A planet requires 330 Earth days to complete its circular or

A planet requires 330 (Earth) days to complete its circular orbit around its sun, which has a mass of 3.4 x 10^30 kg. What are the planet\'s (a) orbital radius and (b) orbital speed?

Solution

Let orbital radius be r and orbital speed be v

Then, T = 2*pi*r/v

330*24*3600 = 2*pi*r/v

r = 4.537*10^6*v

use Grvitational force = centrepetal force

G*M*m/r^2 = m*v^2/r

G*M/r = v^2G*M = v^2*r

(6.673*10^-11*3.4*10^30= v^2 * 4.51*10^6*v

v^3 = 7.55*10^13

v = 4,22*10^4 m/s

r = 4.537*10^6*v = 4.537*10^6* 4.51*10^4 = 2.04*10^11 m

Answer: a) 2.*10^11 m

b) 4.22*10^4 m/s