It takes 29.5 days (2.55x10^6 s) for the moon to complete a full cycle. Mass of moon=7.35x10^22 kg. Radius from Earth to moon=3.85x10^8 m. Calculate the mass of the Earth using this information.

Question

anonymous · Answer

Assuming it is making a circular motion, its aceleration is v^2/r, considering the formula for the force that a body makes in another equal to the force that the moon feels you can isolate the mass of earth. Is that clear?

anonymous · Answer

Kind of...

anonymous · Answer

In other words:
$$F=ma=GMmr^{-2}$$And then the aceleration would be:$$a=GMr^{-2}$$

anonymous · Answer

So, big M is the mass of the Earth, and little m is the mass of the moon? And so I just solve for big M?

anonymous · Answer

Yes, and do you understand why the aceleration of the moon is v^2/r or Va*r, where Va is the angular velocity?

anonymous · Answer

Yes, I do

anonymous · Answer

Do I have to take that into account in solving the problem?

anonymous · Answer

well, that is the little a, so yes.

anonymous · Answer

Oh, now I understand. I solve little a, and then plug that into the equation to find M.

anonymous · Answer

Thats it.

anonymous · Answer

Thank you so much!

anonymous · Answer

Tour welcome

anonymous · Answer

So, v=2 pi r/T, right?

anonymous · Answer

For velocity, I got 9.49x10^14. And then, for acceleration, I got 2.34x10^37. Is that right?

anonymous · Answer

For my final answer, I got 5.2x10^42. Is that right?

anonymous · Answer

I got the same numbers but in very different scales, what units did you use?

anonymous · Answer

Just for you to know, I got 5.2x10^24Kg