Question

A satellite moves round the earth in a circular orbit of radius R making one revolution per day. A second satellite moving in a circular orbit, moves round the earth once in 8 days. The radius of the orbit of the second satellite is

A 8 R
B 4 R
C 2 R
D R

Answer 1

The orbital radius of the second satellite is 8 times the radius of the first satellite orbiting Earth, based on Kepler's third law of planetary motion, hence the answer is A. 8R.

Step-by-step explanation:

The question pertains to the concept of satellite motion around Earth and primarily deals with Kepler's third law of planetary motion. Kepler's third law states that the square of the orbital period (T) is proportional to the cube of the radius (r) of its orbit, i.e., T² ≈ r³. In this question, a satellite orbits Earth with a period of one day (T1 = 1 day) and the second satellite orbits in 8 days (T2 = 8 days).

Using Kepler's law, for two satellites with periods T1 and T2 and radii R1 and R2, we have the proportion (T1²/R1³) = (T2²/R2³). Given that the first satellite has a radius R, we can find the radius of the second satellite's orbit by setting up the ratio (1²/R1³) = (8²/R2³). Solving for R2 gives us R2 = R ∙ 2³ = 8R, meaning that the second satellite's orbital radius is 8 times that of the first, so the correct answer is A. 8R.