Orbital Decay

[bcampdaddy]

If our moon is distancing itself from Earth due to the slowing of its orbital speed, why do our satellites burn on re-entry when their orbits decay?

[snailboy]

I’m interested to know where you heard/read that. If an object is in a stable orbit and slows down, it will be pulled in by the planet. It would have to speed up its orbit to be flung away.

[Tripler]

I’ve heard that too, that the moon moves one inch away from the earth every year.

As far as satellites and such: “Orbital Drag” is a factor. Many Low Earth Orbits LEOs are at the highest reaches of the atmosphere. The miniscule but repeated impact of atmospheric molecules induces a negative velocity on the orbiting craft, thus slowing it down, reducing it’s kinetic energy and thus a corresponding movement closer to the Earth.

The moon for all practical purposes is so friggin’ far away that it’s not affected by the atmosphere. I don’t have my college notes anymore, but it’s possible that the kinetic energy of the moon has just enough energy to be slipping away from the Earth.

Tripler
Either that, or the Man in the Moon is purposely piloting away from our planet.

[Tripler]

Oh, and I’ll submit this darned cool link from NASA that will let you real-time track satellites in orbit.

You’ll note that there are two distinct areas where the satellites (points of white) are: There’s a big band way the hell out there, on a more or less equatorial plane, and then there’s a “near earth” bunch, swarming over Earth like bees on flower garden.

The “way the hell out there” band are the geosynchronous satellites, that follow the rotation of the earth, “hovering” over one fixed point in the sky/on the globe. Their distance is way out there because their velocities are so slow. Atmospheric drag isn’t a problem with them.

It’s the ones closest to the globe that have problems with orbital decay–again, from atmospheric drag. They tend to get help to restore their orbits from firing small rockets or even piggyback rides from spacecraft or other satellites (I can’t think of any of the latter though . . .)

Tripler
That’s a fun link though. Play with it some. . .

[David_Simmons]

The moon is being pulled along in its orbit by the gravitation resulting from the earth’s tidal pull. This causes the moon to speed up slightly in its orbit but that speeding up results in the moon’s motion going off at a tangent to its present orbit. As a result the moon retreats slightly from the earth until its orbital distance and speed in orbit match for equilibrium. The result is that the increased kinetic energy of the moon from the tidal pull is being converted to potential energy by moving the moon away from the earth against the pull of gravity. This happens on an incremental basis. That is, the moon is speeded up continually by little teeny increments of velocity. This results in little teeny incremental motions away from the earth. The process goes on all of the time.

The moon’s gravitation pulls the earth into a slightly oval shape with two very small tidal bulges one pointing toward the moon and another on the side of the earth opposite the moon. Because of friction as the earth rotates, these tidal bulges are slightly displaced from a precise line from earth to moon with the bulge on the side of the earth facing the moon being slightly advanced. Since this bulge is closer to the moon than the bulge on the opposite side of earth it exerts a stronger gravitational pull on the moon and thus pulls it along in its orbit and speeds it up slightly.

The burning up of artificial satellites as their orbits decay is an entirely different animal. Their orbits decay because they are traveling in a thin atmosphere and they burn up because the enter the thicker atmosphere at high speed and the friction with the atmosphere heats them to incandescence. Like a meteor.

[KP]

If our moon is distancing itself from Earth due to the slowing of its orbital speed…

Short answer: it isn’t. End of problem.

Longer answer: the moon’s orbit is very noticeably eccentric–i.e. it’s an ellipse with a long (major) and short (minor) axis. Where a circle has one center, the ellipse has two points which have some of the properties of a center, and are called foci. The eccentricity is defined as the ratio between the distance between foci and the major axis, but you can probably envision it this way. Let’s call the place where the major and minor axes cross “the centroid” – the middle of the ellipse, much like the center of a circle is the middle of a circle. If the focus is 1/10th of the way from the centroid to the ellipse, teh eccentricity is 0.1, if it’s 1/4th of the way out, the eccentricity is .25, etc.

The higher the eccentricity, the more “squished” or “stretched” the shape of the ellipse is. The “high point” (maximum altitude or distance from the parent) of an orbit is called the apogee, the lowest point (minimum altitude or distance) is called the perigee.

