What if gravity were proportional to sin(r)/r² instead of 1/r²? | Not-Quite-Physics Simulations

Two simulations of the three-body problem. The forces between the masses in the simulation on the left are proportional to 1/r². The forces between the masses in the simulation on the right are proportional to sin(r)/r². In both simulations, all three masses have the same starting positions and velocities.

The simulation on the right is basically nonsense - it's just for fun.

- all masses equal
- symmetric start
- 25fps, 60s

#Physics #PhysicsSimulations #ThreeBodyProblem #Gravity

[BRORIGIN]

could you do sin(r)/r^3 next? because then for small r it would go like 1/r^2, recovering Newtonian

[qh]

I think the behavior is pretty much expected. Near a zero of sin(r) the force will behave like hooke's law, so you just get a harmonic oscillator.

[Mutual_Information]

A creative question with a beautiful answer. Well done.

[clown]

I absolutely love seeing stable orbits with alternative equations for gravity. I'd love to know the software that you're using for this

[Vaigg]

What are you using to simulate these? This looks loke fun to play with.
Maybe the next one can use exponentials or logarithms.

[terryzacharie]

a gut feeling is telling me this is big.

[celanimaddr]

I should eat more fish so I have the omega 3 acids necessary to understand these comments and video

[v.t.]

It is so satisfying and unsatisfying at the same time

[chaitanya]

Why all your simulations fail at the end ?

[viperking]

What would it look like from earth? Like what would we experience

[meable]

idea: gravity is proportional to 1/sqrt(r) if you've not done it already

[aSpyIntheHaus]

We are living in the wrong universe. Sin(r) gravity is sooo much cooler. Look how stable that was