Chapter 8: Problem 8
The force of gravitational attraction on a mass \(m\) at distance \(r\) from the center of the earth \((r>\text { radius } R \text { of the earth })\) is $$m g R^{2} / r^{2}$$. Then the differential equation of motion of a mass \(m\) projected radially outward from the surface of the earth, with initial velocity \(v_{0},\) is $$m d^{2} r / d t^{2}=-m g R^{2} / r^{2}$$. Use method (c) above to find \(v\) as a function of \(r\) if \(v=v_{0}\) initially (that is, when \(r=R) .\) Find the maximum value of \(r\) for a given \(v_{0},\) that is, the value of \(r\) when \(v=0 .\) Find the escape velocity, that is, the smallest value of \(v_{0}\) for which \(r\) can tend to infinity.
Short Answer
Step by step solution
Key Concepts
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