Question Time. Astrophysics related.
My friends and I have had a discussion and cannot think of a solution.
If a large object, e.g. the size of the moon but completely hollow is orbiting an even bigger object e.g the earth (Tidally locked) and there was a very small object, e.g. a pencil at the center of this hollow bodied moon what would the pencil do?
Would it remain at the center of the 'moon' or slowly gravitate towards the sides?
>>8047173
The pencil would feel no gravitational force from the hollow body that it's inside - https://en.wikipedia.org/wiki/Shell_theorem
The pencil would only feel a gravitational force from the earth, and would stay orbiting in the centre of the moon.
>>8047173
By Gauss' law gravitational force at a point a distance r away from the centre of this sphere is only dependent on the amount of mass enclosed by the sphere of radius r. That is to say, if you have no mass inside if the sphere then the gravitational field inside of it will be 0.
So the pencil remains where it is, regardless of if it is at the centre or anywhere else inside the moon.
>>8047173
The pencil wouldn't feel any gravitational effects from the hollow moon but it would feel centrifugal forces on it. It would move to the back of the moon on the far side away from the planet.
>>8047205
If the moon and the pencil feel the same gravitational acceleration (ie the pencil is in the centre of the moon) it would stay there, as the pencil would feel no relative acceleration.
>>8047201
Now that I consider the orbits though, if the pencil is off-centre in any way which makes it closer or further away from the earth, it would orbit with a different period and so approach the sides of the moon.
>>8047205
>centrifugal forces
Lrn2orbit
>>8047212
OP here, I am inclined to agree with this.
But in the event that our moon object is in a state of rotation (not tidally locked) will the pencil reach the side/wall even if it is directly in the center?
>>8047249
I'm no astronomer but if Kepler's 3rd law is applicable here, for an object of smaller mass to stay in the same orbit it's orbital period needs to be smaller aka it would need to move at higher speed. So only if the mass of the pencil matches mass of the shell it could stay in the same orbit at the same speed.
>>8047301
>implying earth and moon don't orbit the sun with the same period
GTFO
>>8047249
What would rotation have to do with it? It's the mass distribution that matters, and for a spherical shell like the one you've described it'd be constant regardless of weather or not it was rotating.
>>8047301
>for an object of smaller mass to stay in the same orbit it's orbital period needs to be smaller
That... is completely wrong.
