Question

Two satellites of a planet have periods of 32 days and 256 days. If the radius of the orbit of the former is R, the orbital radius of the Latter is ______

Options

• `R/4`

• 2R

• 4R

• `R/2`

Answer 1

Two satellites of a planet have periods of 32 days and 256 days. If the radius of the orbit of the former is R, the orbital radius of the Latter is 4R.

Explanation:

The time period of satellite,

T = `(2pir)/sqrt("GM"/"r") = (2pir^{3"/"2})/sqrt("GM")`

i.e. T ∝ r^3/2 or r ∝ r^2/3

so `"r"/"R" = (256/32)^{2/3}` = 4 or r = 4R