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https://www.uwgb.edu/dutchs/planets/cratform.htm This has a nice explanation regarding this.

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Although the force is radial, the direction of motion is not the direction of the force, rather it is the direction of the velocity at any time $t$. In order to find out the dependence $\mathbf{v}(t)$ one must solve the equations of motion $\mathbf{F}(\mathbf{r}, \dot{\mathbf{r}})=m\mathbf{a}$. Doing so with the gravitational potential $V(r) = ... 1 What will be destroyed? The Moon or the Death Star? Both. You are ignoring length contraction. At a "mere" 0.90 c, the 385000 km between the Earth and the Moon is length contracted to 168000 km. The perceived distance grows ever smaller with increased speed: 54000 km at 0.99 c, 17000 km at 0.999 c, 5450 km at 0.9999 c. You are also ignoring human ... 0 In addition to what @JohnRennie points out, the radius value that you would use for$\frac{v^2}{r}$calculations at the perigee and apogee are not the ordinary distances that you would use for the Newtonian gravity. To calculate the radial acceleration at the apogee and perigee, you must use the inverse of the curvature of the path. For an ellipse this ... 5 You ask: what is the exact average distance r we must consider when we determine the centripetal force and consequently the pull of the Earth$v^2/r\$, is the semi-major axis 384,399 or rather 384,748 Km, and is average distance 385,000? and, is average speed 1.022 or 1.023 Km/s? Does the pull vary during the revolution? But this is not a well defined ...

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If the earth and moon were both stationary initially, the moon would fall into the earth as you said. But they were not. Earth was moving around the sun when the moon was formed from the earth. And so the moon also started revolving around the earth. Infact even now the moon is falling towards the earth, but the earth is continually moving away so that the ...

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The moon always poses the same face to the earth because its rotation period around its axis is equal to its revolution period around the earth. It is this way due to tidal locking. See: https://en.wikipedia.org/wiki/Tidal_locking

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