As we have just celebrated the Earth
completing another orbit around the
sun, it is a good time to ask the
question: why does the length of
a year have the value it does?
This value is determined by
the distance between Earth and
the sun, as described by Kepler’s
third law. This law states that the
cube of the semi-major axis of an
elliptical orbit is proportional
to the square of the period of the orbit.
If we measure time in Earth years
and distance in astronomical units,
then p=1 and a=1, and the
cube of the semi-major axis is equal
to the square of the period.
Kepler derived this law based on
Tycho’s observations of the planets.
Not long after that Newton showed
how this law can be derived from
his more general law of gravity.
Here are the details,
where a is the semi-major axis of
the orbit, G is Newton’s gravity
constant, M is the mass of the sun,
and p is the period of the orbit.
……………..
–Douglas Downing
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