Question

A satellite has a kinetic energy X, potential energy Y and total energy Z in a given orbit. How are they related

• A. $Z=Y=-2X$
• B. $Z=Y/2=-X$
• C. $Z=2Y=-2X$
• D. $2Z=Y=-2X$

Answer 1

Answer: (D)

$2Z=Y=-2X$

Let mass of satellite is $m$ and mass of earth is $M_E$ , satellite is rotating in radius $R$ and Speed of satellite is $v$.

Now balance the forces on satellite the satellite.

$\Rightarrow$ Centripetal force = Gravitational force

$\Rightarrow \frac{m{v}^2}{R}=\frac{G{M}_{E}m}{R^2}$ $\Rightarrow \frac{1}{2}m{v}^2=\frac{G{M}_{E}m}{2R}$ $\Rightarrow \text{Kinetic Energy X}=\frac{G{M}_{E}m}{2R}$ .....1

$\Rightarrow \text{Potential Energy Y}=-\frac{G{M}_{E}m}{R}$ .....2

$\therefore \text{Total Energy Z}=\text{Kinetic Energy}+\text{Potential Energy}=-\frac{G{M}_{E}m}{2R}$ .....3

From the equations 1 , 2 and 3 , $2Z=Y=-2X$