Gravity and a moving Treadmill

[LM542]

I imagine gravity works similar to a treadmill and my question is based on the same assumption

Imagine a very very long treadmill with a person on it. The treadmill starts and the person moves to the right.
But the treadmill has wheels and drives faster to the left. The person now moves to the left despite being pulled back.

Question:
A spaceship flies at 12 o’clock and a fast and big planet is coming from 5 o’clock and heads to 10 o’clock.
The planet is faster than the pull of its gravity and if I apply the treadmill example, the spaceship should now accelerate like the person on the treadmill.

Is that possible or is it BS?

 

[jbriggs444]

I imagine gravity works similar to a treadmill and my question is based on the same assumption

The assumption is incorrect. Gravity does not resemble a treadmill. In particular, the speed of the hypothetical treadmill does not somehow correspond to a speed of gravity.

 

[rootone]

Gravity is equivalent to a continuous acceleration, not some given velocity.
However, about your space ship, yes that concept of using the gravitational field of a planet combined with it's orbital velocity does work and is used as a way to 'slingshot' long distance space probes at very high velocity while using a minimal amount of onboard engine propulsion.