Different Gravity laws?

[Only2ndplace]

So here's an idea about something that would add a whole lot to Universe Sandbox²
and just really fits the idea of a N-body gravitational simulation:

The possibility of different laws for gravity.

As you all probably know: The Newtonian gravitation between to bodies of mass M and m is
                                          F = - G*M*m*r^(-2)
                                          Inversely proportional to the square of the distance.

But what about general F = - G*M*m*f(r) laws, where f(r) is any kind of function dependend on the distance r?

Even just starting with laws with f(r)=r^n, where n is a number the user can put in, would leave tremendous room for experimentation.

Here's a few brain teasers of what happens for different n:

• For forces with n bigger or equal to -1 there is no escape velocity, which means for example that bodies in a simulation, where F is proportional to 1/r will never leave the solar system completely
• If n is smaller or equal to -3 (for example 1/r^3) there are no stable circular orbits. Planets will just spiral into their suns.
• There are only closed orbits (which means the planet will return to its starting position after one orbit) for some n (for example n = -2 or n = 1). In other cases, you will get weird flower like orbits.
• My favorite: For n = 1, F is proportional to the distance or in other words, the planets act, as if invisible springs would be attached between them.
  In this configuration, the planets also run around their star in ellipses, but the star is in the middle of the ellipse and not in it's focus point (As can be seen in the picture).
  Additionally, while the time for the orbit in our universe grows with the distance from the sun, in this universe, it's totally independent of the ellipse. All planets would have the same length of year!

Needless to say, there's all kinds of crazy possiblities
If you would like to check some of them out in a 2D-Sim without fancy graphics, here's a link to a gravity simulation, where you can change the force law: http://testtubegames.com/gravity.html

[JMBuilder]

This might be a fun way to "simulate" other dimensions with different laws of physics.

What would be a way to make orbits geosynchronous regardless of distance? The equation would need to take an objects rotation into account in some way, and I'm terrible at math. :/

An elliptical geosynchronous orbit would be really wonky since the orbiting object would need to accelerate on both its ascent and descent.

[Only2ndplace]

What would be a way to make orbits geosynchronous regardless of distance?

Well, I think it's safe to say, that it's impossible to get gravitational law, that only depends on distance, where there's a geosynchronous orbit for any rotational speed at all distances, because gravity isn't changed, if a body rotates (if we ignore relativity).

So instead, as you probably assumed, the gravitational law would have to be dependend on rotation also.
In that case, there are probably many different ways to do this.

For example, if we assume gravity works like this F = m*v^2/r where v is the rotational speed of the sun around it's axis, then it would just be the equation for a general zentripetal force (force on objects, that move in a circle).
In this case, all planets would spin around the star, as if they were rigidly connected to it, like a spinning plate.
However, this would come with all kinds of complications. For example it would break Newton's third law.

If you think that's kooky, I have this alternative for you:
Take the spring law: F = GmM*r.
There can be circular orbits just like in our universe and as I already said, the rotational period for bodies at all distances is constant.
However you can't let your sun spin at any speed you want. For this to work, it's velocity would need to be exactly v= R*sqrt(G*M)/(2*pi), where R is the suns radius and M is it's mass.

If you chose a sun with appropriate radius you can in this case get geosynchronous orbits for all distances

[tesco]

aww hell yeah

[JMBuilder]

Oh hey, what would an eccentric binary star system look like with those alternate physics?

[Angel Armageddon]

Well...
The laws of physics are unchanging.
The devs want Universe sandbox^2 to be, probably, as realistic as possible.
So adding the ability to change how newtonian gravitational physics work, wouldn't be very realistic.

BUT, they do want to make US2 to be fun and useful.
So adding this would be better than leaving it out.
But one problem remains.

Newer users, and some current users, are not very intelligent on how to use the sim and all of its "tools".
So a "users guide" would be very good to have, or a demo/tutorial that would show users how to use the sim, and shows you all sorts of other things.
And can be optional.