Finding Kelper's Constant with only radius or period given.

[zeion]

Homework Statement

I'm given a chart that states the r average and T in Earth days for the moons of Uranus and I have to find the Kepler's constant for the last four moons, which only gives me either the radius or period.. I am confused. How can I find K with only r or T? I need at least the mass of Uranus yes?

The Attempt at a Solution

Am I suppose to find out the mass of Uranus myself somehow?

 

[LowlyPion]

What is Kepler's constant?

Isn't it going to be the same for any orbits of the same body - Uranus in this case?

K = T²/r³

 

[zeion]

I'm being asked to find K for each individual moons; each of which has a different period and radius. I was given both the T and r for the first four so I could find K easily, but for the last four I'm only given either r or T, which I think would require me to use

GM/4(pi)^2 = K = r^3 / T^2

But since I wasn't given mass of Uranus (M), I can't :/

The formula IS K = r^3 / T^2 right?

 

[LowlyPion]

I'm being asked to find K for each individual moons; each of which has a different period and radius. I was given both the T and r for the first four so I could find K easily, but for the last four I'm only given either r or T, which I think would require me to use

GM/4(pi)^2 = K = r^3 / T^2

But since I wasn't given mass of Uranus (M), I can't :/

The formula IS K = r^3 / T^2 right?

I think the point is that you use Kepler's Constant from the ones you are given to determine the other missing variables for what you aren't given, because it should be after all a constant for objects orbiting the same body right? Kepler's 3rd Law?

http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion#The_Third_law

T1²/r1³ = T2²/r2³

 

[zeion]

Oh okay, I think you're right.
Thanks.