I have heard it said many times that any type of friction of a body while in orbit, such as atmospheric or some other medium, will cause the orbit to steadily deteriorate and the body to spiral inward toward another gravitating body. Now, I figured that would be true for a body close to Earth, whose distance from the center of mass isn't that much greater than that of the radius of the body, but if the distance is much greater, wouldn't the body just begin to slow down and fall inward, but gain momentum while doing so, miss the other body by some degree, and then curve around and come back the same way?

That is what I was thinking about, so I took one of my gravitational orbit simulation programs and added a constant deceleration in the line of travel and a funny thing happened. What would otherwise have been a perfectly circular orbit becomes elliptical under these conditions, but when it comes back to the same point it started from (the furthest or closest distance), it regains the same distance and velocity it originally had when it began, and so it is stable, but the entire orbit will steadily precess. With a constant deceleration applied in the line of motion, the precession is opposite the line of travel of the orbit. With one that is proportional to the speed, the shape of the orbit changes, but there is no precession. And with a deceleration that varies with the square of the speed, the orbit precesses in the same direction of the line of travel. Surprisely, it doesn't even matter how great an acceleration is applied. The orbit just becomes more elliptical.

So my question is, does anybody know anything about this, and what it is that would cause a body to spiral inward, which I hear so much about? Isn't something like this the reason that electrons are not believed to orbit, since they would spiral in as they lose energy? Also, I'm wondering if there might be some correlation to the precession of the planets and the deceleration of the Pioneer probes in this manner. Would anyone happen to know how fast they were travelling?

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"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."

If the object loses energy continuously to friction (which it does), it can't regain the same altitude with the same velocity after one orbit, because that would indicate that it has lost no energy.
So from that alone it seems there must be something wrong with your simulation.

Grant Hutchison

Thanks, Grant. I thought about that, too. The simulation comes out right for the planets (and binary star systems) when considering only gravity. All I changed were two lines, where I determined how the vectors of speed changed due to the acceleration of gravity, in the x and y directions over very small intervals of time. It already had that figured in for gravity, so I just subtracted a*vx/v in the x direction and a*vy/v in the y, applying some constant deceleration for a. I then tried just a*vx and a*vy for a deceleration that varies with speed, and a*vx*v and a*vy*v for variation with the square of the speed. That is all. Of course, a in the last two cases would have units that are inverse to time, a'=a/v, and distance, a'=a/v^2.

With such a simple deviation to the program, I don't see right away where it would be in error. It actually works similar to the way I would have thought it to, except for the precession, which I didn't expect. It's similar to the slingshot effect, I think. I always wondered where the energy came from for that as well. It seems contrary to intuition that it should keep that extra energy. For a body in orbit, friction would cause the body to decelerate and fall inward, but the body would actually gain momentum as it does so, causing it to "fall" past the gravitating body even faster than it otherwise would have, apparently producing a sort of slingshot effect of its own. It eventually slows down and comes back in the same way, according to the program, and very little or no deterioration of the orbit is observed (none can be determined for the preciseness I can get it), but only a precession of the orbit.

__________________
Let's put together the pieces of The Grand Puzzle . (website)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."

Grant. Agreed, and the idea that electrons exist in circular orbits, as Bohr imagined, was very soon after modified by Sommerfeld to include elliptical ones, but the planetary model reigns supreme there. Scrodingers wave equation gives a more realistic view.

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A third rate theory forbids
A second rate theory explains after the fact
A first rate theory predicts...A. Lomonosov

It sounds like the deceleration is not constant, but applied at
the apoapsis or some other point in the orbit.

Electrons can't orbit because the force on them from Earth's magnetic
field is far stronger than the force of Earth's gravity.

-- Jeff, in Minneapolis

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"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

Thanks, trinitree. According to the simulation, if the electron consistently loses energy, the orbit does become elliptical. But apparently, the only way its orbit can deteriorate and the electron fall into the nucleus is if all of its speed relative to the nucleus is lost at once, so it falls straight in. Even then, however, any magnetic field the nucleus might contain would tend to accelerate the electron in a direction perpendicular to its line of travel in the meantime, so it still would not fall directly in, but probably deviate in such a way that it would effectively regain an orbit.

