A satellite X of mass m is in a concentric circular orbit of radius R about a planet of mass M - AQA - A-Level Physics - Question 14 - 2017 - Paper 2

To determine the kinetic energy of the satellite X in a circular orbit, we can start by using the formula for gravitational force and centripetal force.

1. Gravitational Force: The gravitational force acting on the satellite X is given by:

   $F_g = \frac{GMm}{R^2}$

   where:

   • $G$ is the gravitational constant,
   • $M$ is the mass of the planet,
   • $m$ is the mass of the satellite, and
   • $R$ is the radius of the orbit.

2. Centripetal Force: For the satellite to maintain a circular orbit, the gravitational force must equal the centripetal force required to keep it in orbit:

   $F_c = \frac{mv^2}{R}$

   where:

   • $v$ is the orbital speed of the satellite.

3. Equating the Forces:

   Setting the gravitational force equal to the centripetal force:

   $\frac{GMm}{R^2} = \frac{mv^2}{R}$

4. Solving for v:

   Rearranging gives:

   $v^2 = \frac{GM}{R}$

5. Kinetic Energy (KE):

   The kinetic energy of the satellite is given by:

   $KE = \frac{1}{2}mv^2$

   Substituting the expression for $v^2$:

   $KE = \frac{1}{2}m\left(\frac{GM}{R}\right) = \frac{G Mm}{2R}$

Therefore, the kinetic energy of the satellite X is:

Answer:

$KE = \frac{G Mm}{2R}$

Hence, the correct option is A.