Kepler’s Third Law
3) The orbital period of a planet is proportional to
its semi-major axis, in the relation P2 ~ a3
The more
general form of this law (crucial for determining all masses in
Astronomy is
For the planets (with the Sun as the central mass),
you can take the units to be AU for a (semi-major axis) and years for P
(with M
in solar masses). Then all the numbers are “1” for the Earth.
Kepler didn’t understand
the physical basis of these laws (though he suspected they arose because the Sun attracted the
planets, perhaps through magnetism he
speculated.
Example: if Jupiter is at 5 AU, how long
is its orbital period?
