# Planet Mass and angular radius

## Homework Statement

Suppose that we see a planet in our Solar System that we measure to have
an orbital period (around the Sun) of 18.0 years. We look at it with a
telescope and see that it has a moon. From repeated observations, when
the planet is near or at opposition, we note that the orbit of the moon is
and a period of 10 days.

## Homework Equations

Keppler's Third Law:
r3/T2 = GM/4(pi)2

## The Attempt at a Solution

I think that I need to determine the linear radius of the moons orbit and use that combined with it's period to solve for M in the equation r3/T2 = GM/4(pi)2.

I am not sure exactly how to do so, first i converted arcminutes to radians:

Then using Keppler's Third Law and the information given in the question I determined that the distance from the earth (where the orbital radius is viewed from) to the planet is the semi-major axis of the planet - the semi major axis of the earth:
Aplanet= (18^2)^(1/3) = 6.87 AU Aearth=1 AU

So the distance from earth to the planet would be 5.87 AU.

This is where i'm not really sure what to do. To get the radius of the moon's orbit do I just convert 5.87AU to meters and then multiply by the angular radius of
3.5*10-4rad? (Or perhaps my method is completely wrong in which case any advice on where I am going wrong would be helpful)

Thanks.