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So just a thought experiment: I take my rocket and fly through space. Meanwhile I pick up some piece of debris that experiences no (big) gravitational pull. I attach it with an infinitely long rope to a turbine connected to my spaceship. If the rope gets pulled, energy will be created for my spaceship. I take the debris, and place it close enough to a planet for it to be pulled downwards. The debris falls, the rope pulls, the turbine rotates, the ship gets energy.

Now, I might miss something obvious, but where does that energy come from if "energy can not be created, only converted". Of course the debris loses potential energy when falling, but where did that energy come from? It only got it when it entered the orbit?

My first explanation would be a small loss of mass of the planet pulling, but that doesn't seem right either.

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  • $\begingroup$ When you "place" your chunk of debris so that it will fall toward the planet, what stops your ship from falling along side of it? $\endgroup$
    – Ohm's Lawman
    Commented May 6 at 16:13
  • $\begingroup$ @Ohm'sLawman Thrusters, or simply flying the debris significantly closer... It doesn't really matter here, the important part is the debris suddenly falling, what happens to the ship doesn't matter as much $\endgroup$
    – TheBest_Kappa
    Commented May 6 at 22:52
  • $\begingroup$ FYI: A turbine is a machine that harvests energy from a flowing fluid. You probably want to pay out the rope from a winch. $\endgroup$
    – Ohm's Lawman
    Commented May 7 at 13:51

2 Answers 2

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In the case with the planet, the potential energy gained is negative. Or if you like, the falling object ends in a lower potential energy state than it started, and this energy is converted to kinetic energy which you can harvest. Your falling rock turning a turbine is equivalent to water turning a turbine in a hydroelectric dam, as it falls from a higher to lower elevation.

In your first example, energy is actually being stolen from your ship. Your ship's kinetic energy is being transferred to the passing rock by the rope, speeding it up and slowing your ship down by some amount. If this pulling action happens in a way that pulls on a turbine and starts it spinning, that rotational kinetic energy of the turbine was pulled from the translational kinetic energy of your ship, slowing it down.

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  • $\begingroup$ thanks, but I still don't understand how the rock has any potential energy to begin with as it was not in any gravitational field at the start of the interaction. Is potential energy just something things have, even in the absence of gravity around them? Or do you mean the planet loses the potential energy, which would lead me to believe that mass (since it exerts gravity) automatically has some potential energy to "offer" $\endgroup$
    – TheBest_Kappa
    Commented May 5 at 23:59
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    $\begingroup$ @TheBest_Kappa The debris has potential energy in the fact that it's very "high up" in relation to the surface of that planet. It's the same way a book has potential energy for being on the top of a shelf - it doesn't matter how it got there it just matters that it's there. In that way everything in space has "potential energy" relative to other massive objects. $\endgroup$
    – Señor O
    Commented May 6 at 0:05
  • $\begingroup$ @SeñorO so every object in the universe has potential energy relative to any other object that exists? Meaning that earth has potential energy in relation to a star in another galaxy? $\endgroup$
    – TheBest_Kappa
    Commented May 6 at 0:07
  • $\begingroup$ @TheBest_Kappa yes it does. If the Earth were moved closer to the star in the other galaxy, it would lose potential energy and gain kinetic (though the change in potential energy would be very close to zero until Earth got within a solar system range distance to the star). This is the case because the range of the force or gravity is infinite, though it gets arbitrarily weak at large distances. $\endgroup$
    – RC_23
    Commented May 6 at 0:57
  • $\begingroup$ @RC_23 oh wow, that's so cool! Thank you for explaining it, really crazy to think about how everything is connected in many more ways than just space or time $\endgroup$
    – TheBest_Kappa
    Commented May 6 at 9:03
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I asked, "When you 'place' your chunk of debris so that it will fall toward the planet, what stops your ship from falling along side of it?"

You answered,

Thrusters,... It doesn't really matter here, the important part is the debris suddenly falling, what happens to the ship doesn't matter as much.

What happens to the ship is crucial. You are proposing to power a generator on-board the ship by paying out a rope that is attached to the falling rock. The amount energy available for you to harvest, $W$ (for "work",) depends on the tension, $T$.

$$W=\int{}T(x)\,dx$$

If you keep the tension constant throughout the process, then that simplifies to $W=Tx$ where $x$ is the length of rope that your ship lets out.

The point is, if $T=0$ (no tension), then $W=0$ (no energy.)

If your ship is not rigidly attached to the planet (e.g., by being docked to a very tall tower that stands on the planet) then the only way I can imagine for your ship to maintain that tension is by continuous use of thrust.

Also, you're going to have to spend some energy in order to change the trajectory of your space rock so that it heads toward the planet. I haven't taken the time to completely understand the situation, but I'll be surprised if the minimum amount of energy needed to work the thrusters throughout the whole process is any less than the amount of energy you can harvest from the falling rock.

Actually, you said,

Thrusters, or simply flying the debris significantly closer...

It's not at all clear what you mean by that. Flying the debris closer than what? Your ship is transporting the "debris" from somewhere. The debris is travelling along with your ship. If your ship does not fire its thrusters, then how is it ever going to move away from the debris?

The ship must move away from the debris in order for you to harvest any energy. $W=Tx$. If $x=0$ (no movement,) then $W=0$ (no energy available for harvest.)

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