12 Planetary Motion
Kepler rejected the epi-circle on epi-circle model of how planets moved and decided to
work out an orbit for Mars that best fit Tycho’s data. It was still dangerous to suggest that
the sun lay at the center of the solar system. The all-powerful Catholic Church had burned
Friar Giordano Bruno at the stake for believing Copernicus. No other scientist had dared
come forth to support Copernicus’s radical notion. Still, Kepler was determined to use Copernicus’s organization for the universe and Tycho’s data to make sense of the planets.
Kepler tried many ideas and mathematical approaches that didn’t work. His bad eyesight prevented him from making his own astronomical sightings. He was forced to rely entirely on Tycho’s existing measurements. In bitter frustration, he was finally driven to
consider what was—at the time—unthinkable: planetary orbits that weren’t perfect circles.
Nothing else explained Tycho’s readings for Mars.
Kepler found that ellipses (elongated circles) fit far better with the accumulated readings. Yet the data still didn’t fit. In desperation, Kepler was forced to consider something
else that was also unthinkable at that time: maybe the planets didn’t orbit the sun at a
constant speed.
With these two revolutionary ideas Kepler found that elliptical orbits fit perfectly with
Tycho’s measured planetary motion. Elliptical orbits became Kepler’s first law. Kepler
then added his Second Law: each planet’s speed altered as a function of its distance from the
sun. As a planet flew closer, it flew faster.
Kepler published his discoveries in 1609 and then spent the next 18 years calculating
detailed tables of planetary motion and position for all six known planets. This was also the
first practical use of logarithms, invented by Scotsman John Napier during the early years of
Kepler’s effort. With these tables of calculations (which exactly matched measured planetary ?6?F???2??W?W"&?fVBF?B?R?BF?66?fW&VBG'VR??WF'???F?????gV?f7G3??WF?v26??VBF?R???F???WBf?"sR?V'2?6??6R?G2F?66?fW'????3??WF?( ?2?&&?B?2F?R?V7B6?&7V?"???7BV??F?6??b?????WG2?B?G2f'F?W7B??B?2r?B&???????g&??F?R7V??B?G2?V&W7B?B?0????B?3B&???????v??v?V??WF??2B?G26??6W7B??G2?&&?B7GV???6?2??6?FRF?B?b?WGV?R?f?"#?V'2?WB?bWfW'?#C???WF??27GV??6??6W"F?F?R7V?F???WGV?R?2?F?B?67W'&VBg&???s?F??????f?"F??6R#?V'2?WF?v27GV??F?RV?v?F???WB???W"6??"7?7FV??B?WGV?Rv2F?R???F?????&RF?W???&P?67W"?????W?W"??Wr??&??F?fW"???2??G&W?W"?????7F?'??b7G&????g&??F??W2F??W?W"??Wr??&??F?fW"???2?Vfb?F?'??F?R&?6R?bV&???FW&?66?V?6R??Wr??&??6?'&?FvRV??fW'6?G??&W72???2????'F???????F?R??'F????7F?'??b7G&?????B6?6????w???Wr??&????'F??????R??7FW?V?6???''V6R??W?W.( ?2??6?6?7G&?????&??6WF????&??6WF??V??fW'6?G??&W72???r??