Why does kinetic energy become zero at infinity during escape?

[Rachana MN]

Why does a planet's kinetic energy become 0 when it reaches infinity? And why does a planet's kinetic energy get converted to gravitational potential energy when subjected under another planet's gravitational field?
Escape velocity seems very abstract to me!

 

[mfb]

Why does a planet's kinetic energy become 0 when it reaches infinity?

That is the definition of the escape velocity. If the kinetic energy is still positive then the object was faster than the escape velocity, if the object cannot reach infinity then it was slower.

And why does a planet's kinetic energy get converted to gravitational potential energy when subjected under another planet's gravitational field?

That's how the potential energy is defined: the possibility to get converted to kinetic energy.