# What is the outward force on the Moon that makes it go in orbit rather that falling straight to the Earth? [duplicate]

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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.

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

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• possible duplicate of Why doesn't the Moon fall upon Earth? – Javier Sep 28 '15 at 11:30
• 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. – anna v Sep 28 '15 at 11:40
• A body in motion stays in motion does not require a force to stay in motion. – WillO Sep 28 '15 at 13:12
• @WillO Yeah but what's keeping the body in motion. In this case: what's keeping the moon in motion? – Anonymous Sep 28 '15 at 15:29
• @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. – WillO Sep 28 '15 at 16:12

## 1 Answer

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.

• 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. – Gert Sep 28 '15 at 12:50