Hi, I am aware that in order for energy to be conserved the reference frame that you are using must be inertial. However, consider the situation where you are using the reference frame of the earth and there is a decently sized planet directly above on course for collision. The two have a gravitational potential energy U between them. My question is as the two approach, the earth is clearly not in an inertial reference frame. I know that it would be wise to use the center of mass frame in this situation, but if I were to stick to the earth, to convert to an inertial reference frame wouldn't I simply add a force equal in magnitude and opposite in direction to the earths motion to give it a zero net force? Then following this I would give the approaching planet an additional ''downward'' (in relation to the earth) force that is equal to it's mass x earth's acceleration? Now this seems fine, but if I were to run an integral for this fictitious force plus the original gravitation force multiplied by the distance just before collision, it seems like the approaching planet receive an amount of kinetic energy gained that is much higher than the potential energy lost, violating c.o.e. . So are fictitious forces only really useful for examining relative motion and not energy transfer? I understand using the center of mass frame would provide an inertial frame that would get rid of these problems but for the sake of the question I'm being stubborn and sticking with the earth. Also, when calculating the binding energy needed to separate two masses in orbit, should the center of mass frame always be used to determine kinetic energy? As I understand E = K + U must equal zero or larger for the masses to seperate to 'infinity', and using a different reference frame could easily result in a kinetic energy that easily exceeds this boundary even though the two masses are certainly still bounded. If the center of mass frame is used, do I simply add the kinetic energy of each mass relative to c.o.m. and then add the (negative)gravitational potential energy? Finally, a standard conceptual question that I have trouble visualizing. Imagine two similar masses, if they have the correct initial angular momentum, will they 'orbit' the center of mass between them or will they actually orbit each other? Should angular momentum for this system then be calculated with respect to the center of mass for each mass and then added together to determine the total angular momentum? Thank you for any help! Excuse my typos it is late and I am very tired haha.