In this problem you are to make use of the formula P^2 = 4(pi)^2/mu *a^3, together with the fact that mu = G(m1 + m2). Assume, as is approximately correct, that the semi-major axis for the Earth's orbit about the Sun is 93 million miles and that the period is 365 days. Also assume that the semi-major axis for the Moon's orbit about the Earth is 240 thousand miles and the period is 28 days.
Calculate the value of mu for the Earth-Sun System, the value of mu for the Moon-Earth system, and then,assuming that the mass of the Earth is negligible in the first system (ie that mu for the Sun is just G times the mass of the Sun) and the mass of the Moon is negligible in the second, estimate the ratio of the Sun's mass to the Earth's mass.
You can look up the values on the Internet to see that your results are reasonable, but the calculation is to be based on Kepler's Law as described above. If you do this correctly the result will be a fair approximation of the currently accepted value.
Let us denote
P1 = 365 days = the Earth about Sun rotation period
P2 = 28 days = the Moon about Earth period
a1 = 93,000,000 miles = semi-major axis of the Earth about Sun orbit
a2 = 240,000 miles = semi-major axis of the Moon about Earth orbit
m1 = the mass of the Sun
m2 = the mass of the Earth
m3 = the mass of the Moon
As we ...
This solution contains step-by-step calculations to determine the value of mu for the Earth-Sun systems using the formulas aforementioned in the question set. Explanations are included.