Question

Two satellites A and B of the same mass are orbiting the earth at altitudes R and 3R respectively, where R is the radius of the earth. Taking their orbit to be circular abtain the ratios of their kinetic and potential energies.

Answer 1

Given:

Mass of satellites A and B is same

Altitude of A's orbit from earth = R

Altitude of B's orbit from earth = 3R

To find:

Ratios of A's and B's respective kinetic and potential energies

Answer:

• Let mass of satellites of A and B = m and the mass of earth = M
• We know that, the kinetic energy in the orbit = Half its gravitational energy
• Kinetic energy of A = GMm/[2×(2R)²].  -(1)
• Kinetic energy of B = GMm/[2×(4R)²]   -(2)

• The ratio of kinetic energies of A to B = equation (1)/(2) = 4

• Potential energy of each satellite = mgH
• Potential energy of A = mg(2R).  -(3)
• Potential energy of B = mg(4R).  -(4)
• The ratio of potential energies of A to B = equation (3)/(4) = 2