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Aug 12, 2019 at 23:17 comment added Farcher You have a sign error because you have defined positive velocity to be down in the limits of the integral, while positive radial coordinate is up. The $V$ as the upper limit in the left hand side integration is the component of velocity in the outward from the Earth's centre direction.and so there is nothing wrong with this limit as written.
Aug 12, 2019 at 20:56 history answered JEB CC BY-SA 4.0