Two Jupiter-size planets are released from rest 1.40×10^11m apart. What is their speed as they crash?
There is an external force between thise 2 jupitors
U know there is a gravitational attractional force between jupitors
at the start, the amount of energy in the system (grav potential) is -G mm /r G = Newton's constant, look it up if you don't know it m = mass of jupiter - look it up r is the 1.40×10^11m you provided when they are touching, that potential energy will be -Gmm /(rj + rj) where rj is the radius of jupiter, again look it up. at that point, due to the symmetry, *each* planet will have KE = 1/2 m v ^2. ergo 2 * 1/2 m v ^2 = Gmm ( 1/2rj - 1/r ) v^2 = Gm ( 1/2rj - 1/r ) i make it about 30 km/s there's a bucket load of science in this and i do not know at which level you are currently working so i took the view that this was a good way to start.
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