PLASE answer for PART A,and B (Figure 1) A satellite of mass m is in a circular

Question

PLASE answer for PART A,and B

(Figure 1) A satellite of mass m is in a circular orbit of radius R2 around a spherical planet of radius R1 made of a material with density p. ( R2 is measured from the center of the planet, not its surface.) Use G for the universal gravitational constant. Part A Find the kinetic energy of this satellite, K. Part B Find U, the gravitational potential energy of the satellite. Take the gravitational potential energy to be zero for an object infinitely far away from the planet.

Explanation / Answer

A)
Kinetic Energy of Satellite is given by = GMm / 2R

Where M is mass of Planet
m is mass of Satellite
G is Gravitational Constant
R is Radius of Circular orbit of Satellite = R2

Now Density = Mass / Volume
Mass of Planet (M) = Density () * 4/3 * PI * R13

Substituting Value of M in above equation -

K.E = G * () * 4/3 * PI * R13 * m / 2R2
K.E = (2GR13 m) /3R2

B)
Potential Energy of a satellite in a circular orbit is given as -
P.E = -GMm / r

Substituting Value of M and Solving similarly Potential Energy comes out to be -

P.E =  - (4GR13 m ) /3R2

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