Mass of Planet X in Solar Masses

[srivens]

Planet X is observed to have a small moon. This moon is observed to orbit the planet once per month at a distance of 15 Planet X diameters. What is the mass of Planet X in solar masses? [Hint: Use Newton's form of Kepler's Third Law: P2 is proportional to a3/M, where M is the mass of Planet X (assuming that the mass of the moon is negligible in comparison).]

the diameter of planet X is .0008 au as derived from previous problems. so 15 planet x diameters would be .012

So this would be a correct?
And p would be 30 days?

so the mass would be M = .012^3/30^2?

If this is correct am i missing something because i cannot come up with the correct anwer.

 

[srivens]

figured it out... thanks anyway

 

[kyle8921]

Yes, your approach is correct. However, there are a few things to note:

1. The unit of AU (astronomical unit) is a measure of distance, not diameter. So, the diameter of Planet X would be 0.0008 AU, not the other way around.

2. The period (P) should be in years, not days. So, P should be 1/12 years (or 0.083 years) since the moon orbits once per month (which is 1/12 of a year).

3. The unit of mass in Newton's form of Kepler's Third Law is in terms of solar masses, not kilograms. So, the final unit for the mass of Planet X would be in solar masses.

With these corrections, the calculation would be as follows:

M = (0.012^3 / 0.083^2) * (1 solar mass) = 0.0000134 solar masses

Therefore, the mass of Planet X in solar masses would be approximately 0.0000134 solar masses.