Question

Using the gravitational pull between the Earth and the Moon and knowing the distance Earth - Moon R = 384000 km, calculate the mass of the Earth. The range is known = 6.67 × 10-¹¹ Nm² / kg², the orbital period of the Moon is T = 27.3 days.

Answer 1

Using the Kepler's Third Law, we get:

$$\dfrac{T^2}{R^3}=\dfrac{4\pi^2}{GM_E},$$ $$M_E=\dfrac{4\pi^2R^3}{GT^2},$$

$M_E=\dfrac{4\pi^2\cdot(3.84\cdot10^8\ \dfrac{m}{s})^3}{6.67\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}\cdot(27.3\ days\cdot\dfrac{24\ h}{1\ day}\cdot\dfrac{3600\ s}{1\ h})^2}=6.0\cdot10^{24}\ kg.$