# If gravitation causes constant acceleration why moon does not fall into earth? [duplicate]

If moon travels with constant speed in one direction and earth gravitation causes constant acceleration in perpendicular direction why moon does not eventually fall into earth? I mean if gravitation causes moon to fall faster each second (10m/s2) shouldn't after time velocity toward earth be big enough to cause it to fall ?

• Certainly this is a duplicate of some other question! – David Hammen Sep 10 '14 at 19:45
• Possible duplicates: physics.stackexchange.com/q/9049/2451 and links therein. – Qmechanic Sep 10 '14 at 19:48
• The value of g (10m/s2) doesn't apply to the moon, since that is Earth's surface gravity. It's about 1000 times smaller when you are as far away as the moon. – richardb Sep 10 '14 at 20:25
• XKCD's related explanation: "To avoid falling...into the atmosphere, you have to go sideways really, really fast." – Reinstate Monica Sep 10 '14 at 20:40

## 2 Answers

It can be said that the tangential speed of the moon in its orbit is represented by a vector that is constant in magnitude, but not so his direction. This variation of the vector direction (always remains tangent to lunar orbit), is actually a change in velocity, and therefore acceleration.

Why the moon does not fall on the ground? Simplifying to a circular orbit, the centripetal force acting on the moon's is the gravitational force, while by the movement itself, a centrifugal force that keeps the system in balance, is generated.

• You could also explain that the gravitational force isn't so much pulling the moon to the earth as stopping the moon from flinging itself off into space. – PipperChip Sep 10 '14 at 19:20
• @PipperChip Yes! It's a very good point of view! Tanks for your comment... ! – Martin Petrei Sep 10 '14 at 19:23

Acceleration can change velocity in two ways - by changing its magnitude, and by changing its direction.

Essentially, Earth's gravity is constantly steering the moon around the Earth.

Your initial premise - "If moon travels with constant speed in one direction" - is incorrect. The moon's direction is constantly being changed by the gravitational acceleration.