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Physics
Classical Physics
Mechanics
Exploring the Logical/Geometrical Explanation of Escape Velocity
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[QUOTE="PeroK, post: 6345651, member: 493650"] The algebraic "coincidence" is that when you set the centripetal force equal to the central force, you get something of the form: $$\frac{v^2}{r} = \frac{k}{r^2}$$ The ##r## cancels on the denominator, which is similar to integrating the force to get the potential. You'll get a factor of ##n -1## for any force of the form ##1/r^n##. In this case ##n = 2##, so the factor is ##1##. Then, for the escape velocity you are setting ##\frac 1 2 v^2## equal to the potential which is where the factor of ##\sqrt 2## comes in. [/QUOTE]
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Forums
Physics
Classical Physics
Mechanics
Exploring the Logical/Geometrical Explanation of Escape Velocity
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