 7,8 km/s (about 28.000 km/h) it doesn't fall back, but reaches a low circular orbit with a period of about one and half an hour. At higher velocities up to 11,2 km/s (40.300 km/h), elliptical orbits will result. Corresponding to Keplers 2nd law, the object is faster nearer to earth and slower at larger distances. With more than 11,2 km/s launching speed, the spacecraft leaves the earth in a hyperbolic orbit.

How to bring a satellite to a geostationary orbit?

This orbit is circular and located in the plane of the equator. In these conditions, the satellite describes a revolution in one day and remains in the same place with respect to the Earth. This is why communication and television satellites are placed on this orbit.

The launch of the rocket is made at locations near to the equator. After 5 minutes of acceleration in two stages the vehicle reaches the height of the first (circular) orbit. The third stage increases speed up to 10,2 km/s, the perigee velocity of a very elliptical orbit (called transfer orbit) with its apogee in 36.000 km. There an apogee engine gives the satellite the right velocity (3 km/s) and direction for the circular orbit.

The XMM orbit

Die Umlaufbahn des XMM Röntgenteleskops

Die stark elliptische Umlaufbahn bringt das XMM bis auf 114.000 km Höhe, die Umlaufzeit beträgt 48 Stunden. Damit kommt das Teleskop jeden zweiten Tag in die gleiche Position über der Erde (Kontakt mit der Bodenstation!). Die große Höhe ist notwendig, denn das Röntgenteleskop kann nur ausserhalb des Strahlenschutzgürtels der Erde (Magnetfelder) messen.