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Gravity, Free energy, and proving my pet idiot wrong.

  1. Apr 17, 2012 #1
    I have a pet idiot, you know the type. "Perpetual motion is the future, we dont understand everything!"

    Well we've been discussing gravity, (and magnets, oh how he goes on about magnets).
    He doesnt seem to be able to see the difference between force and energy.
    I've finally gotten him to understand that an apple dropping from 1 meter and accelerating is not the creation of energy as energy had to be put in to get the apple to the height in the first place.

    What I cant explain to him is the following:

    A rock is traveling through space heading towards the planet Earth. Its traveling slowly relative to the earth, only about 50kph. As it's heading towards the earth, then eventually it encounters the earths gravity. It accelerates towards the earth and eventually impacts.
    When it impacts it's going much faster than 50kph. Does that additional velocity mean more energy, and if so where did it come from.

    Please dont let my idiot carry on like this. He's looking so smug right now, because I dont know the answer.
  2. jcsd
  3. Apr 17, 2012 #2


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    Why should it make a difference if it is a rock or an apple? Both just convert potential energy into kinetic energy. The fact that the rock wasn't "put up there" by humans, doesn't change the fact that it "always" had potential energy with respect to the Earths surface.

    So yes, we could potentially use rocks flying to us from space as an energy source. It has nothing to do with perpetual motion. I just don’t think it is practical.
  4. Apr 17, 2012 #3
    Here's a perpetual motion device for your opponent:

    Take a somewhat heavy, but small object. Attach it to a strong, but thin string, and hook the string to the ceiling. Deflect the body from the vertical and let it go. Voila! It's converting kinetic to potential energy indefinitely. If your adversary complains that it stops pretty quickly, just place the device in a vacuum sealed chamber.
  5. Apr 17, 2012 #4
    This is a typical example of conversation of energy. There is nothing wrong with it.
    Where K is kinetic, and P is potential energy. In Earth gravity field, P is proportional with distance of object from Earth, and K is proportional with velocity of object (squared). As the object falling, it’s potential energy is decreasing, so it’s kinetic energy must rising (so it’s velocity must be rising), so that final sum can be constant.
  6. Apr 18, 2012 #5
    Thanks guys. Gives me some ammo for him.

    Dumbing it down a little I'm going to hit him with the K+P=constant, and that gravity doesnt create energy, it converts it. Not that it will convince him of course.
  7. Apr 18, 2012 #6
    We don't know...some random collision, a supernova, ultimately the big bang. It doesn't matter. Every object in space has a certain potential energy compared to another object. Yeah you can capture that space rock and get energy out of it, but only once. If you want to keep going, you have to put it back up there.

    His question is akin to asking "where did the energy of the sun come from". Again, we might not know exactly what it's detailed history is, but the point is it's there NOW, and there's only so much of it before it runs out.

    If he asks where the energy for the big bang came from...well, I don't think we can answer that one yet.
  8. Apr 18, 2012 #7
    No, but your adversary is right. "Creating energy" always means converting one form of energy into another one, more accessible. We should be able to harness the final form for our purposes, as well as store and distribute it efficiently to consider the conversion process useful.

    In this respect, a meteorite falling on Earth is not something we can harness energy from. Furthermore, even if we did, we would have to have a constant supply of them, to consider them a viable energy source.

    Let us make the following order of magnitude estimate. The potential energy of a body falling from infinity towards the Sun decreases. If the initial velocity of the object (in the heliocentric reference frame ) was zero, then, its radial velocity at a distance r is:
    0 = \frac{m v'^2}{2} - \frac{G M m}{r} \Rightarrow v' = \sqrt{\frac{2 G M}{r}}
    But, the orbital speed of the Earth around the Sun is:
    \frac{G M}{r^2} = \frac{v^2_0}{r} \Rightarrow v_0 = \sqrt{\frac{G M}{r}}
    Thus, the speed of the body is [itex]\sqrt{2}[/itex] times bigger than the orbital speed of the Earth. However, the former is in the radial direction, whereas it is in the tangential direction for the latter. Thus, when we try to find the relative velocity of the body with respect to the Earth, we should use Pythagoras Theorem:
    v^2 = v'^2 + v^2_0 = 3 v^2_0

    The orbital parameters of the Earth are [itex]r = 1 \, \mathrm{AU} = 1.5 \times 10^{11} \, \mathrm{m}[/itex], and [itex]T = 1 \, \mathrm{y} = 3.2 \times 10^7 \, \mathrm{s}[/itex]. Thus, the orbital speed of the Earth is:
    v_0 = \frac{2\pi \, r}{T} = 2.9 \times 10^4 \, \mathrm{m}/\mathrm{s}
    Finally, the kinetic energy per unit mass of a meteor is:
    \frac{E_k}{m} = \frac{3 v^2_0}{2} = 1.3 \, \frac{\mathrm{GJ}}{\mathrm{kg}}
  9. Apr 18, 2012 #8
    This may seem as a large caloric value. And, indeed, it is. Compared to the energy of burning coal ([itex]24 \, \mathrm{MJ}/\mathrm{kg}[/itex]), it is 540 times higher!

