# What imparts the linear motion or the tangential velocity to natural satellites like the moon to enable them to be in orbit around the earth?

From Newton's laws of motion & gravitation, it is clear that the force of gravitation provides the necessary centripetal force which acts along the line joining the centre of masses of the earth & the moon. However, from understanding Newton's orbit concept, an initial tangential linear velocity is needed so that the moon just manages to escape "falling in" to the earth, by moving tangentially. Since there is no friction in outer space, no further acceleration is needed but some initial velocity is needed. Where did it come from ? Also, what happens during high & low tides when the moon is closer & further to the earth ? How does it "fall off " & "get back" on its orbit ? And while we are on the topic, why does the moon , earth, etc spin on its axis?

## 1 Answer

The solar system is believed to be formed from coalescing material. As the material contracts, the tangential velocities are magnified, owing to conservation of angular momentum. Angular momentum is $$\mathbf{L} = \mathbf{r} \times m\mathbf{v}$$, so as the radius decreases, the tangential velocity rapidly increases to maintain the same $$\mathbf{L}$$. So small differences in the linear velocities of the original components resulted in relatively large linear velocities between the final bodies.

As for the effect of tides, the Wikipedia article on formation and evolution of the solar system covers this. Essentially, the Earth's moon is gradually receding from the Earth owing to tidal effects.

A somewhat analogous phenomenon happens when a bathtub is drained. Fill a bathtub with water. Once the water is very still, open the valve to drain the tub. A rotational flow will form near the water outlet. Where does the tangential linear velocity come from?