__________________
Let's put together the pieces of The Grand Puzzle . (website)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."

grav,

I see now that you apparently wrote or modified the program yourself,
so my comment may not be applicable.

I also see from trinitree's post that you may have been talking about
electrons "orbiting" in atoms, in which case my comment is definitely
not applicable.

For a rather superficial intro to how objects in orbit behave, see my
webpage on orbital speed:

http://www.freemars.org/jeff/speed/

The little animation shows a satellite being slowed down each time
it passes close to the Earth, so that the orbit becomes progressively
less elliptical. As it is slowed more and more, it actually moves
faster and faster!

-- Jeff, in Minneapolis

__________________
http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

The deceleration is applied consistently to the body throughout the entire orbit.

Sorry about the confusion there. My reference to electrons was meant for those within atoms.

[EDIT-Oh, looks like you already caught that, and thanks for the link.]

__________________
Let's put together the pieces of The Grand Puzzle . (website)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."

Your link shows the orbit becoming more and more circular as it enters the Earth's atmosphere and then rapidly decaying. My simulation is very simple and it does not demonstrate this. I'm wondering if that may be because I am applying a constant deceleration to the orbitting body, while the deceleration due to the atmosphere would obviously increase as one approaches Earth. I want to apply that to my simulation. How would atmospheric drag increase with proximity to the Earth? Would it be approximately proportional to the inverse of the distance from the center of the Earth?

__________________
Let's put together the pieces of The Grand Puzzle . (website)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."

Is it possible that the reason your simulation isn't behaving the way we think it ought to behave .... is a sign error? If you add some acceleration in the x-direction of the form vx/x, and if your simulation places the origin at the center of the massive body, then you might be decelerating the object for half its orbit, then accelerating it for the other half, causing zero net effect on the total energy.

Just a guess. I've done similar things in the past :-/

Simply put:

If it is behaving as you claim, the simulation is not simulating the conditions you believe it to be. A steady deceleration will create a spiraling in effect, rather than the one you describe, as it continuously loses energy and drops in altitude to make up for it. My bet is that you made a small error (like the kind I make about once a minute ) that caused zero net effect, possibly the one that stupendousman described.

Thanks very much, everyone. When I was readjusting the perimeters for a deceleration that varies with the distance, I noticed the variables were out of place, just as Grant and the rest of you were saying. Thanks for correcting me on that. As simple as my couple of lines were to add in, I still managed to screw it up somehow, placing them in the lines for distance instead of velocity. I'm going to have to stop staying up late at night working on this stuff, I guess. My eyes must tend to go buggy or something. In a way, it worked out for the good, though. I now have a program for precession, although it does not show how that precession is produced. I had found before that precession acts as if the body just travels some extra distance per orbit, which remains a constant regardless of the distance from the gravitating body. Now I can experiment with it.

Anyway, to make up for asking about this in the first place, although I'm glad I did, I'll rerun the programs, correctly this time, and post the results here if anyone is interested. The one I ran for a deceleration that varies with distance shows a steady deterioration of the orbit, spiralling inward at a faster and faster speed, although the orbit remains basically circular. Maybe I can eventually drum up some calculations based upon the program as well. Thanks again.

__________________
Let's put together the pieces of The Grand Puzzle . (website)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."

Well, I've rerun the programs. For a deceleration that is proportional to 1/d^n and/or v^n, where n is an integer equal to or greater than zero, an originally circular orbit deteriorates faster with greater n, and remains circular. Nothing too interesting about that, I guess. For a deceleration in proportion to d^n and/or 1/v^n, the orbit seems to converge upon some tighter orbit and slow. It doesn't converge very quickly, however, so it's difficult to tell if it remains there or continues to decay at an ever slower rate. Beginning with an ellipse, a deceleration that varies with 1/d remains elliptical in about the same proportion. An originally elliptical orbit with a deceleration that varies with v/d or v^2/d, though, becomes more and more circular as it decays.

