Change in GPE and Ek as object approaches a planet

[Saado]

This is not a homework question.

Whilst looking over at previous exam papers on classical physics, I came across this question in the attachment. I always assumed gravitational potential energy increased as you moved further away from a mass. But the expected answer to this question shows the GPE increasing as the rocket gets closer to the planet. I'm assuming the increase in kinetic energy is due to the field strength of the planet but I can't get my head around why the magnitude of the potential energy is increasing instead of decreasing as the object moves closer to the planet.

 

[Nugatory]

The expected answer in the attached thumbnail shows the gravitational potential energy decreasing (slope of curve is negative) as the ship moves from A to D and then remaining constant. Where do you see anything increasing in that curve?

 

[Saado]

Oh I see my problem. I read the graph as the magnitude increasing but realized that's wrong. Thank you.

 

[Adithyan]

Only the magnitude is increasing; the negative sign before magnitude makes it decreasing.

 

[PJC01]

As an experienced scientist, I can offer some insight into this phenomenon. It is true that in most cases, gravitational potential energy decreases as an object moves closer to a planet. This is because the object is moving against the gravitational force and therefore the force is doing negative work, reducing the object's potential energy.

However, in this specific scenario, we must also consider the work done by the rocket's engines. As the rocket approaches the planet, its engines are firing, providing a force that is pushing against the gravitational force. This work done by the engines increases the object's kinetic energy, but it also increases the object's potential energy.

Think of it this way - as the rocket gets closer to the planet, the gravitational force increases, and therefore the engines must provide more work to counteract it. This additional work increases the object's potential energy, even as its kinetic energy also increases.

So, in summary, the increase in potential energy as the object approaches the planet is due to both the increasing strength of the gravitational force and the work done by the engines to counteract this force. It is a complex relationship, but it is important to consider both factors when analyzing changes in energy in a gravitational system.