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Gravity & Energy Conservation

Southwind17

Philosopher
Joined
Sep 6, 2007
Messages
5,154
If a hypothetical body, say a meteorite, for example, floating slowly through space ventures within the gravitational pull of, say a planet (yes, I know it's always within the gravitational pull of the planet, but let's say the overriding pull of the planet over and above all other astral bodies) such that its course is diverted towards the planet, to which it then begins to accelerate, where and how does the energy transfer occur from the planet to the meteorite? Or, put another way, what (presumably potential) energy is "lost" from the planet?
 
Ignore meteorites for a minute, and think about, say, bricks.

You have a brick on a string. If you cut the string, the brick falls to the ground. The brick, now being on the ground, won't fall any more, even if you cut the string into tiny pieces.

It's lost gravitational potential energy with respect to the ground.
 
There is no loss or transfer of energy. Speaking classically, what happens is that both the meteoroid and the planet lose potential energy and gain the exact same amount of kinetic energy.
 
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Ignore meteorites for a minute, and think about, say, bricks.

You have a brick on a string. If you cut the string, the brick falls to the ground. The brick, now being on the ground, won't fall any more, even if you cut the string into tiny pieces.

It's lost gravitational potential energy with respect to the ground.

Yes, but the brick had to be raised from the ground in the first place, requiring energy exertion by the "raiser", a person, for example, who derives his energy from the Earth. In this scenario I can clearly understand where the energy "chain" starts and where it stops. The meteorite is completely different, because it does not acquire potential energy from the Earth, or if it does, how does it?
 
If a hypothetical body, say a meteorite, for example, floating slowly through space ventures within the gravitational pull of, say a planet (yes, I know it's always within the gravitational pull of the planet, but let's say the overriding pull of the planet over and above all other astral bodies) such that its course is diverted towards the planet, to which it then begins to accelerate, where and how does the energy transfer occur from the planet to the meteorite? Or, put another way, what (presumably potential) energy is "lost" from the planet?

You're misleading yourself here, I think, by insisting that each component of the system must have a portion of energy that belongs to itself and not to the other component(s) of the system. In reality, the system as a whole has a potential energy. Taking the highly simplified example of a universe containing only two bodies, the gravitational potential energy for the system as a whole is defined, but to suggest that one of those two bodies has GPE independent of the other is absurd. We commonly use the approximation that a light object in the Earth's gravitational field has a GPE of its own, but that approximation is based on the assumption that the mass of the Earth is so great that the mass of the smaller object is negligible by comparison.

In your example, remember that as the meteorite's course is diverted towards the planet, at the same time the planet's course is diverted towards the meteorite. Remember, also, that whether this represents an increase or a decrease in the kinetic energy of the planet depends entirely on your frame of reference; however, the sum of the changes in kinetic energies of the two bodies must be the same in all inertial frames of reference, because it's equal to the decrease in GPE of the system as a whole. Again, neither the planet nor the meteorite has GPE of its own independent of the other; it's the system as a whole that possesses GPE.

Dave
 
There is no loss or transfer of energy. Speaking classically, what happens is that both the meteoroid and the planet lose potential energy and gain the exact same amount of kinetic energy.

Unfortunately, for me this explanation raises more questions than it answers:

What potential energy are you referring to that both bodies lose, particularly the planet, who's seeming transfer of energy is more manifest? What is the physical effect on the planet of it losing this potential energy? Does it's gravitational force weaken, for example? I doubt it. Speaking classically, how, exactly, is the kinetic energy "gained", to use your word?
 
Unfortunately, for me this explanation raises more questions than it answers:

What potential energy are you referring to that both bodies lose, particularly the planet, who's seeming transfer of energy is more manifest? What is the physical effect on the planet of it losing this potential energy? Does it's gravitational force weaken, for example? I doubt it. Speaking classically, how, exactly, is the kinetic energy "gained", to use your word?
Think of it this way - you have a closed system with 2 bodies, e.g. a meteorite and the Earth. Thus the total energy in the system must be conserved.
Each body has a kinetic energy due to their movement.
Each body has a potential energy due to the gravity of the other body - see this Wikipedia article.
If one body approaches the other then it will gain kinetic energy (gravity will pull on it) and lose potential energy. The other body will also gain kinetic energy and lose potential energy. If one body is a meteorite and the other is the Earth then the meteorite will gain a lot of kinetic energy and lose a lot of potential energy. The Earth will gain a tiny bit of kinetic energy and lose an ever smaller bit of potential energy.
 
What is the physical effect on the planet of it losing this potential energy? Does it's gravitational force weaken, for example?

No - it gets stronger. Gravitation potential energy is always negative, and this makes it more negative.

It might help you to remember that the energy isn't stored in the planet and the comet. It's also stored in between and all around, in the gravitational field.
 
Speaking classically, how, exactly, is the kinetic energy "gained", to use your word?

F = G.M1.M2/R^2

F = MA, so A = F/M

V = integral A dT

KE = M.V^2/2

In words, the force of gravity accelerates the body, resulting in an increase of kinetic energy. It's trivially simple Newtonian mechanics. If you want to look at the mechanism of the gravitational interaction, on the other hand, classical physics won't cut it. Newtonian mechanics simply represents gravity as force at a distance.

Dave
 
If [...] a meteorite [...] floating slowly through space ventures within the gravitational pull of [...] a planet [...] such that its course is diverted towards the planet, to which it then begins to accelerate, where and how does the energy transfer occur from the planet to the meteorite? Or, put another way, what (presumably potential) energy is "lost" from the planet?