Let’s compare two orbits with the same apogee (maximum altitude) as the moon (roughly 250,000 miles): one with an eccentricity of .999999 (with a perigee of 1320 feet) and one with an eccentricity of 0 (a circular orbit with a perigee of 250,000 miles). Which has the higher energy? The one with the higher eccentricity. The easiest way to toss a ball to the altitude of the moon is to throw it straight up, but then it will come crashing down to exactly the same spot - a perigee (we’re talking about a hypothetical, not the actual Earth-moon system) The highest energy orbital with that apogeee is a circle. If you add any energy to an object in circular orbit, the object MUST rise farther at some point than it was before, and will tehrefore no longer have the same apogee as the moon.

A higher eccentricity orbit allows a higher apogee with less energy. In other words, energy can be considered, crudely, as a cumulative function of how high an object is, and how long it stays that high. Straight up-and-down minimizes the time at larger altitudes, while a circular orbit maximizes it.

As the Moon loses energy, its orbit may become more eccentric, and its apogee can become higher – but it’s perigee will be lower), and its average distance (over time) will be less. Alternately, it’s orbit could become rounder, with a lower apogee and a higher perigee, and an average over time that is still less than it was.

I don’t know where you got the idea that the Moon is growing farther from the Earth (care to prove a cite?), but unless some other body were pulling the Moon from the Earth (none is), the average distance will decrease over time, not increase. The apogee may increase, the perigee may increase, but never both together, and whichever one increases, the other will dcrease enough to more than make up for it.

I’m fairly certain that the apogee is decreasing andf the perigee is increasing. Why? Well, in very crude terms: the earth and the moon are actually orbiting each other (equal and opposite reaction) and the Earth is losing energy due to the sloshing of the tides caused by lunar gravity. If the Earth’s orbit were becoming more eccentric, the sloshing of tides would become even more dramatic [between the highest and lowest tides) but if the orbit becomes more circular, the sloshing will become more uniform and regular. I think that tyou can see, intuitively, that the system is going totry to dcrease the sloshing. (This crude analogy could be dangerous if applied indiscriminately, but it gives the right image in this case)

Since the Earth’s orbit is becoming “rounder” (more regular) and the Earth and Moon co-orbit, the Moon’s orbit is becoming rounder, too. The moon doesn’t go as far from the Earth as it did a thousand or million years ago, but it doesn’t come as close either. The differences are small, but definite. The average orbital distance is decreasing as the Earth-Moon system loses energy… and the Moon is Falling.

[Stranger_On_A_Train]

@snailboy

I’m interested to know where you heard/read that. If an object is in a stable orbit and slows down, it will be pulled in by the planet. It would have to speed up its orbit to be flung away.

As recalled from a lecture in Orbital Mechanics: “In orbital ballistics, you speed up to slow down. You slow down to speed up. I’m sorry; that’s just the way it is.”

When you fall into a lower orbit, your velocity (radial and angular) speed up in order to maintain the same kinetic energy. When you go to a lower orbit, you slow down for the same reason.

David Simmons and KP both provide more extensive, if slightly contradictory, explainations of the specifics of the situation. The truth is that the moon is moving further away, and the earth’s rotation is slowing to provide the energy for it to do so. At some point, barring a Space: 1999 style disaster in which the moon flings off to explore the universe, the earth and moon will come to equilibrium with the earth and moon tidally locked to each other and rotating about a common center of mass (which will reside well beneath the earth’s surface, making it appear as if the moon is just going 'round the earth.) See this site from Case-Western for a fairly simple explaination.

Stranger

[Stranger_On_A_Train]

@Stranger On A Train

When you fall into a lower orbit, your velocity (radial and angular) speed up in order to maintain the same kinetic energy. When you go to a lower orbit, you slow down for the same reason.

:smack: tangential and angular. Your radial velocity varies with your proximity to the locus of your (elliptical) orbit. (For a circular orbit, it is zero.)

Stranger

[David_Simmons]

@KP

Short answer: it isn’t. End of problem.

