Kepler's Laws
Kepler's third law can be expressed in
two distinct forms:
p2
= a3
Which is convenient when "p"
is the planet's period in years and "a" is
the semimajor axis in astronomical units. This form of Kepler's law
can only be used when a body is orbiting a relatively stationary body.
Newton's form of Kepler's third law is
the much more generalized form and is relevant for any two bodies orbiting
each other. Newton's form reads as follows:
p2
= a3 (4p2
/ G(m1 + m2))
In this form, "G"
is the universal constant of gravitation, 6.67x10-11,
and "m1"
and "m2"
are the masses of each orbiting body.
Kepler's third law gave modern science
the first clues as to the presence of dark matter when its predictive powers
were used in conjunction with observed speeds of galactic rotation curves.
The results showed a considerable discrepancy between what was actually
observed and what was predicted. What was found was that the speeds
of bodies orbiting the proposed center point of mass were much faster than
they should be. The speeds of orbiting bodies in a galaxy should
resemble those in the solar system where the further a body is from the
center point of mass, the slower its speed. In fact, the speeds of
bodies orbiting the center of mass were almost constant regardless of their
orbital radius. This implied that there was considerably more mass
present than was observed.