Question

(a) Is the acceleration due to gravity of earth 'g' a constant? Discuss.
(b) Calculate the acceleration due to gravity on the surface of a satellite having a mass of 7.4 ✕ 10²² kg and a radius of 1.74 ✕ 10⁶ m (G = 6.7 ✕ 10⁻¹¹ Nm²/kg²). Which satellite do you think it could be?

Answer 1

No, acceleration due to gravity of the earth, ‘g’, is not constant at all places. This is because the earth is not a perfect sphere, so its radius is not same at all the places on its surface. Since the radius of the earth is minimum at the poles, the value of ‘g’ is maximum at the poles. The value of ‘g’ is minimum at the equator, as the earth’s radius is maximum.
a) 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
$$\begin{gathered} \mathrm{g}=\frac{6.7\times {10}^{-11}\times 7.4\times {10}^{22}}{{\left(1.74\times {10}^6\right)}^2} \\ =\frac{6.7\times {10}^{-11}\times 7.4\times {10}^{22}}{{\left(1.74\times {10}^6\right)}^2}\left({10}^{22-11}={10}^{11}\right) \\ =\frac{6.7\times 7.4\times {10}^{11}}{1.74\times 1.74\times {10}^{12}}\left({10}^{11-12}={10}^{-1}\right) \\ =16.376\times 10 \end{gathered}$$^-1 =1.6 m/s²
Answer: g = 1.6m/s²
The satellite is Moon.