Question

A satellite is revolving around a planet in a circular orbit close to its surface and ρ is the mean density and R is the radius of the planet, then the period of ______.

(G = universal constant of gravitation)

Options

• `sqrt((3pi)/(rhoG))`

• `sqrt(pi/(rhoG))`

• `sqrt((2pi)/(rhoG))`

• `sqrt((4pi)/(rhoG))`

Answer 1

A satellite is revolving around a planet in a circular orbit close to its surface and ρ is the mean density and R is the radius of the planet, then the period of `underlinebb(sqrt((3pi)/(rhoG)))`.

Explanation:

According to the deduction of Kepler's third law and with the help of Newton's law, the law of period is given by,

or `T^2 = (4pi^2)/(GM)r^3 ⇒ T = 2pisqrt(r^3/(GM))`

where r is the radius of orbit and M is the mass of the planet or star.

As the satellite is very close to the planet, thus r = R

Also mass (M) = density (ρ) × volume (V)

= `rho xx 4/3piR^3`

∴ T = `2pisqrt(R^3/(G xx 4/3piR^3)) = sqrt((3pi)/(rhoG))`