…

… The average orbital distance is decreasing as the Earth-Moon system loses energy… and the Moon is Falling.

Sorry, you’re mistaken.

Stranger has provided one cite. Here are some more.

From Britannica “… Tidal friction slows the Earth’s rotation, but the angular momentum of the Earth-Moon system remains constant. Consequently, the Moon is slowly receding from the Earth, with the result that the month and the day are both getting longer. Extending this relationship back into the past, both periods must have been significantly shorter hundreds of millionsof years ago, and this hypothesis is confirmed by measuring the diurnal andtide-related growth rings of fossil corals.”

And also from this site. “The Moon is receding from Earth about 1.6km every 28,000 years due to the complex gravitational interactions with the Earth. If this rate continues, the Moon from Earth will appear 15 percent smaller in about one billion years.”

[David_Simmons]

By the way becampdaddy did you by any chance come to this question by visiting Science Against Evolution?

If so, forget everything you read on that site. He doesn’t have the slightest idea what he is talking about.

[Lumpy]

Does anyone know how far from the Earth you have to be before the few atoms you encounter stop being predominantly nitrogen & oxygen, and start becoming primarily hydrogen & helium?

[Stranger_On_A_Train]

@Lumpy

Does anyone know how far from the Earth you have to be before the few atoms you encounter stop being predominantly nitrogen & oxygen, and start becoming primarily hydrogen & helium?

IANA planetologist, but that’s a hard question to answer precisely. Here’s a simple answer. For the most part, hydrogen and helium in the superstratosphere (is that the proper term?) isn’t really in orbit per se, but rather in constant exchange between “loose” gas and outgassing from the atmosphere.

There is a point, or rather a boundary, in which the mean atmosphere of solar space and of Earth come to an equilbrium between gravity, pressure of solar wind, and pressure of Earth’s atmosphere, but I’d imagine it is kind of a twisted teardrop shape (the tail pointing away from the sun) rather than a nice spherical boundary.

Stranger

[Chronos]

Quoth KP:

Which has the higher energy? The one with the higher eccentricity.

I’m pretty sure you meant that the other way around. For two objects in orbit with the same apogee (furthest point), the one with the lower eccentricity has more energy.

And as others have said, while the Earth-Moon system is (very slowly) losing energy, that energy is coming from the rotation of the Earth slowing. Eventually, of course, the Earth and Moon would become tidally locked, and after that point, any further energy loss (by what mechanism I don’t know, since tides would then be fixed) would have to result in the Moon getting closer. But the timescale for the former is huge (longer than the lifespan of the Sun), so it’s not something to worry about.

[bcampdaddy]

@KP

Short answer: it isn’t. End of problem.

Longer answer: the moon’s orbit is very noticeably eccentric–i.e. it’s an ellipse with a long (major) and short (minor) axis. Where a circle has one center, the ellipse has two points which have some of the properties of a center, and are called foci. The eccentricity is defined as the ratio between the distance between foci and the major axis, but you can probably envision it this way. Let’s call the place where the major and minor axes cross “the centroid” – the middle of the ellipse, much like the center of a circle is the middle of a circle. If the focus is 1/10th of the way from the centroid to the ellipse, teh eccentricity is 0.1, if it’s 1/4th of the way out, the eccentricity is .25, etc.

The higher the eccentricity, the more “squished” or “stretched” the shape of the ellipse is. The “high point” (maximum altitude or distance from the parent) of an orbit is called the apogee, the lowest point (minimum altitude or distance) is called the perigee.

Let’s compare two orbits with the same apogee (maximum altitude) as the moon (roughly 250,000 miles): one with an eccentricity of .999999 (with a perigee of 1320 feet) and one with an eccentricity of 0 (a circular orbit with a perigee of 250,000 miles). Which has the higher energy? The one with the higher eccentricity. The easiest way to toss a ball to the altitude of the moon is to throw it straight up, but then it will come crashing down to exactly the same spot - a perigee (we’re talking about a hypothetical, not the actual Earth-moon system) The highest energy orbital with that apogeee is a circle. If you add any energy to an object in circular orbit, the object MUST rise farther at some point than it was before, and will tehrefore no longer have the same apogee as the moon.

