Question

How much work must an external force do on the satellite to move it from a circular orbit of radius 2 Re to 3 Re, if its mass is 2000 kg? The universal gravitational constant 6.67 × 10−11 N · m2 /kg2 , the mass of the Earth 5.98 × 1024 kg and its radius 6.37 × 106 m. Answer in units of J.

Answer 1

Answer:

20872108843.53741 Joules

Explanation:

Re = Radius of Earth = 6.37×10⁶ m

M = Mass of the Earth =  5.98 × 10²⁴ kg

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

m = Mass of satellite = 2000 kg

Potential energy

$U_1=G\frac{Mm}{(2Re)}$

$U_2=G\frac{Mm}{(3Re)}$

$U_1-U_2=6.67\times \:\:\:10^{-11}\frac{5.98\times \:\:\:10^{24}\times \:\:\:2000}{2\left(6.37\times \:\:\:10^6\right)}-6.67\times \:\:\:\:10^{-11}\frac{5.98\times \:\:\:\:10^{24}\times \:\:\:\:2000}{3\left(6.37\times \:\:\:\:10^6\right)}\\ =20872108843.53741\ Joules$

Energy required to move the satellite is 20872108843.53741 Joules