What if...

[goaowonk]

Last week, while I was thinking about parallel universes, I had an idea: how would it be if Gravitational Forces were inversely proportional to r^x when x is not 2?

I mean: when else than Fg ~ 1/r^2

 

[Artlav]

It would suck.
A lot.

Actually that inverse square law is deeply entangled in the laws of physics, you would have to butcher up everything to get it to be linear, so the world would be completely different.
And since we don't know the generic law of our universe, there is no way to predict just what would it look like.

But if we look at face value, and assume gravity changed without altering anything else...
Smaller planets and stars, gravity being a major force along with EM.
Much more black holes.

Orbits would look different.
Here is the program to try it: http://spaceway.1gb.ru/files/grav.zip
grav_lin.exe is linear gravity, grav_sqr.exe is regular one.
WASD controls, TRZXCV - are the keys.

Regular orbit:

Linear orbit, with G constant reduced 100 times to prevent collapse:

In short, no stable orbits.

---------- Post added at 15:13 ---------- Previous post was at 15:08 ----------

With r^3 and above the situation becomes even worse - the orbits spiral down

So, while ^1 was kind of stable (if not repetitive), ^3+ is simply unstable.

 

[goaowonk]

Wow. I assume that fractional exponents will behave in a similar way.

Will see the program when there's a PC available :thumbup:

Sent from my Deltaglider using Potatolk.

 

[Quick_Nick]

This is a little off-topic, but there has been plenty of speculation on universes with a different number of dimensions, which would "in theory" (as much of a theory as you can make for an imaginary universe) have different values for x in your gravity function.
http://arxiv.org/abs/gr-qc/9702052
I've heard that everything would fall inward in a 2D universe, but I feel like you could have some very large spacious structures. It's not a topic that makes total physical sense, but it is interesting to think about.

 

[thepenguin]

It would suck.
So, while ^1 was kind of stable (if not repetitive), ^3+ is simply unstable.

^x is stable under any value of x, so long as the orbit is perfectly circular.

I think every value of x has one stable orbit.

Edit: I'll solve the equations later.

 

[Artlav]

^x is stable under any value of x, so long as the orbit is perfectly circular.

I think every value of x has one stable orbit.

Sure. And a supercritical pellet of plutonium is stable so long as no atoms spontaneously fission.

There are no perfect orbits in the real world, so what matters is what would happen when one gets perturbed.

 

[thepenguin]

Sure. And a supercritical pellet of plutonium is stable so long as no atoms spontaneously fission.

There are no perfect orbits in the real world, so what matters is what would happen when one gets perturbed.

Under the same logic, X=2 orbits are unstable, due to the possibility of something perturbing them in a similar manner. I think we can assume the perturbations to be relatively small for the purposes of this exercise, though. Under that logic, nothing major would happen for a few billion years, but it would eventually expand or collapse (just like the moon, diemos, and phobos will). The problem is not unique to X>2 orbits, given a long enough timeframe.

 

[Linguofreak]

Wow. I assume that fractional exponents will behave in a similar way.

Will see the program when there's a PC available :thumbup:

Sent from my Deltaglider using Potatolk.

If the exponent is less than 3, there will be some stable orbits. Centrifugal force as a function of radius for constant angular momentum is an inverse cube repulsive force, gravity is an attractive force. If the exponent for gravity is less than that for centrifugal force, then there's a range of angular momenta for which a graph of the effective potential for the combination of the two forces will have a local minimum at some radius. If such a minimum exists, there are stable orbits. If the exponent for gravity is 3, the best you can get is where angular momentum is such that gravity and centrifugal force exactly cancel out and the potential graph is flat. If the exponent for gravity is greater than 3, then the best you can get is a local maximum in the effective potential (where you can have a very carefully balanced circular orbit).

Interestingly, in General Relativity, there's a term that causes centrifugal force to fall off as the orbital radius approaches the Schwarzschild radius, with the result that once you get too close to a black hole, all trajectories either escape or fall in and there are no stable orbits.

Under the same logic, X=2 orbits are unstable, due to the possibility of something perturbing them in a similar manner. I think we can assume the perturbations to be relatively small for the purposes of this exercise, though. Under that logic, nothing major would happen for a few billion years, but it would eventually expand or collapse (just like the moon, diemos, and phobos will). The problem is not unique to X>2 orbits, given a long enough timeframe.

No. The point is that for X < 3, if you are in a stable orbit, you can always find some perturbation (though it may be very small) in any given direction that will leave you in another stable orbit. For X >= 3, there is no such perturbation. Any perturbation will leave you on an escape (or infalling) trajectory.

