Answer to Question #164167 in Mechanics | Relativity for 12-STEM

Question

Compare the gravitational force of attraction on a 1.0 kg object when it is at the surface of the moon to the gravitational force on the same object when it is at the surface of the Earth. (Mass of the moon = 7.35 x 10 ²² kg, radius of the moon = 1.738 x 10⁶ m ; mass of the Earth = 6 x 10 ²⁴ kg, radius of the Earth = 6.4 x 10⁶ m)

Answer 1

The gravitational force of attraction on a 1.0 kg object at the surface of the Moon can be calculated as follows:

$$F_M=\dfrac{GM_Mm}{R_M^2},$$ $$F_M=\dfrac{6.67\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}\cdot7.35\cdot10^{22}\ kg\cdot1\ kg}{(1.738\cdot10^6\ m)^2}=1.62\ N.$$

The gravitational force of attraction on a 1.0 kg object at the surface of the Earth can be calculated as follows:

$$F_E=\dfrac{GM_Em}{R_E^2},$$ $$F_E=\dfrac{6.67\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}\cdot6.0\cdot10^{24}\ kg\cdot1\ kg}{(6.4\cdot10^6\ m)^2}=9.8\ N.$$

Let's compare the forces:

$$\dfrac{F_E}{F_M}=\dfrac{9.8\ N}{1.62\ N}=6.0,$$ $$F_M=\dfrac{1}{6}F_E.$$

As we can see from the calculations, the Moon's gravitational force of attraction on a 1.0 kg object is about 1\6th of that of the Earth.