Why do you think that energy is transferred from the planet to the meteorite?

As the meteorite falls towards the planet, potential energy of the meterorite turns into kinetic energy of the meterorite. Or, in plain English, the meteorite gets closer to the planet and speeds up.
 
Why do you think that energy is transferred from the planet to the meteorite?

Because if the course of the meteorite is diverted, as I stated, then it must be because of an external influence, or force/energy, a little like billiard balls, but without the contact. Given the scenario I described such force/energy can only come from the neighbouring planet. Given the law of conservation of energy it must, intuitively, if not logically, therefore, be transferred from the planet to the meteorite. The meteorite gains kinetic energy, so the planet must lose some corresponding energy.
 
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Because if the course of the meteorite is diverted, as I stated, then it must be because of an external influence, or force/energy, a little like billiard balls, but without the contact. Given the scenario I described such force/energy can only come from the neighbouring planet. Given the law of conservation of energy it must, intuitively, if not logically, therefore, be transferred from the planet to the meteorite. The meteorite gains kinetic energy, so the planet must lose some corresponding energy.

Yes, but there are three available energy sources. Planet kinetic energy, meteorite kinetic energy, and gravitational potential energy. Two objects falling towards one another will both increase their kinetic energy; this is accompanied by a decrease in the gravitational potential energy.

Nothing mysterious about gravity here; if you put a + and a - charge near one another, they can accelerate towards one another (both increasing kinetic energy) at the expense of a decrease in the potential energy of the electrostatic fields between them. Ditto for two magnets, exchanging kinetic energy for potential energy of magnetic fields.
 
Because if the course of the meteorite is diverted, as I stated, then it must be because of an external influence, or force/energy, a little like billiard balls, but without the contact. Given the scenario I described such force/energy can only come from the neighbouring planet. Given the law of conservation of energy it must, intuitively, if not logically, therefore, be transferred from the planet to the meteorite. The meteorite gains kinetic energy, so the planet must lose some corresponding energy.

You could say that the force of gravity on the meteorite "comes from" the planet, but the force of gravity isn't the sort of thing that gets "used up". After pulling on the meteorite, increasing its speed, the planet's gravity is still around to pull on other things. What got "used up" in increasing the meteorite's speed was the height of the meteorite above the planet. Before, it was far from the planet; now, it's closer. That's why it makes sense to consider its speed as being one form of energy (kinetic) and its height as being another (potential). As one increases, the other decreases, and so the total energy remains the same.
 
What has been discussed here, as far as energy being converted from one form to another, is definitely true. However, there is usually more to it than that. Consider a Jupiter probe from Earth that uses Venus as a "slingshot" to increase it's velocity. In the cases so far, it would gain kinetic energy while falling into the gravity well of Venus, and then loose it again as it climbed out. Since it has farther to climb out (all the way to Jupiter) than it had going in (from Earth), it seems hardly worth the effort for what would, at most, be a simple change in direction during the fly-by.

The point is that Venus has kinetic energy of it's own, in it's orbit around the sun. The trick is to rob it of some of that energy, adding it to the probe, and thus very much increasing it's velocity, while minusculely retarding Venus in its path. In this case we have an actual transfer of energy from one body to another. This transfer also obviously occurs if any of the bodies collide, whether elastically or inelastically (or anything in between).

Another possibility can be seen by examining the earth-moon system. The moon is slowly increasing its distance from earth, thereby increasing it's potential energy. Where is that energy coming from? It happens that the equatorial bulge that the Earth maintains accelerates the moon periodically, asymmetrically. Its costs the earth some small angular energy and momentum to do so. Eventually the moon will be much farther away and the earth's day will be slowed until it synchronizes with the moon. Another example of energy transfer - remember that rotating masses also have a form of kinetic energy in proportion to their angular velocity squared, as well as whatever linear energy they have.

I heard someone speak above about the energy being distributed within the system. That is true, in the sense that separating bodies increases the potential energy between them, but energy is also intimately tied to mass (or inertia, linear or rotational) and so it is quite proper to speak of a mass having kinetic energy and potential energy with respect to another mass. Without mass neither exists (that is, potential and kinetic cannot; chemical, acoustic, nuclear, hydraulic, radiational, etc, etc certainly still do). However, k & p energy can only be measured from some arbitrary platform, and only then can numbers be assigned of energies to the masses in the system.
 
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BTW, the case on Mars (I just discovered today) is the opposite of what it is on Earth: the twin moons of Mars are decreasing their orbit radius continuously, for the same reason, but the forces act against the satellites rather than for them. Eventually each satellite will come within the Roche limit (a distance that depends on the densities of the bodies and the size of the primary) and tidal forces will tear it apart, and Mars will develop a ring system. This is a case where kinetic energy of revolution around Mars is being transferred to the rotational kinetic energy of Mars. See http://en.wikipedia.org/wiki/Roche_limit for info on the Roche Limit, and http://antwrp.gsfc.nasa.gov/apod/astropix.html for a beautiful picture of Phobos, including crater Stickney.
 
Three words: Newton's Third Law

The action-reaction pair of forces (loosely speaking "Earth acts on meteor" and "meteor acts on Earth") allows for each body (Earth & meteor) to lose PE and gain KE. The forces of interaction serve as the mechanism of this energy transfer or work.
 
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