    However, the abundance of falling meteorites is MANY times smaller than the abundance of coal.
  10. Apr 18, 2012 #9


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    With ~15000 tons of material per year (see here), falling stuff releases an energy of ~20 PJ per year or ~0.6 GW. That is equivalent to a small power plant. And most of the mass is distributed in dust particles, impossible to harvest.

    However, a small asteroid, caught in geostationary orbit, would have a potential of about 60MJ/kg. With ~1km^3 of rock (~2g/cm^3), you could get 10GW out of it for 400 years, using a space elevator.
    That is probably not efficient to use it as a power plant, but it is a lot of potential energy.
  11. Jun 20, 2012 #10
    Since your friend is an idiot and so am I, here is a very simple way to explain it.

    The earth and the passing asteroid actually move towards each other because they both have gravity and the total movement force is split equally between their two points. Only, the asteroid is much smaller than the earth so the same amount of force placed on the asteroid makes it accelerate much faster than the massive bulk of the earth, in fact due to the gravity of the sun, the earth barely moves at all.
  12. Jun 20, 2012 #11


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    An even better device: attach a strong but thin string to a somewhat heavy but small object. Swing the object about your head by the string and then hit your adversary on the head with it!

    If your adversary complains, put him in a vacuum sealed chamber!
  13. Jun 20, 2012 #12


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    This may be a good approach. Often PPMs use this idea of dropping weights. It works for things like Hydro-electric dams because the Earth's weather lifts the water vapour back up (raises the potential energy). It is harnessing energy from the sun, (which is providing the evaporative heating.)

    But it's harnessing unused energy, not a new source of energy.

    You may be able to get him to concede, if his devices make use of unused energy sources.

    For any system he comes up with, ask him how the material gets back up.
  14. Jun 20, 2012 #13
    "For a believer no proof is necessary, for a non-believer no proof is possible".

    I forget who.
  15. Jun 20, 2012 #14


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    I hope nobody smart, because it's wrong.

    I guarantee non-believers will become believers if presented with proof. You can prove a positive.
  16. Jun 21, 2012 #15


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    Even with a proof (which is just good evidence), you should not believe something in the religious sense (be 100% convinced). You should think of it as more likely.

    Edit @DaveC426913: In this case, I would assign some reasonable probability to dreams and drugs.
    Last edited: Jun 21, 2012
  17. Jun 21, 2012 #16


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    (Well, if a colossal mile-tall white-bearded old man appeared before my eyes, turning the clouds into fluffy, scampering bunnies, then waved his hand to cause the Moon to turn into a dove and fly down and land on his shoulder - I would believe. The burden would shift to skeptics to convince me that this is not God. :smile: )

    but this is waaay off-topic.
  18. Jun 21, 2012 #17
    While this is true about the earth's atmosphere, water vapor would also rise due to diffusion as long as the atmosphere was a gaseous system above 0 kelvins.
  19. Jun 21, 2012 #18


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    If it has to do with the movement and composition of the atmo, I would call it "weather". :smile:
  20. Jun 21, 2012 #19
    Sure, but my point is that solar energy isn't necessarily required to lift the water in the water cycle. ;)
  21. Jun 21, 2012 #20
    Is water vapor in sufficient concentration to condense into rain if it diffuses upwards in a gaseous atmosphere?
  22. Jun 21, 2012 #21
    That depends on partial pressure of the water vapor, absolute pressure and temperature. As long as there is a temperature gradient then there could be some point where the air would become supersaturated with water vapor, or at least it seems so to me. Weather is preeety complex.
  23. Jun 21, 2012 #22
    Temperature gradient implies heat flow. How can there be a (stationary) temperature gradient if there is no external heat source?
  24. Jun 21, 2012 #23


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    It is necessary. Without solar energy the Earth would cool down drastically, freezing the water and stopping pretty much all weather. As the Earth loses it's heat over time the temperature would finally approach that of the CMB, which is around 4 kelvin. Get out your mittens.
  25. Jun 21, 2012 #24
    Right, but diffusion can do work against a potential well as long as the medium is still a fluid.

    You got me there! Maybe the diminishing pressure of the atmosphere could be used to facilitate it? The atmosphere is very complex. In fact, many kilometers into the sky it becomes HOTTER. The thermosphere is estimated to be around 1000 celsius, but it is so thin that all thermometers still read closer to 0! The proper question to ask would be - how would earth look if it was suddenly encased in a 100% reflective, insulating bubble. The pressure gradient would still exist.
  26. Jun 22, 2012 #25
    How is this relevant to diffusing water vapor condensing back into liquid drops?!
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