Mass of Jupiter given a Moon's mass, orbital velocity and distance.

[contrivance]

Hello all, been meaning to make an account here and participate but haven't been around to it. So sorry that my first post is asking for homework help! :|

Homework Statement

The planet Jupiter has a moon Europa (m = 5x10^22kg) that is orbiting at a velocity of 14,000m/s at a distance of 7x10^8m measured from the center of Jupiter to the center of the moon. What is the mass of Jupiter?

Homework Equations

According to the lecture notes for class, we have the law of universal gravitation $F=\frac{Gm1m2}{r^2}$ and then the formula for "Velocity of a satellite in orbit" $V=\sqrt{\frac{GM}{r}}$. There's more things like field theory, etc but may not be relevant.

The Attempt at a Solution

I can't seem to get a good result, google says the mass of Jupiter is 1.898x10^27kg although when I plug the numbers into the velocity formula and solve for M, i keep getting a mere 205604.

This exact same question is posted on yahoo answers, but the first guy's solution is something beyond my course, and everyone else just doesn't seem to be right.

I'm stuck, not sure what formula/equation I need to use and what throws me is that with all the given information I'm not sure if it's all needed or if it's there for distraction.

I would really like just a quick hint to get me in the right direction instead of an entire work through :)

 

[voko]

The first guy uses Kepler's third law. The others use essentially your method. Their results are correct within the accuracy of the original data.

 

[Bandersnatch]

when I plug the numbers into the velocity formula and solve for M, i keep getting a mere 205604.

Here's a hint:
Dividing by a^-b means the same as multiplying by a^b

 

[contrivance]

The first guy uses Kepler's third law. The others use essentially your method. Their results are correct within the accuracy of the original data.

I see, this makes sense now. Well after all this stress last night I discovered I was making a calculator error. putting too much information in at once and forgetting to put parenthesis where needed to get the correct result. I see that our result isn't actually that far off from Google's and my professor has been known to round given information up or down significantly.

I solved for $M$ in the Velocity equation and ended up with about 2.0x10^27 as others did.

What's funny about that Yahoo answer post is I just noticed it was posted three days ago so it might have been posted by someone in my class.

Thanks friends!

 

[Nickie]

I would suggest starting by reviewing the equations and concepts related to orbital motion and gravity. It seems like you may be mixing up some of the equations and variables. The first equation you listed, F=\frac{Gm1m2}{r^2}, is the law of universal gravitation, which relates the gravitational force between two objects (in this case, Jupiter and its moon Europa) to their masses and the distance between them. The second equation, V=\sqrt{\frac{GM}{r}}, is the formula for the velocity of a satellite in orbit, which relates the mass of the central object (Jupiter) to the velocity and distance of the orbiting object (Europa).

To solve for the mass of Jupiter, you will need to use both of these equations and the given information about Europa's mass, velocity, and distance from Jupiter. I would suggest setting up the equations with the known values plugged in and solving for the unknown variable (in this case, the mass of Jupiter). It may also be helpful to double check your calculations and make sure you are using the correct units for each variable. Good luck!