
What formula can show if two planet will fall into each other in a specific orbit?

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If they are already orbiting, they will collide into each other only if one of the planets slows down its orbiting speed. The formula you have here is for calculating gravitational force. You need another formula to calculate the centripetal force of one of the planets F = (m * v^2) / r. If they are orbiting, then the centripetal force of one of the planets is equal to gravitational force of the other planet that attracts it, so they are like in equilibrium. I would try thinkng in this direction.
No idea, I am not an astrophysicist. Try to ask chatgpt, it should help.
Do you mean immediately, in their present trajectories? You need to calculate their orbit from their relative masses and current velocity, then determine if the closest approach of their centers is less than the sim of the radii.
I'm not an expert on this matter.
But I feel gravitational forces play a major role in guiding them. As does source fuels. The latter is something I learnt from binary stars.
Do they have a star? Are they abandoned from their system? Is a blackhole close?
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You mean like collide or not?
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