 

[jedidia]

Actually that inverse square law is deeply entangled in the laws of physics

It's a geometrical law, really. As such, I cannot even imagine how it could be different no matter how weird the universe. A circle wouldn't be a circle in that universe...

 

[T.Neo]

So if I understand correctly, the discussion is basically this, but with physics?

 

[Artlav]

It's a geometrical law, really. As such, I cannot even imagine how it could be different no matter how weird the universe. A circle wouldn't be a circle in that universe...

There are Non-Euclidean geometries, there are geometry-less and space-less universes, there are likely ways to make a universe that we don't understand yet.

Geometry is only a high-level concept, down at the bottom you get space less wave functions and configurations, defined relative to each other.
Or some fractal equation, defined independently of anything.
Or a cellular automaton, defined locally.
Or some other not yet understood thing.

 

[Linguofreak]

It's a geometrical law, really. As such, I cannot even imagine how it could be different no matter how weird the universe. A circle wouldn't be a circle in that universe...

The properties of the particles that carry a force can have an effect: Photons are uncharged and massless, so electromagnetism ends up being a mundane inverse-square force, and the same applies more or less to gravity (the graviton, if it exists, is massless, and gravity is a mundane inverse square force in weak gravitational fiels, but General Relativity changes the geometry when escape velocities approaching c are involved).

With the strong force, the carrier particles, gluons, are also massless, but they all carry "color charge" (the charge associated with the strong force), and as a result they interact one another, causing the strong force not to fall off with range at all (a Wikipedia article on the subject says that the force between two quarks is about 160,000 Newtons regardless of distance, and by some accounts I've heard, the force even increases with distance). As a result, quarks don't have to be separated from each other by very far before the potential energy between them is enough to cause pair production, which is why we don't see the strong force on macroscopic scales (anything the size of a proton or bigger ends up being neutral with respect to color charge).

With the weak force, two of the particles that carry it (the W bosons) are charged with respect to the weak force (and also have electrical charge), while the third (the Z boson) is uncharged, but all three are massive, and this somehow causes the weak force to drop off more quickly than inverse square.

So you could probably postulate some kind of weird graviton with properties that caused gravity to behave differently.

 

[jedidia]

There are Non-Euclidean geometries, there are geometry-less and space-less universes, there are likely ways to make a universe that we don't understand yet.

Well, I'm still one of the poor sods that has to think of a circle as an image, not an equation...

Looking at Escher's works and not having my head explode is about the closest I can get to expierienceing impossible geometry.

 

[PennyBlack]

Just wondering why people are useing the laws of physics in this universe to predict the behaviour of parrallel universes where they may all be different. It's somewhat irrational to me dispite not understanding a single word/formula presented. :facepalm:

We need to create a Transversal Internet Connection to compare your figures with your alternates. Otherwise, it's pure conjecture.!!! :lol:

 

[thepenguin]

Just wondering why people are useing the laws of physics in this universe to predict the behaviour of parrallel universes where they may all be different. It's somewhat irrational to me dispite not understanding a single word/formula presented. :facepalm:

We need to create a Transversal Internet Connection to compare your figures with your alternates. Otherwise, it's pure conjecture.!!! :lol:

May I ask what the problem with pure conjecture is? I think it's far more nonsensical to disregard a phenomenon because it has no bearing on our universe. Sometimes the calculations must be appreciated as calculations, and as pure math, not applied physics.

 

[PennyBlack]

I've no problem with pure conjecture at all sir, I love alternate universe stuff and enjoyed reading the thread. Not that I understand the laws of physics in this universe, what with the amount of times I fall over.

I used to use a simulator called Gravity. Making minor solar systems, trying to create a stable system with as many planets as possible in it and on the rare events of doing so, enjoyed throwing a rouge star into the mix. I imagined the panic of those in the Goldilox Zone as the world was thrown into the viod at breakneck speeds... :thumbup:

 

[Izack]

We need to create a Transversal Internet Connection to compare your figures with your alternates. Otherwise, it's pure conjecture.!!! :lol:

But conjecture is fun!!

Edit: Nevermind! Where did that second page come from? :lol:

 

[Andy44]

These discussions fascinate me, but it's kind of like discussing "what would the world be like if we were never born". Well, to those of us who exist, that's kind of pointless...

I still read it, though.

I wonder what an alternate universe version of Andy44 would be like, though. Would he have an evil Spock goatee?