Question

A space expedition discovers a planetary system consisting of a massive star and several spherical planets. The planets all have the same uniform mass density. The orbit of each planet is circular.
In the observed planetary system, Planet A orbits the central star at the distance of 2R and takes T hours to complete one revolution around the star. Planet B orbits the central star at the distance of R. Which of the following expressions is correct for the number of hours it takes Planet B to complete one revolution around the star?

a. 1/â8T
b. 1/2T
c. 1/3â4T
d. 2T
e. â8T

Answer 1

Answer:

T/√8

Explanation:

From Kepler's law, T² ∝ R³ where T = period of planet and R = radius of planet.

For planet A, period = T and radius = 2R.

For planet B, period = T' and radius = R.

So, T²/R³ = k

So, T²/(2R)³ = T'²/R³

T'² = T²R³/(2R)³

T'² = T²/8

T' = T/√8

So, the number of hours it takes Planet B to complete one revolution around the star is T/√8