Context.

**This **is the scenario we have been discussing:

When an object enters the gravity of a star from outside its sphere of influence at a certain angle, it gains speed and then can be thrown out.

...

I was just giving a scenario where an object may gain sufficient speed to escape the gravitational field.

These statements are incorrect.

Specifically:

1] Since the body entered the well from outside, it

**already** has all the energy it needs to exit the well.

2] And gets

**no more**. (because if were to gain energy, it would leave faster than it came in, wrt the central body).

The gravitational-potential energy is

**converted **to kinetic energy on the in-fall, and then converted

**back **to g-potential energy again on the outfall, with no gain or loss in energy.

3] Thus, the object does not "

**gain** sufficient speed to escape". It already

**had **it. It was never in danger of

*not* escaping.

4] Finally, the

**angle **doesn't matter. As long as it does not

*actually *intersect the central mass, it

**will** follow the hyperbolic trajectory ,

*regardless* of angle of entry.