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I thought Newton gravitational theory of course is about attraction. but I saw the claim

"the shorter distance (angular momentum)$^2$/$r^2$ repulsive behavior of Newtonian gravitational theory"

in the book GRAVITATION by MTW p 637 line 1, and don't understand it.

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    $\begingroup$ MTW mean the centrifugal potential. $\endgroup$ – Qmechanic Jun 25 '18 at 17:31
  • $\begingroup$ The link provided by @Khushal has it all. Note that it’s not a property of the gravitational force, but more a property of any force with central potential (force with no torque). Basically if you start with enough side velocity, you can never reach $r = 0$ even if the force is only attractive. Tell us if you need clarification. $\endgroup$ – Andrea Jun 26 '18 at 8:08
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Read this Wikipedia article on Effective potential. Look at the Gravitational potential section, you will find that the particle has a repulsive force arising due to centrifugal potential and an attractive force arising due to Gravitational potential. These two potentials together govern the trajectory of a particle in an orbit around a massive body.

https://en.wikipedia.org/wiki/Effective_potential

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