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bob012345

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- How to do the integral for an object falling under Newton's Gravitational Law without approximating a constant acceleration of gravity ##g##.

I realized I never actually derived the kinematic equations of motion for the exact Newtonian gravitational force. For an object falling near the surface of the earth, how do we handle integrating the equation of motion to derive the kinematics equations without using the approximation of constant g?

Starting with ## \large \frac{d^2y}{dt^2} = -\frac{GM}{y^2}##, how do we untangle this? Then simplify the solution with the assumption the acceleration is constant to get the usual equation.

Starting with ## \large \frac{d^2y}{dt^2} = -\frac{GM}{y^2}##, how do we untangle this? Then simplify the solution with the assumption the acceleration is constant to get the usual equation.

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