earth and moon proportionality

[Guest staranova]

Mass of moon is 1/81 Earth's mass

Gravity of moon is 1/6 Earth's gravity

WHY!

[ensonik]

Good question. I don't know the answer other than to say the obvious thing, which is that it must be comprised of heavier materials.

[swansont]

Mass of moon is 1/81 Earth's mass

Gravity of moon is 1/6 Earth's gravity

WHY!

 

Because gravity depends on not just mass' date=' but distance.

 

F=GMm/r[sup']2[/sup]

 

You should be able to deduce the relative size of the moon from the numbers you have.

[ensonik]

Because gravity depends on not just mass' date=' but distance.

 

[/quote']

 

Could you expand on what you mean here?

[ecoli]

Force of gravity = Gravitaional constant * mass of object 1 * mass of object 2 divided by the distance between the centers of the objects squared.

 

Objects that are further apart will have less gravitational attraction then objects that are closer together.

[Anarchaus]

Because gravity depends on not just mass' date=' but distance.

 

F=GMm/r[sup']2[/sup]

 

You should be able to deduce the relative size of the moon from the numbers you have.

 

You see this in stars too, a supergiant is massive, but it could float in water if you had a huge tub. But if you have a white dwarf, which is around 1 solar mass, its about the size of earth, and it's pretty solid, the g well at the surface is real steep, the excape velocity is around 6000 km/s. Compared with a measily 11 km/s at the earths surface(6000 km).

 

A neutron star(20 km across) is about 150,000 km/s, and a stellar black hole(5-? km), at the event horizon is of course 300,000 km/s at any size. But a star, like our sun(600,000 km) is 300km/s

[ensonik]

Force of gravity = Gravitaional constant * mass of object 1 * mass of object 2 divided by the distance between the centers of the objects squared.

 

Objects that are further apart will have less gravitational attraction then objects that are closer together.

 

So basically without the Earth the moon would have an extremely weak gravitational pull. It's strong pull in relation to it's mass is essentially derived from object 2 (Earth)?

[swansont]

Could you expand on what you mean here?

 

I did. I gave the equation - it depends inversely on the square of the distance.

[swansont]

So basically without the Earth the moon would have an extremely weak gravitational pull. It's strong pull in relation to it's mass is essentially derived from object 2 (Earth)?

 

It would depend on the mass of the object in question. The gravitational field, given by GM/r² is what you should look at.

[ensonik]

It would depend on the mass of the object in question. The gravitational field, given by GM/r^{2[/sup'] is what you should look at.}

 

^{The objects in question are the Earth and Moon, right? While I appreciate you pointing me towards a fuller mathematical understanding of gravity, this thread is about two specific bodies and their relationship. So can I assume that my earlier remark about the moon deriving it's pull from the Earth was accurate, or not?}

[AzurePhoenix]

basically, it's the density of the object being spread across a greater volume, rendering the gravity as more diluted, yes?

 

Or more like spreading butter over bread, the more area you spread over the thinner it is. So the moon's gravity is not related to the earth's proximity.

[ensonik]

basically' date=' it's the density of the object being spread across a greater volume, rendering the gravity as more diluted, yes?

 

Or more like spreading butter over bread, the more area you spread over the thinner it is. So the moon's gravity is not related to the earth's proximity.[/quote']

 

My original comment said it must be heavier/denser, which sounds like what you're saying. But then there's this talk of distance between two objects playing a role.

[Janus]

The objects in question are the Earth and Moon, right? While I appreciate you pointing me towards a fuller mathematical understanding of gravity, this thread is about two specific bodies and their relationship. So can I assume that my earlier remark about the moon deriving it's pull from the Earth was accurate, or not?

 

No, that remark was not correct.

 

Let's see if we can make things clearer. The force acting between two bodies is equal to the formula given already:

 

[math]F= \frac{GMm}{d²}[/math]

 

G is the universal gravitational constant.

 

M is the mass of one body and m the mass of the other

 

d is the distance between their centers.

 

Using this we can calculate the force between the Earth and a 1kg mass sitting on its surface:

The radius of the Earth is 6,378,000 m so this is d

The mass of the Earth is 6 x 10^24 kg

so we get:

 

F= [math]F = \frac{((6.673 x 10-11)(1)(6 x 10^{24})}{6,378,000^2}=9.8N[/math]

 

For the Moon,

 

Mass = 7.35 x 10^23kg

radius = 1,735,000m

 

So the force acting on the same 1kg weight sitting on the Moon is:

 

F= [math]F = \frac{((6.673 x 10-11)(1)(7.35 x 10^{22})}{1,735,000^2}=1.6N[/math]

 

1/6th that of if it was sitting on the Surface of the Earth.

 

So we can see that even though the mass of the Moon is only 1/81 that of the Earth, an object sitting on the Moon's surface is is less than 1/3 as far from the Moon's center than an object sitting on the surface of the earth is from the Earth's center is. This is why the force of gravity on the surface of the Moon is 1/6 that of that on the surface of the Earth.

[AzurePhoenix]

So, in my idiot terms, I'm right?