wtg62 wrote:r^-2 - Default *yawn*
Oh, come on, you can do better than that! Conic sections, closed orbits, stars at foci, our universe's law... Say something about it other than "yawn"!
wtg62 wrote:r^-3 - Spiral 'orbits'.
Also, stable orbits are impossible.
wtg62 wrote:r^0 - Stable orbits are impossible.
Also can be written as "1" (or any other constant). There must be something special about this gravity law besides that...
wtg62 wrote:r - All orbits are stable. Can also be inputted as r^1.
Stars are ellipses' centers. Harmonic motion. So on.
wtg62 wrote:r^x - Where x is a positive number more than 1. Objects are pulled with greater force the further away they are from each-other, allowing star/flower shaped orbits to be made.
x just has to be a positive number. It doesn't have to be greater than 1. Also, I've noticed that flower-shaped orbits are formed with pretty much every gravity law. I'm just wondering whats special about them.
wtg62 wrote:tan(r) - Crazy orbit shapes, planets oscillate back and forth. They really are fascinating. Can be written as sin(r)/cos(r)
They're actually not that
crazy (unless you send it into one of the asymptotes).
wtg62 wrote:sin(1/r) - Creates flower patterns.
Like I said, a bunch of stuff creates flower patterns. Also note how it gets crazier the closer you are to the star.
wtg62 wrote:cos(1/r) - Similar to sin(1/r), just more extreme.
How is it more extreme?
wtg62 wrote:tan(1/r) - Trajectory predictions are weird, and do not predict what'll actually happen. Things are flung about, everywhere. Can be written as sin(1/r)/cos(1/r)
I don't have much to say about this.
wtg62 wrote:sec(r) - Similar to tan(r), although shapes can be a little more weird. Can be written as 1/cos(r).
How can they be weirder? It's not very similar to tan(r) either in terms of orbits except for the flower shapes, which are really common anyways. Also, objects can't help but hit the asymptotes unless they have enough motion in one of the areas where secant is positive, so this is a good law to see some of the areas where the GSim isn't so precise (also see "Strange oscillations": viewtopic.php?f=7&t=107
wtg62 wrote:r-1 - Caught by A Random Player. Objects attract and repel each-other at certain distances, meaning they'll go back and forth.
Also, what about other polynomial functions? It could be really cool seeing how objects attract one instant and repel the next. For that matter, all rational functions might be cool studying.
wtg62 wrote:abs(tan(r)) - Similar to tan(r), just that the force of gravity is never negative. (*boing* *boing*)
I'd expect a lot of objects to fall into the asymptotes without the negative force acting as a buffer.
wtg62 wrote:tan(tan(r)) - Unpredictable results may occur. Objects are pulled about in random directions if more than one object with mass is present.
Hmm, interesting. You could also do sin(tan(r)), which would do the same thing, but without the infinite gravities, so it would be more precise.
wtg62 wrote:tan(sin(r)) & tan(cos(r)) - Try giving r a coefficient and this'll be more effective. Basically certain distances pull your objects or push them.
This is basically the same as sin(r) and cos(r), except it's pointier. The coefficient thing holds true for all trigonometric functions. You can also put a coefficient by cos(r), and the higher it is, the crazier. π/2 is the point at which you get infinities.
ARP wrote:(That means only a line segment and a triangle. If the sim extends into 3D space, it also includes a tetrahedron.)
Wait, so how would you get a triangle?
AlternateGravity wrote:1/r^2 produces elliptical orbits and seems to be the only inverse law to produce elliptical orbits.
It also produces other conic sections, like parabolas and hyperbolas.
AlternateGravity wrote:I was able to get stable orbits in r^0 easily.
Hmm... Wtg said it was impossible to get r^0 to produce stable orbits. I'm confused.
Nobody ever notices my signature. ):