Gravitation

Step 1: State Kepler's Third Law of planetary motion. For objects orbiting the same central body, the square of the orbital period ( ) is directly proportional to the cube of the semi-major axis of its orbit. For a circular orbit, this is the radius ( ).

Step 2: Set up a ratio for the two satellites. Let be the period and radius for the first satellite, and for the second.

Step 3: Rearrange the formula to solve for the unknown period, .

Step 4: Substitute the given values and calculate . - hours - km - km The ratio of the radii is .

Step 1: State the formula for the orbital velocity of a satellite. The velocity ( ) of a satellite in a circular orbit of radius around a planet of mass is given by equating the gravitational force to the centripetal force: This shows that the orbital velocity is inversely proportional to the square root of the orbital radius: .

Step 2: Set up a ratio for the two satellites A and B.

Step 3: Substitute the given values and solve for . - - -