Question

The energy required to move a body of mass m from an orbit of radius 2R to 3R is?

Answer 1

Step 1: Given data

Radius,

$R_1=2R$

$R_2=3R$

Step 2: Formula used

The energy at the radius $R$ is given by:

$E=-\frac{GMm}{R}$

Here,

E is the energy required.

R is the radius.

M is the mass of the earth.

m is the mass of the body.

Step 3: Energies at the radius $2R$ and $3R$ can be written as

$E_1=-\frac{GMm}{2R}$

$E_2=-\frac{GMm}{3R}$

Step 4: The energy required to move a body of mass m from an orbit of radius 2R to 3R

$$\begin{gathered} E=E_2-E_1 \\ =-\frac{GMm}{3R}-\left(-\frac{GMm}{2R}\right) \\ =\frac{GMm}{6R} \end{gathered}$$

Hence, the energy required is $\frac{GMm}{6R}$.