Question

Calculate the acceleration due to gravity on the surface of a satellite having a mass of 7.4 x 10²² kg and a radius of 1.74 x 10⁶ m (G = 6.7 x 10^-11 Nm²/kg²). Which satellite do you think it could be ?

Answer 1

g = GM /R²
g (acceleration due to gravity) = ?
G (Gravitational Constant) = 6.7 × 10⁻¹¹ Nm² kg⁻²
M (mass of satellite) = 7.4×10²² kg
R (radius of satellite) = 1.74 ×10⁶ m
g = GM /R²    
g = `(6.7 xx 10^-11 xx 7.4 xx 10^22)/(1.74 xx 10^6)^2`
= `(6.7 xx 10^-11 xx 7.4 xx 10^22)/(1.74 xx 10^6)^2`  `(10^(22-11)=10^11)`
= `(6.7 xx 7.4 xx 10^11)/(1.74 xx 1.74 xx 10^12)`
= `16.376 xx 10^-1`
= 1.6 `"m/s"^2`
Answer : g = 1.6 `"m/s"^2`
The satelite is moon .