Question

By considering the success of Newton proved Kepler's law, determine the mass of the earth from the period T and radius r of the trajectory moon around the earth, with T = 27.3 days and r = 3.85. 10 ^ 5 km!

Answer 1

Do you know the equation for the law of periods?

Answer 2

nothing ..

Answer 3

Ok, law of orbits equation is given by

\[T ^{2}=\frac{ 4\pi ^{2} }{ GM }R ^{3}\]

Where T squared is the period of the moon's orbit squares, G is the gravitational constant, R is the radius of the moon's orbit and M is the mass of the Earth.

Rearrange to find M, make sure you convert your time period to seconds and km to metres.
Tell me what you get I've got an answer which looks ok

Answer 4

the result is very strange .... :)

Answer 5

Is it something in the magnitude of 10^24?

Answer 6

yeah ,,,

Answer 7

6.071 x10^24 kg?

Answer 8

I'm confused :(

Answer 9

Ok, this is how I did it:

Rearranged to solve M

\[M=\frac{ 4\pi ^{2} }{ T ^{2}G }R ^{3}\]

Then put the values in. R=385 X10^6 metres, T= 2.35872 X10^6 seconds and G=6.67X10^-11

You should get the value of M to be 6.0721x10^24 kg.

Answer 10

The accepted value of M is 5.972x10^24. The values are very close together so the value we calculated to be is probably correct

Answer 11

oh ... I know ... I'm very grateful ...

Answer 12

It's okay, go over Kepler's Laws, they're closely related to Newton's Law of gravitation.