Question

two satellites are in orbit around a planet. one satellite has an orbital radius of 8 x 10⁶ m. the period of rotation for this satellite is 1 x 10⁶ s. the other satellite has an orbital radius of 2 x 10⁷ m. what is this satellite's period of rotation?

Answer 1

To calculate the second satellite's period of rotation, one can use Kepler's third law, which relates the period of an orbit to the cube of the orbital radius, and by knowing the first satellite's orbital radius and period, the second satellite's period can be computed.

Step-by-step explanation:

To find the period of rotation (T2) for the second satellite, we need to apply the principles of Kepler's third law, which relates the orbital radius and the orbital period of a satellite. This law indicates that the square of the period of an orbit (T) is directly proportional to the cube of the radius of the orbit (r).

Given that we already know the period (T1) and the orbital radius (r1) of one satellite, and the orbital radius (r2) of the second satellite, we can set up a proportion based on Kepler's third law:

(T1)^2 / (r1)^3 = (T2)^2 / (r2)^3

Plugging in the values provided for the first satellite (r1 = 8 x 106 m, T1 = 1 x 106 s) and for the second satellite's orbital radius (r2 = 2 x 107 m), we can solve for T2.