# Density of the moon and earth

1. Nov 14, 2004

### envscigrl

problem:

The mass of the earth is 5.98E+24 kg and its radius is 6370 km. The radius of the moon is 1738 km. The acceleration due to gravity at the surface of the moon is 1.62 m/s2. What is the ratio of the average density of the moon to that of the earth? (no units)
I am very confused as to how I find the density of planets given the equations and information I have. We are studying kepler's Laws and Newtons Law of Gravity. I feel like maybe I am missing some info or something.

Thanks for the help!

2. Nov 14, 2004

### Phymath

density will be denoted p
$$p= \frac{m}{v}$$
$$m_2a = \frac{G m_1 m_2}{r^2}$$

$$1.62 = \frac{G m_1}{(1738*10^3 m)^2}$$
$$m_{moon} = m_1, \ \frac{(1.62)(1738*10^3)^2}{G} = m_1 = 7.33 * 10^{22} kg$$
$$p_{earth} = \frac{(5.98 *10^{24})}{(\frac{4}{3}pi (6370)^2)} = 3.52*10^{16} kg/km$$
$$p_{moon} = 5.79*10^{13} kg/km$$
$$p_{earth} : p_{moon} = 43.34 \ p_{moons} \ to \ every \ 1 \ p_{earth}$$

Last edited: Nov 14, 2004