Satgen333   Johannes Kepler   by GM4IHJ                       12 Aug 95

For many Radio Amateurs, first acquaintance with Kepler and his orbital
elements, came with W3IWI Dr Tom Clark's epoch making article in Orbit
magazine for March 1981. Titled Basic Orbits , it introduced a major
change in the way most Amateurs tracked satellites.

Keplers story however, really began 400 years ago , even before the
general use of telescopes , when the Danish astronomer Tycho Brahe built
and operated a quite sophisticated naked eye observatory on the island of
Hven. Brahe was a controversial character , who perhaps deserves his own
report, but his importance for us and for Kepler , was that in 1583, he
made accurate measurements of the position of the planet Mars.

Later Brahe received from the young German mathematician Kepler, Keplers
first incorrect treatise on planetary motions, and being unable to accept
what Kepler said , Brahe invited Kepler to come to Hven, but Kepler had no
money and could not come. Then fate intervened and Brahe fell out of
favour in Denmark and was forced to head south to Prague in Bohemia where
Kepler was now working at the court of Emperor Rudolph II. Brahe died
within 2 years of getting to Prague , but despite opposition from Brahe's
relatives, Kepler kept possession of Brahes Mars records and began to use
them to try to work out the orbit of the planet.

Gradually after many false starts, Kepler came to realise that the orbit
was an ellipse around the Sun, and reasoning that this was also the case
for the other planets, he began to put together his Rudolphine Tables
which would provide the first ever accurate past and future location
predictions for all the known planets.

Despite problems when the Emperor failed to pay him, and religious wars
forced him to flee to Linz in Austria, Kepler continued working on the
tables greatly assisted by the new mathematics of logarithms invented by
the Scot John Napier. Indeed now that Kepler was treating the Sun as the
focus of the planetary ellipses, he was able to speed up the prediction
calculations by tabulating the logarithms of the planetary radius vectors
and the earths radius vector in a double entry table , there by permitting
rapid calculation by pre electronic computer standards, of the planets
past and future positions seen from the earth, with far greater accuracy
than had previously been the case.

Even when he had completed the tables it seemed for a time that Kepler
would not get them published. First Tycho Brahes relatives complained that
their man had not been given enough credit, then he had to move from Linz
to Ulm to get a publisher who would take on the task. 

Eventually however publication was achieved in 1627. Then a further 60
years were to pass before Isaac Newton showed mathematically that the
elliptical orbits were a natural consequence of cosmic laws. But that is
another story, as is the event a further 330 years later again when in
1957, Sputnik one the first artificial satellite of the earth , was able
to confirm that Keplers methods applied equally well for both natural and
unnatural objects.