How to derive escape velocity

[@Zodiaczero2]

For anyone who wonders why potential energy is -GMm/r, I want to add a further point I I will explain where that gravitational potential energy equation comes from and why it is not mgh. So, we use the definition of energy or work as force times distance, expressed as E = Fs. However, this equation is applicable only for constant forces. If the force changes with location, we need to use calculus. Considering a tiny change in energy, dE = F ds, then energy is given by E = ∫ F ds, where the force of gravity is represented by F = -GMm/r^2, which is a function of radial coordinate (r). Thus, E = ∫ F dr = -GMm/r^2 dr. Now, we want to know the potential energy when an object is infinitely far away, which is not zero. Therefore, we need to integrate from r to infinity. After solving the integral, we find that E = -GMm/r. This represents the gravitational potential energy. Potential energy is negative because gravity is an attractive force. In old physics, it was simplified to mgh, but it should actually be -mgh, as T = P + V, not T = P - V.

[@MuwanguziPeter-o6d]

Thanks for the content

[@AstroPhil2000]

@@MuwanguziPeter-o6d thanks 😊