How do we know that the escape velocity formula is what it is? How was it determined?
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It’s the velocity that sets the kinetic energy of an object equal and opposite to the gravitational potential energy.
Kinetic energy is mv^(2)/2, gravitational potential energy is mgh. Set them equal and cancel mass, and we get v^(2)=2gh.
Little g is gravitational acceleration on earth, but we can generalize it to be GM/h^(2), where G is the gravitational constant, M is the mass of the object you’re escaping from, and h is the height from the center of mass.
Sub that into the previous formula to get v^(2)=2MG/h, and can root both sides to get v=(2MG/h)^(1/2).
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