Um, one more question. Does friction drag vary with v or v^2? I've looked it up, but haven't found too much. One site seems to say that it varies with Dv, though, where D is the density of the medium.

__________________
Let's put together the pieces of The Grand Puzzle . (website)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."

It is directly proportional to the density of the fluid, and proportional to the velocity squared. It is also directly proportional to the frontal area. That doesn't exactly work in extreme cases like this (where the object's velocity is much higher than the average particle speed in the fluid), but will give a decent estimation.

If the Earth's atmosphere were simple throughout, the density and therefore the drag at any given speed would increase about tenfold for every ten miles of descent. This is a characteristic of any gravitationally bound atmosphere. We derived the formula in college physics but unfortunately I cannot remember the exact math technique after 40 years. It is an exponential function of the elevation from the ground, not from the center. The spiraling in would be slow at first but would increase catastrophically as the satellite dropped below about 100 miles.

My father observed this experimentally while tracking satellites for the Navy Department during times of sunspot minimum. During solar max the upper atmosphere puffed up and all bets were off. At low altitudes, say up to 100 miles there was not much change, but at altitudes of about 500 miles the air density increased by a factor of close to 1000 over that of solar min, and satellites that otherwise would have stayed up forever started spiraling in during solar max.

The normal exponential decrease of drag with higher elevation makes the drag on a highly elliptical orbit insignificant except around perigee. The satellite can blast through that bad zone a few times, but the loss of energy means it rises to a lower apogee each time, while the perigee does not change much. Thus it decays into a low circular orbit before spiraling in.

Is this "faster and faster" the result of the gravtational potential being converted to kinetic energy?

If the orbit is lower, but faster, then gravitational potential is lost to kinetic energy because of the lowering of altitude.

Orbits are fascinating but I have never studied them.

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My invisible elf ??? Why he is made of dark matter and lives off of dark energy !!!
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Thank you again, cjl. That will be very useful.

__________________
Let's put together the pieces of The Grand Puzzle . (website)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."

Now this is very interesting indeed. I replaced 1/d with 10^(d/10^9), where d is originally about 10^10, in order to gain the same initial deceleration for the original speed and distance, so I could compare rates of deterioration of each orbit with that of the first, but the result for this was VERY surprising. I had expected the orbit to decay at an exponential rate or something. It did not. For an originally elliptical orbit, beginning at the perigee, the orbit rises to a smaller apogee each time, with about the same difference between successive orbits, but the perigee remains almost precisely the same. Of cource, the slower rate of decay would be because any distance greater than that of the perigee observes a resistance that is exponentially less. This continues until the orbit becomes circular, but once the distance at the apogee drops below the distance to the perigee, the resistance becomes exponentially greater there, and the entire orbit quickly falls inward and strikes the Earth.

Now, all of this seems fine so far, the same as what Jeff Root has demonstrated. But a very strange thing happens if you take the Earth away (or consider it a point mass). Everything proceeds as stated before, but with nothing to fall directly to and strike, what will happen? Will the orbit continue to spiral inward? No. Will it barely miss the point mass and get slingshot away? No. Will it get slingshot back into a larger orbit and start the whole process over again? No. What does seem to happen is that the orbitting object begins to fall almost directly toward the center, but then begins to slow down dramatically until it comes to an almost complete stop, and then begins to orbit in place! I don't understand this yet. The new orbit is extremely tight, so I can't even see it (I'll have to enlarge the parameters), but the "number of orbits" counter keeps ticking, very rapidly at this point. If there is nothing wrong with the program this time, then this might tell us something very important. It could explain some things about atoms. Perhaps the electrons do not orbit, except when they are initially being captured, but eventually just begin to oscillate in place. Something similar should also happen with black holes. I'll keep working with it and see what it shows. If anybody else knows anything about this, please let me know.

__________________
Let's put together the pieces of The Grand Puzzle . (website)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."