What happens to gravity in one dimension of space?

  • #1
KeplerJunior
25
0
I recently heard that it was found how gravity would behave in different dimensions of space. Apparently, while in our 3 dimensions of space gravity is F= x/r^2, in 4 dimensions it would be F=x/r^3, so it would be weaker, and in 2 dimensions it would be F=x/r so it would be stronger.What it didn't say was what would happen in 1 dimension, it follows from the above that it would be F=x/r^-1, which simplifies to F=xr, which would indicate that gravity would get stronger as you went further away from the object. Is this what would happen? And if so does that mean gravity would become a repulsive force?
 

Answers and Replies

  • #2
D H
Staff Emeritus
Science Advisor
Insights Author
15,450
687
You skipped over a key integer. Hint: What integer is between -1 and +1?
 
  • #3
KeplerJunior
25
0
Oh of course, so would it just be x/r^0 so x/1, so x. So then distance wouldn't change anything in 1 dimension
 
  • #4
Jarfi
385
12
I recently heard that it was found how gravity would behave in different dimensions of space. Apparently, while in our 3 dimensions of space gravity is F= x/r^2, in 4 dimensions it would be F=x/r^3, so it would be weaker, and in 2 dimensions it would be F=x/r so it would be stronger.What it didn't say was what would happen in 1 dimension, it follows from the above that it would be F=x/r^-1, which simplifies to F=xr, which would indicate that gravity would get stronger as you went further away from the object. Is this what would happen? And if so does that mean gravity would become a repulsive force?

Um, actually, the integer x/r dr is xln(r). Which means the equation of gravity in one dimension would be:

f(r) = gravitational force = xln(r). So gravity would according to this increase with increased distance, something I find hard to believe. It means the further you are away, the stronger it'd pull, well until you get to a distance of 0, then it starts to push you away again... because ln(r)<0 if r<1. This is something similar to strong force, it's repulsive at a certain closeness, but if they stray too for from each other it becomes a very strong attractive force.
 
Last edited:
  • #5
Flatland
218
11
I thought that gravity did not change with distance in 1 dimensional space?
 
  • #6
WannabeNewton
Science Advisor
5,829
547
It doesn't. Laplace's equation in one dimension for the gravitational potential exterior to a point mass is simply ##\frac{\mathrm{d} ^2 \varphi}{\mathrm{d} x^2} = 0## so ##\varphi = Ax + B## and ##g = - \frac{\mathrm{d} \varphi}{\mathrm{d} x} = -A##.
 
  • #7
Jarfi
385
12
It doesn't. Laplace's equation in one dimension for the gravitational potential exterior to a point mass is simply ##\frac{\mathrm{d} ^2 \varphi}{\mathrm{d} x^2} = 0## so ##\varphi = Ax + B## and ##g = - \frac{\mathrm{d} \varphi}{\mathrm{d} x} = -A##.

So I was wrong?
 

Suggested for: What happens to gravity in one dimension of space?

Replies
3
Views
322
Replies
1
Views
757
Replies
3
Views
727
Replies
10
Views
452
  • Last Post
Replies
4
Views
492
Replies
21
Views
2K
  • Last Post
Replies
28
Views
4K
  • Last Post
Replies
15
Views
2K
Top