Which has more gravitational pull, the moon or a nebula?

[md65536]

I recently saw an astronomy picture that had the moon in it and a nebula which looked as big as the moon.

I can't remember where I saw it... does anyone know if there are nebulas that actually look as big as the moon from Earth? And how far away would such a nebula be?

 

 

 

Here's my puzzle:

 

Suppose you had a nebula that looks as big as the moon.

Suppose that this imaginary nebula happens to be as dense as the moon.

Which would have a stronger gravitational pull on us?

 

You can assume the nebula is spherical and whatever distance away you want. Say, 100 light years.

[md65536]

Well no one seems to want to answer but I'm interested in whether my reasoning is right, so...

 

 

In this example, the nebula would have greater pull.

 

The area that an object with a given length and width takes up in the sky is proportional to r^2.

Gravity is proportional to 1/r^2.

This means that 2 objects of identical depth and density that look the same size from Earth, will have the same gravitational pull on us.

 

This example nebula is on the order of lightyears in depth, while the moon is a fraction of a lightsecond in depth. The example nebula would have some millions or trillions of times the gravitational attraction as the moon, even though it is so much further away. Its mass is proportional to the cube of its dimensions, so it would have astronomically more mass.

 

 

In reality however the moon has much stronger pull, because a nebula is so much less dense. While the nebula has millions or trillions of times the depth, it is so astronomically less dense that its density plays a much more important role than its size, and it would have probably negligible gravitational pull on us. While nebulae may be on the order of light years in diameter, they only have a mass of perhaps a few solar masses. A nebula formed from a supernova would have about as much pull on us as the star that it formed from.

 

 

[Axioms]

If it had the same density as the moon i predict that it would form a black hole.

I guess thats just my logic, the mass will clump together and a massive black hole would form.

Scary thought though

 

 

[md65536]

If it had the same density as the moon i predict that it would form a black hole.

I guess thats just my logic, the mass will clump together and a massive black hole would form.

Scary thought though

I agree.

The idea of a nebulae-sized moon-like mass is pretty absurd in reality.

I'm sure that it would have many (billions of?) times the mass of the entire universe.

Even the sun is a lot less dense than the moon.

I was thinking of calculating it for comparison, but I feel too lazy to.

 

 

[Janus]

Well no one seems to want to answer but I'm interested in whether my reasoning is right, so...

 

 

In this example, the nebula would have greater pull.

 

The area that an object with a given length and width takes up in the sky is proportional to r^2.

Gravity is proportional to 1/r^2.

This means that 2 objects of identical depth and density that look the same size from Earth, will have the same gravitational pull on us.

 

 

 

 

However, the volume, and therefore the mass, of objects with the same density is proportional to r³.

[md65536]

However, the volume, and therefore the mass, of objects with the same density is proportional to r³.

Yes, where r is the radius (or side length, etc) of the mass.

With astronomical sizes of nebulae, the mass would be astronomically larger (note the 3 dimensions of emphasis!).

 

Note that this use of r is different from the previous use, where it was used to denote distance from us. However, the ratio of radius_nebula/distance_nebula was chosen to be the same as radius_moon/distance_moon. -- So in this case I guess it's proportional to r³ whether r is radius or distance.

 

 

 

Even though the mass of the mythical moon-density nebula is cubically proportional to r,

its gravitational pull is only linearly proportional to r, as described earlier.

It would still be astronomically greater though, because the radius of the nebula is astronomically many times the moon's.

Edited October 19, 2011 by md65536