Question

A satellite is orbiting Earth with a distance R = 2REarth from Earth's center. If the satellite is moved to a distance R = 4REarth (twice as far away), its potential energy would be ____________ what is was before.

Answer 1

Answer:

Half

Explanation:

Given that:

• radial distance of satellite from the earth, $R=2R_E$

Now, if the satellite is moved to a distance $R=4R_E$

We  have the mathematical expression for the potential energy fue to gravitational field as:

$U=\frac{G.M.m}{R}$ ...................(1)

where:

$G = 6.67\times 10^{-11}\ m^3.kg^{-1}.s^{2}$

M = mass of earth

m = mass of satellite

R = radial distance of satellite

Now from eq. (1) initially we have:

$U=\frac{G.M.m}{2R_E}$

after the satellite is moved, we have:

$U'=\frac{G.M.m}{4R_E}$

$\Rightarrow U'=\frac{G.M.m}{2(2R_E)}$

$\Rightarrow U'=\frac{1}{2} \times U$

which is half of the initial condition.