Question

If given the orbital period and radius of Venus, how would one determine the mass of the Sun?

Answer 1

Orbital Period as in revolution period

Answer 2

Yes

Answer 3

And mean orbital radius

Answer 4

is orbital peroid and radius both given

Answer 5

Yes

Answer 6

use kepler's third law

Answer 7

we have radial velocity=2(pi)r/T
centrifugal force = gravitational force
therefore,GMm/r^2=mv^2/r [m=mass of the planet,G=universal gravitational constant,M=mass of the sun,v=circular velocity]
the equation turns into GM/r = v^2
so mass of the sun M=r.v^2/G
now use v=2.(pi).r