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 = 4.53*10^6*v

use Grvitational force = centrepetal force
G*M*m/r^2 = m*v^2/r
G*M/r = v^2
G*M = v^2*r
(6.673*10^-11 * 3.4*10^30) = v^2 * 4.53*10^6*v
v = 36861.01m/s

r = 4.53*10^6*v
= 4.53*10^6* 36861.01= = 166980375300 = 1.66*10^11 m