Gravitational Potential and Satellite Motion

[kingyof2thejring]

Astronomers observing a distant solar system have noticed a planet orbiting a star with a period of 4.44x107 s. The distance from the planet to the star is 4.28x1011 m. Calculate the mass of the star, in kg.

ihave used v = 2*pi*r/T and v=(2Gm/r)^1/2
i get 8.75e18
is this the way to calculate m
thanks in advance

 

[mezarashi]

The more logical thing to do (imho) is:

$$F = \frac{mv^2}{R} = \frac{GMm}{R^2}$$

Which simplify into Kepler's law, with the subsitution: $$v = \frac{2\pi R}{T}$$

 

[BobG]

Why are you finding velocity if the problem asked for the mass of the star?

You can use Kepler's third law, or:

$$\tau^2=\frac{4 \pi^2 a^3}{G(M+m)}$$
Unless the planet is very, very big for a planet, it can be disregarded, eliminating the little m from the equation. The rest is rearranging the equation to solve for big M.