# Gravity in 2D

1. Aug 31, 2006

### DaveC426913

Flatland deals with macroscopic issues. What about the physics of Flatland?

What is the strength of 2D gravity? Does it still fall off as the square of the distance, or would it be linear? And mass increases as the square of radius, not the diameter, right?

2. Aug 31, 2006

### Cyrus

It's flatland! gravity is inconsequential! DUH!

3. Aug 31, 2006

### scott1

I don't think that would be a good answer.

I'm assuming that flatland is based off of Euclidean geometry which describes geometry of a world without matter. And according to einstien you need matter to curve spacetime so a "flatlander" would not be effected by gravity because there is no way to for a flatlander to feel gravity.

But for some reason I still don't think this answers your question...

4. Aug 31, 2006

### Cyrus

If FLATLAND has no up or down, what does gravity matter??

Have you read the book Flatland?

5. Aug 31, 2006

### Arian

I disagree, flatland might be populated by flatoms. Flat-atoms.
Well, then we have the idea that these flatoms might by a strange flat force or flattey, flat-gravity, be drawn together into stars or planets. These planets would have a very large effect and if were drawn on a piece of paper, would crumple the paper downward. Things trying to escape the flearth, flat-earth, would need enough force to ovesome the crumple in the paper.

The streanght of gravity is :

2-D:2/1
3-D: 1
4-D: 1/2
5-D: 1/4
6-D: 1/8

Two times bigger in flatland.

Note: I wrote like a entire 10 page desgin of the physics of a flatland (not populated by squares of course but possible beings, like flumans. hehe

6. Aug 31, 2006

### scott1

No but I have seen what 2-D looks like.(I'm currently reading it online right now).

Reread my post I ment that if a world had no depth(not up or down) there could be no gravity.

7. Aug 31, 2006

### scott1

Can you post it here on PF it might be useful in answearing the orginal question.

8. Aug 31, 2006

### Cyrus

Up or down is exactly what makes something have depth! Flatlanders only know front, back, and side to side.

Yes, there can be gravity. But it matters not (because the flatlanderes wont have one clue about detecting it)!

Last edited: Aug 31, 2006
9. Aug 31, 2006

### -Job-

Why is depth needed in order to have gravity? And why doesn't a 2D world have depth? Is there a favored depth axis?

10. Aug 31, 2006

### Cyrus

:rofl: Omg..... <smacks myself in the face>

11. Aug 31, 2006

### -Job-

What's so funny? Are you laughing at yourself? A relativistic equivalent for gravity in a 2D universe would be that of a plane bent at a point, such as a flat plastic bag with a lead circle inside the bag. The behavior is similar. Anything inside this bag that approaches the lead circle will be accelerated towards the lead circle. So people living inside the bag will detect the influence of a force when approaching the circle, or any other body for that matter, which would be their gravity. The bag is 2D, think two flat plastic sheets close together. Bodies in the universe will be 2D objects in between the plastic sheets. They can move in 2 axis. Their depth is measured as the shortest distance to an object, just as with us in 3D.
I think what you should be laughing at is your inability to think conceptually, though it's no laughing matter. Anyway, to respond to the OP, i'd say it would still decrease quadratically with distance, rather than linearly.

Last edited: Aug 31, 2006
12. Sep 1, 2006

### Cyrus

Maybe I am missing something here.......but 2D cannot have any depth to it since there is NO z coordinate.

Explain to me, how does something 'fall' when there is no z direction? I'd like to hear it....

13. Sep 1, 2006

### daveb

I would think it's similar to the ball ont the rubber sheet analogy we use to picture what a 4D sphere looks like in 3D, but Flatlanders would have to conceptualize the effects of gravity as a 2D disk on a line rather than a 3D ball on a sheet. Physically, the 2D gravity would look exactly like the ball on sheet (at least to us). Just like creatures in a 5D universe would use the analogy of a 4D hypersphere on a 3d cube to demonstrate what ours looks like.

14. Sep 1, 2006

### Hootenanny

Staff Emeritus
How about two massive particle placed in this 2D plane. According to the laws of gravitation, would these two particle be attracted to each other?

15. Sep 1, 2006

### Cyrus

Yes, but the OP said how would something 'fall' and I'm saying that entire premise is flawed!

16. Sep 1, 2006

### Hootenanny

Staff Emeritus
Where was 'falling mentioned'? I can't seem to find it

17. Sep 1, 2006

### Cyrus

Ah you are right, my fault Hoot. However, this is exercise would amount to making up physical laws because we have no observation of a 2D world. It would be pure speculation, do you not agree?

18. Sep 1, 2006

### -Job-

There is no preferred "up/down" axis, and no preferred depth axis. There's no "falling" in 3D either, just an acceleration due to gravity which we identify as downwards, but i'm sure you can position yourself such that it is sideways.
In 3D the gravitational interaction of two bodies can result in acceleration in any direction. The same thing would apply in 2D. The 2D disk inside the plastic sheets, under the influence of gravity, could accelerate in any direction describable by a 2D vector.
In 2D gravity causes bodies to come together, just as in 3D.

Last edited: Sep 1, 2006
19. Sep 1, 2006

### Cyrus

Would there be a gravitational attraction? I dont know... possibly. This is a 3D world, I dont live in a 2D world.

I do know that if there was no gravity, it would make no difference because they would not float away. If there was infinite gravity, they would not feel it because there would be nothing of them to be 'crushed' either. (They have no depth)

Last edited: Sep 1, 2006
20. Sep 1, 2006

### Hootenanny

Staff Emeritus
While I totally agree with you there, it is possible to 'fall' towards a massive body to the left, right, forwards or backwards; normally one thinks of falling 'down', since flatlander's have only two axes they will have no concept of falling 'down' because they are only aware of left, right, forwards and backwards. Imagine yourself water skiing and the boat you are holding to begins to accelerate forwards from your veiwpoint, would you describe yourself as falling?