Given these values, determine the mass of the Earth

[osakabosaka]

Homework Statement

The moon orbits the Earth at a distance of 3.84 x 10^8 m from the centre of Earth. The moon has a period of about 27.3 days. From these values, determine the mass of the Earth

Relevant Equations

F = G(Mm)/r^2
F = mv^2/r

Honestly at a loss. Don't know where to start, what formulas to use. Any help would be greatly appreciated!

 

[etotheipi]

Homework Statement:: The moon orbits the Earth at a distance of 3.84 x 10^8 m from the centre of Earth. The moon has a period of about 27.3 days. From these values, determine the mass of the Earth
Relevant Equations:: F = G(Mm)/r^2
F = mv^2/r

Honestly at a loss. Don't know where to start, what formulas to use. Any help would be greatly appreciated!

What type of motion is the moon undergoing about the Earth? Does that help you to write down an $F=ma$ relation of some sort?

It might help to know that for two spherically symmetric masses, $r$ in Newton's law of gravitation is taken to be the distance between the centres.

 

[osakabosaka]

Gravitational force?
So is starting out with something like Fg=Fc alright?

 

[etotheipi]

Gravitational force?

$\vec{F_{g}}$ is definitely the centripetal force.

So is starting out with something like Fg=Fc alright?

Give it a shot and see what you get!

 

[osakabosaka]

Fc = Fg
(mv^2)/r = (Gm1m2)/r^2

not sure what to do with velocity or if this is a dead end

 

[etotheipi]

Fc = Fg
(mv^2)/r = (Gm1m2)/r^2

not sure what to do with velocity or if this is a dead end

Well, the centripetal acceleration can be expressed in a few different ways. Most helpful in this context is $a = r\omega^{2}$. That is, $a = \frac{v^2}{r} = \frac{(r\omega)^{2}}{r} = r\omega^{2}$.

 

[PeroK]

Fc = Fg
(mv^2)/r = (Gm1m2)/r^2

not sure what to do with velocity or if this is a dead end

The question to ask yourself is: given the radius and period of circular motion, can you work out how fast the object is travelling?