system
Given the following post, respond as if you're commenting on Reddit:
human
If Potential always equals Kinetic, how do space probes use planets to gain speed?

Wouldn't all of the kinetic energy and speed it gains from getting close to (or "falling" into) the object be lost by trying to escape the gravitational field as well?
gpt
No, the total potential energy of a single object at its apex only equals the total kinetic energy of that object at it's low point *if* the rest of the system remains unchanged. But if the rest of the system absorbs some energy, then its the total energy of the whole system, and not just of the object, that remains constant.

With respect to space probes near planets, this means that the total potential energy of the probe at its apex only equals the total kinetic energy of that object at the low point, if the planet is approximated to be infinitely heavy so that the planet experiences zero acceleration and absorbs and looses zero kinetic energy. This approximation is useful because planets are so heavy compared to space probes, but is not strictly true. In reality, a planet has finite mass and therefore is affected by the space probe in addition to space probe being affected by the planet. It is really a two-body problem. It is the total energy of planet+space probe that stays constant, and not just the total energy of the probe. In short, the space probe gains net energy because the planet looses that same energy. A planet has so much energy that this little loss of energy has a very small effect on its overall orbital motion.