On 'gravity & its energy.'

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On 'gravity & its energy.'

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1guido47
Mar 3, 2013, 6:05 am

Hi group,

Just watched a doco. on Io and its volcanoes, by Brian Green.

Io's volcanoes apparently come from Jupitors (and others) gravitational forces.

Sorry if this is '101', but since "energy is neither created nor destroyed", what is the other side of the equation? We can see/appreciate the energy in Io's "volcanoes" etc.

But what gets "balanced" on the 'other' side of the equation? I do understand that 'gravity' is a mystery, but are there any models/thoughts?

I guess that at my primative/elementary level of understanding (and does ALL understanding of physics, have to be, only through maths?)

I am probably looking for some sort of visual/simple model. And I must confess I DO dislike "simple models" for things like the Higgs field/particle etc.

Your, perplexed,

Guido.

2fredbacon
Modificato: Mar 3, 2013, 12:15 pm

Math definitely helps, but many things can be explained without it. However, a reasonable sounding narrative description can be misleading. That's where mathematics comes in, to quantitatively check your reasoning. Having said that, I'll try to explain "the other side of the equation" for you.

Basically, the way that Jupiter's gravity is heating the interior of Io is by converting the rotational energy of Io's spin into heat energy. To understand how this happens, let's first examine the special case when Io's spin exactly matches its orbit so that it always keeps the same face towards Jupiter (the way our Moon does with Earth). The center of mass of Io is on a stable orbit around Jupiter, but Io is a large moon, not every point within it is making an orbit around Jupiter which matches the orbit of its center of mass. The point on Io's surface which is furtherest away from Jupiter should be in a different orbit with a (slightly) longer orbital period. As a consequence, it is moving too fast for its position. So it wants to move further away from Jupiter (climbing into a higher orbit). The point on Io's surface closest to Jupiter has the opposite problem. It is moving too slowly for its position, so it wants to fall closer to Jupiter and away from Io's center. The result is that Io get stretched, ever so slightly, into a sort of egg shape with the long axis pointing along the radius connecting Io's center of mass with Jupiter's center of mass.

Okay, now that we've covered the situation where Io's rotation and orbital motion are matched so that the same side always faces Jupiter, let's consider what happens when Io is rotating faster.

Let's imagine the surface of Io (at its equator) to be like a clock face with Jupiter to always be in the six o'clock direction, its orbital motion to be towards the three o'clock direction and its rotational motion to be in a clockwise direction.

As Io spins on it's axis, a point on it surface at the equator moves from, say, the 12 o'clock position to the three o'clock position, then six, then nine and finally back to 12. As we saw in our first discussion, that point on the surface wants to be further away from Jupiter at the 12 o'clock position and closer at the six o'clock position. At the three and nine o'clock positions, both forces balance out because it is already in the correct orbit. So, if we were following the minute hand in its path, it would be stretched at 12, slowly relax to its normal length as it reached 3 o'clock. Stretch again as it came to the six o'clock position, relaxing again as it reached nine. It would go through this cycle with every turn around its axis.

Now, if you've ever taken a soft bit of metal and repeatedly bent it back and forth until it broke, you may have noticed that the metal was quite a bit warmer where the metal broke. The constant flexing caused internal friction within the metal as individual atoms moved past each other. The same thing is happening within Io. As Io spins on its axis, different portions of its body move up and down at different rates, generating internal friction. This friction generates heat.

Where does the energy come from? It's stolen from the energy due to Io's rotation on its axis. Kind of like when the friction of your car brakes convert the motion of your car into heat. As Io heats up internally, it loses rotational energy causing it to slow down its rotational rate. This continues until it eventually slows into the tidal locked position and the constant flexing stops.

This isn't a complete explanation. I didn't cover the exact mechanism for converting rotational energy into heat energy. I also didn't cover what happens to Io's orbit as it's spin around its axis slows.

So, did that make sense to you?

