Gravity vs Conservation of energy

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Vahir
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Gravity vs Conservation of energy

Postby Vahir » Thu Nov 06, 2014 7:30 pm UTC

Does gravity contradict the first law of thermodynamics? I've been thinking about this for a while, and it seems to me that it does. Say you generate electricity through gravity (for example, through tidal power). Neglecting mechanical wearing, the generator will continue generating electricity essentially forever (assuming the moon doesn't disappear).

Objects in orbit stay in orbit because the attraction to the object constantly changes their course. Energy is thus expended for satellites to remain in orbit, and yet they would continue orbiting forever, in my understanding of physics.

How do these principles reconcile?

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Re: Gravity vs Conservation of energy

Postby brenok » Thu Nov 06, 2014 7:53 pm UTC

About tides, we have a topic about it on the forums. The energy comes from the rotation of the Earth.

About satellites, they orbit at roughly the same height, so they have constant gravitational potential energy, and constant kinetic energy. They might lose some of those by friction, but then they simply fall down. Mostly there isn't any necessary energy expenditure.

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Re: Gravity vs Conservation of energy

Postby stoppedcaring » Thu Nov 06, 2014 8:39 pm UTC

Nothing can orbit forever due to gravitational wave radiation. But even neglecting gravitational wave radiation, the important question in determining whether something violates conservation of energy is to compare the energy of the system at time t = 0 and its state at time t > 0.

Imagine a satellite orbiting in a perfect circle. At arbitrary time t = 0, it has a particular kinetic energy (determined by its speed) and a particular potential energy (determined by its height above the body it is orbiting). Now, at any time t > 0, it won't be in the same place, but it will still have the same speed and the same height, so it has the same total energy. No change in energy with respect to time means it hasn't violated conservation of energy. Just because something is moving -- even in a circle -- doesn't mean its total energy is changing.

In a satellite moving in an ellipse, the speed and height change, but increases in height are exactly matched by decreases in speed (and vice versa) so the total energy remains constant.

Similarly, a pendulum in a vacuum on a frictionless axle will continue to swing back and forth forever, because it keeps trading its potential and kinetic energy back and forth.

As was pointed out, the tides are sucking potential energy out of the Earth-Moon system, so that's not a free lunch either.

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Re: Gravity vs Conservation of energy

Postby Izawwlgood » Thu Nov 06, 2014 8:40 pm UTC

Not only do objects in orbit not orbit forever, but the tides are a fantastic example of how an orbit isn't a perfectly frictionless interaction ('friction' just meaning that energy is lost over time).

The energy you are extracting from tidal energy is, firstly, extracting a terribly minute amount of energy from a strikingly larger system, and secondly, extracting energy from a system that is not endless. Eventually the moon will be tidally locked, and the tides will cease.

Ask yourself, perhaps, why a solar panel isn't defying the laws of thermodynamics (a rough analogy, but not a perfect one). That energy is coming from somewhere, and is being spent at a given rate. That we're extracting useful work from it isn't really affecting it, but doesn't mean it's an infinite resource.
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Re: Gravity vs Conservation of energy

Postby stoppedcaring » Thu Nov 06, 2014 9:16 pm UTC

Izawwlgood wrote:The energy you are extracting from tidal energy is, firstly, extracting a terribly minute amount of energy from a strikingly larger system, and secondly, extracting energy from a system that is not endless. Eventually the moon will be tidally locked, and the tides will cease.

Eventually the Earth will be tidally locked to the moon. The moon is already tidally locked to the Earth.

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Izawwlgood
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Re: Gravity vs Conservation of energy

Postby Izawwlgood » Thu Nov 06, 2014 9:28 pm UTC

Disclaimer: I am a biologist. Much of what I wrote is probably incorrect, and based on nothing more than a mild obsession with KSP.
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Re: Gravity vs Conservation of energy

Postby stoppedcaring » Thu Nov 06, 2014 9:35 pm UTC

Izawwlgood wrote:Disclaimer: I am a biologist. Much of what I wrote is probably incorrect, and based on nothing more than a mild obsession with KSP.

