Finding the mass of the Earth
We know that the Sun is about 400 times
further away than the Moon, and takes a month to orbit the Earth. Thus,
its semi-major axis is about 1/400 AU, and its period is about 1/12 years.
Since we used AU and years, the mass is
in solar masses. So the Earth is about a million times less massive than the
Sun. To find out how many kilograms (or whatever) it has, we have to use the form of
Kepler’s Law given by Newton, and put in all the physical units [like P(sec),
a(meters), G (mks units)]. In this class, we will always use ratios and avoid
units (so we get relative comparisons).