3Noisy
Mar 3, 2013, 1:44 pm

In other words, tides. Read the short story Neutron Star.

4DugsBooks
Mar 4, 2013, 8:14 pm

Some supplementary info {with pictures!}. Link to page quoted This is "Black Cat Studios" ,Ron Miller, who says he is an illustrator so I would corroborate the details. His The Art of Chesley Bonestell won a Hugo award however. Purty stuff!!

" It is also affected by the gravity of nearby moons Europa and Callisto, as though caught in a tug of war between those moons and Jupiter. These forces cause the surface of Io to rise and fall by as much as 100 meters (300 feet) in the 43 hours it takes to make a single orbit of Jupiter! This movement creates a huge amount of friction within the crust of the moon which in turn generates vast amounts of heat.

5guido47
Mar 5, 2013, 4:14 am

Thanks Fred and group. Great imagery, both 'mind images' and imagine pictures!

I guess I "sort of understood" the 'gravity induced' tides.
Thus there is energy displayed as light, sound etc. coming from gravity?

I guess my question is: Looking at the other side of the equation, is then "GRAVITY" diminished in the Universe. ie. The energy of Gravity becomes light. What is the cost? But since gravity is a property of the curvature of space/time...Oh and where do 'gravitons' (if they exist) fit into all this?

Getting more lost.

Guido.

6mart1n
Mar 5, 2013, 4:53 am

Gravity doesn't have energy to use up in the way that you're thinking, but you're right that it has to be coming from somewhere. In this case, it's kinetic energy - Io's spin will be diminishing over time. There may also be some reduction in the spin of Jupiter itself and of Io's velocity through space, though I'm no sure sure about those.

7guido47
Mar 5, 2013, 7:53 am

Gravity doesn't have energy to use up in the way that you're thinking,...

I guess that is the exact question I am thinking/wondering about.

Gravety = Energy.

What happens?

Sorry, again, if this is '101', but I really seem to be stuck on this point.

Guido.

8mart1n
Mar 5, 2013, 10:06 am

Short answer - gravity is not a form of energy!

Some forms of energy are:
Kinetic energy (i.e. the energy something has due to how fast it's moving)
Heat (the energy in something due to how fast its atoms are moving about)
Chemical energy (e.g. if you set fire to something then the chemicals in it transform into other chemicals; chemical energy is turned into heat energy in the process)

So, you can kind of think of energy as something "stored within" these things/their component particles.

Gravity is a phenomenon which causes a force to be exerted between two objects due to their mass; the greater the mass, the greater the force. Unfortunately (for the purposes of this explanation) it's due to the curvature of spacetime as explained by general relativity. So let's not go there, unless someone better at explaining things than me fancies a crack :-)

A further form of energy that you might be thinking of is potential energy. This is the energy something has due to (for our everyday purposes) its height above the centre of the earth. E.g. you drop an object from a height then it falls, losing potential energy which is turned in kinetic energy as it falls faster and faster.

Does this help at all?

9daschaich
Mar 9, 2013, 9:46 pm

First, thanks to fredbacon for a wonderfully clear explanation of tidal forces. I want to emphasize that general relativity made no appearance in that explanation: these tidal forces can be described in purely Newtonian terms (and, indeed, Newton discussed them in his Principia). Although general relativity does have some effects, I am confident these effects are negligible in this situation, and they should definitely be ignored until you are comfortable with the much simpler Newtonian picture.

Speaking of pictures, when I was a student I had a summer project producing animations to illustrate tidal forces for the Earth-Moon system. My employer seems to have abandoned his Web site before adding this project, so I went ahead and resurrected it here. There may well be errors, but I hope the animations and accompanying explanation and references will prove educational.