Nah you got it right. Except for the direction of tidal locking, haha.

Another example of why tides don't violate conservation of energy...suppose a sentient, industrialized ant colony discovered a carousel at an amusement park. They observed that during the day, the carousel would spin up for a certain amount of time, then slow down, then repeat. Excited, they hooked up a tiny dynamo to the underside of the carousel and extracted dramatic amounts of energy every time it spun up, enough to power the lightbulbs of their entire colony.

Their scientists, however, were puzzled because the carousel didn't seem to go any slower when the dynamo was being used.

Of course this is just because the energy extracted via the dynamo is such a tiny fraction of the energy of the carousel that it's not noticeable. Likewise, energy extracted from tides are such a tiny fraction of the potential energy of the Earth-moon system that it's not noticeable.

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Re: Gravity vs Conservation of energy

Postby Frenetic Pony » Fri Nov 07, 2014 2:06 am UTC

brenok wrote:About tides, we have a topic about it on the forums. The energy comes from the rotation of the Earth.

About satellites, they orbit at roughly the same height, so they have constant gravitational potential energy, and constant kinetic energy. They might lose some of those by friction, but then they simply fall down. Mostly there isn't any necessary energy expenditure.


A great way to think about satellites (credits to Qi for the wording, fun show available free on youtube btw) and gravity/orbits in general, is that anything in a stable orbit is constantly "Falling". But it's "falling" into a circle around whatever its orbiting.

This also gives you an easy reasoning as to why you need to speed up, rather than slow down, to de-orbit. You are "falling" into the lowest energy configuration you can. So even if you want to get "closer" to the gravity well, you need to expend energy and speed up, even if you're going "down" the gravity well, because you were already at minimum considering your location and relative motion.

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Re: Gravity vs Conservation of energy

Postby gmalivuk » Fri Nov 07, 2014 2:24 am UTC

You need to expend energy, but you most certainly don't want to speed up if your plan is to de-orbit.
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Re: Gravity vs Conservation of energy

Postby Frenetic Pony » Sat Nov 08, 2014 10:03 am UTC

gmalivuk wrote:You need to expend energy, but you most certainly don't want to speed up if your plan is to de-orbit.


Err, oops! Yeah, derp.

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Re: Gravity vs Conservation of energy

Postby cjameshuff » Sun Nov 09, 2014 5:17 am UTC

gmalivuk wrote:You need to expend energy, but you most certainly don't want to speed up if your plan is to de-orbit.


You want to brake against your motion, but the result is that you do speed up...at least until you reach atmosphere. Start in a circular orbit and brake. You end up with an elliptical orbit with apoapsis at the location where you applied thrust to brake, and a lower velocity than the circular orbit had, but a periapsis on the far side of the orbit at lower altitude and higher velocity.

You can start out at the distance of the moon, lazily circling Earth at 1 km/s, decelerate by a few hundred m/s, and end up whipping around Earth at ~10 km/s. Or in the opposite direction, you accelerate to reach a high and slow orbit.

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Re: Gravity vs Conservation of energy

Postby gmalivuk » Sun Nov 09, 2014 5:30 am UTC

You end up going faster as a consequence, yes, but you still don't "need to speed up . . . [in order] to de-orbit", as that would imply that increasing your speed is what you do directly to start the process.
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Re: Gravity vs Conservation of energy

Postby Frenetic Pony » Sun Nov 09, 2014 11:08 am UTC

gmalivuk wrote:You end up going faster as a consequence, yes, but you still don't "need to speed up . . . [in order] to de-orbit", as that would imply that increasing your speed is what you do directly to start the process.


Ok ok, depending on where it is you are, and hopefully you're above the atmosphere enough to "speed up" at some point, and whether you're heading towards periapsis or apoapsis, and whether you apply thrust or counterthrust, tending towards escape or de-orbit (should there be a better word?) respectively, or maybe just evening out periapsis and apoapsis with respect to the radius from the center of the earth, or etc. etc. it depends on what you're doing when.

There, is everybody happy now? :P


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