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So, we know that the gravity is responsible for pulling the Moon towards the Earth. But because it moves in an orbit, it makes me think that there must be a force that is causing the moon to travel in the direction other than the Earth's. So it doesn't fall straight to the Earth.

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marked as duplicate by Javier, Martin, John Duffield, Carl Witthoft, ACuriousMind Sep 28 '15 at 12:50

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    $\begingroup$ possible duplicate of Why doesn't the Moon fall upon Earth? $\endgroup$ – Javier Sep 28 '15 at 11:30
  • $\begingroup$ Tie a soft weight on a string and whirl it around your head. The string is pulling the weight but the weight does not fall on your head ( unless you stop turning). It is called the centrifugal force and is equal and opposite to the centripetal which your hand gives. $\endgroup$ – anna v Sep 28 '15 at 11:40
  • $\begingroup$ A body in motion stays in motion does not require a force to stay in motion. $\endgroup$ – WillO Sep 28 '15 at 13:12
  • $\begingroup$ @WillO Yeah but what's keeping the body in motion. In this case: what's keeping the moon in motion? $\endgroup$ – Anonymous Sep 28 '15 at 15:29
  • $\begingroup$ @Anonymous: Perhaps my earlier comment was unclear because I inadvertently omitted the word "and". A body in motion stays in motion and does not require a force to stay in motion. $\endgroup$ – WillO Sep 28 '15 at 16:12
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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 $V(r) = -G\frac{mM}{r}$ gives back trajectories which happen to be conic sections. The only case when such trajectories can degenerate in straight lines is when the initial velocity is zero.

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  • $\begingroup$ It might be useful to expand a little on what is meant by 'conic sections', as the asker is unlikely to recognise these as circles, ellipses or hyperbolas. $\endgroup$ – Gert Sep 28 '15 at 12:50

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