10fredbacon
Mar 10, 2013, 11:16 am

I did a little more research into the specifics of the Io system. As I should have realized, Io is already tidal locked to Jupiter. The way that the necessary body flexing occurs on Io is due to its elliptical orbit. The tidal effect is stronger, and thus creates more distortion, when Io is closer to Jupiter than when it is further away. Io's body thus stretches and relaxes (relatively speaking) as it orbits Jupiter. This means that the energy is being converted from Io's orbital energy into heat, not from rotational energy. Over time, this will tend to circularize Io's orbit. As it loses energy with each orbit, it is unable to climb further away from Jupiter to its maximum distance at apogee (which is just a fancy word for the point in its orbit when it is furthest from Jupiter). This loss of energy will continue until its orbit is circular, and the system reaches equilibrium. Without a change in orbital radius, the flexing stops. No energy is lost, so the orbit remains stable.

You would think that the orbit would have circularized by now, but there is a catch. Io and Europa are in a two to one orbital resonance. What does that mean? Io orbits Jupiter twice for every orbit that Europa makes. It just so happens that Io is furthest from Jupiter when it is closest to Europa. So while tidal heating is causing Io's orbit to decay, Europa is trying to pull Io into a higher orbit. Like pushing someone on a swing, every time Io passes Europa at apogee, it gets pulled slightly further away from Jupiter. But this means that it also pulls Europa slightly closer to Jupiter. So the orbital energy Io loses to tidal heating, it regains by stealing it from Europa's orbit.

There's a nice discussion of this at http://www.astro.washington.edu/users/smith/Astro150/Tutorials/TidalHeat/

11DugsBooks
Modificato: Mar 10, 2013, 3:40 pm

Thanks for the link fred. When I first read your post I thought of the explanations and illustrations I had read & seen of objects approaching a black hole - when the inverse square rule of gravity really comes into effect and objects are ripped apart by the difference in attraction of gravity across their mass.

12PaulFoley
Modificato: Mar 11, 2013, 6:56 am

apogee (which is just a fancy word for the point in its orbit when it is furthest from Jupiter)

Hmmm...it actually means furthest from Earth; the correct word for Jupiter {edit:} is apparently apozene :(

13Foretopman
Mar 10, 2013, 9:12 pm

Instead of figuring out the correct word for Jupiter, I prefer to use the general term for the point in any orbit farthest from the body being orbited: apoapsis.

14fredbacon
Mar 11, 2013, 7:48 am

Sorry. Physicist not an astronomer. Learn something new all the time.

15guido47
Mar 11, 2013, 8:56 am

Sorry #13, this the best I could get from the OED.

..................................
apo- prefix

repr. Gr. ἀπο- off, from, away; quite.

1.1 In compounds already formed in Gr., or others analogous to them.

2.2 In modern scientific words, not on Gr. analogies, with sense of ‘standing off or away from each other, detached, separate,’ as apo-carpous.

.............................

Now Tim, who does look at these sites, and is a classics scholar, might be able to help.

Guido.

PS. re. #8. Does a woundup spring count as potential energy?
If not is there any form of PE which isn't associated with a gravitational field?

I guess you can see where I'm going :-)

16daschaich
Mar 11, 2013, 3:05 pm

...is there any form of PE which isn't associated with a gravitational field?

Yes, though I can't see where you're going. This is a good explanation.

17al.vick
Mar 11, 2013, 3:16 pm

Yes, coiled springs count as potential energy.

18DugsBooks
Modificato: Mar 11, 2013, 7:32 pm

Yeah, I was posting in the SF topic section some time ago about The Windup Girl by Paolo Bacigalupi where springs are used as an energy source and the principals behind that...good or bad.

I remember reading in a Reader's Digest in the 1960's as a kid about the guy who invented the springs used on gas pump hoses today, where they spring out but require energy to overcome inertia and contract back. It said he was not a scientist but just banged some different metals together and came up with those properties..This as opposed to a screen door spring where it immediately contracts back. Just a thought that Paolo's concept was valid even though the image in my mind while reading the book was of elephants stomping on old bed springs. ;-)

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