A higher eccentricity orbit allows a higher apogee with less energy. In other words, energy can be considered, crudely, as a cumulative function of how high an object is, and how long it stays that high. Straight up-and-down minimizes the time at larger altitudes, while a circular orbit maximizes it.

As the Moon loses energy, its orbit may become more eccentric, and its apogee can become higher – but it’s perigee will be lower), and its average distance (over time) will be less. Alternately, it’s orbit could become rounder, with a lower apogee and a higher perigee, and an average over time that is still less than it was.

I don’t know where you got the idea that the Moon is growing farther from the Earth (care to prove a cite?), but unless some other body were pulling the Moon from the Earth (none is), the average distance will decrease over time, not increase. The apogee may increase, the perigee may increase, but never both together, and whichever one increases, the other will dcrease enough to more than make up for it.

I’m fairly certain that the apogee is decreasing andf the perigee is increasing. Why? Well, in very crude terms: the earth and the moon are actually orbiting each other (equal and opposite reaction) and the Earth is losing energy due to the sloshing of the tides caused by lunar gravity. If the Earth’s orbit were becoming more eccentric, the sloshing of tides would become even more dramatic [between the highest and lowest tides) but if the orbit becomes more circular, the sloshing will become more uniform and regular. I think that tyou can see, intuitively, that the system is going totry to dcrease the sloshing. (This crude analogy could be dangerous if applied indiscriminately, but it gives the right image in this case)

Since the Earth’s orbit is becoming “rounder” (more regular) and the Earth and Moon co-orbit, the Moon’s orbit is becoming rounder, too. The moon doesn’t go as far from the Earth as it did a thousand or million years ago, but it doesn’t come as close either. The differences are small, but definite. The average orbital distance is decreasing as the Earth-Moon system loses energy… and the Moon is Falling.

KP – We hardly have the space available to teach you basic planetology. Please pull out any scientific journal and see the fact thT the Moon is, in fact, steadily increasing its distance from Earth. This fact makes the rest of your lengthy explanation laughable. Serious question – Uninformed answer.

[bcampdaddy]

@KP

Short answer: it isn’t. End of problem.

Longer answer: the moon’s orbit is very noticeably eccentric–i.e. it’s an ellipse with a long (major) and short (minor) axis. Where a circle has one center, the ellipse has two points which have some of the properties of a center, and are called foci. The eccentricity is defined as the ratio between the distance between foci and the major axis, but you can probably envision it this way. Let’s call the place where the major and minor axes cross “the centroid” – the middle of the ellipse, much like the center of a circle is the middle of a circle. If the focus is 1/10th of the way from the centroid to the ellipse, teh eccentricity is 0.1, if it’s 1/4th of the way out, the eccentricity is .25, etc.

The higher the eccentricity, the more “squished” or “stretched” the shape of the ellipse is. The “high point” (maximum altitude or distance from the parent) of an orbit is called the apogee, the lowest point (minimum altitude or distance) is called the perigee.

Let’s compare two orbits with the same apogee (maximum altitude) as the moon (roughly 250,000 miles): one with an eccentricity of .999999 (with a perigee of 1320 feet) and one with an eccentricity of 0 (a circular orbit with a perigee of 250,000 miles). Which has the higher energy? The one with the higher eccentricity. The easiest way to toss a ball to the altitude of the moon is to throw it straight up, but then it will come crashing down to exactly the same spot - a perigee (we’re talking about a hypothetical, not the actual Earth-moon system) The highest energy orbital with that apogeee is a circle. If you add any energy to an object in circular orbit, the object MUST rise farther at some point than it was before, and will tehrefore no longer have the same apogee as the moon.

A higher eccentricity orbit allows a higher apogee with less energy. In other words, energy can be considered, crudely, as a cumulative function of how high an object is, and how long it stays that high. Straight up-and-down minimizes the time at larger altitudes, while a circular orbit maximizes it.

As the Moon loses energy, its orbit may become more eccentric, and its apogee can become higher – but it’s perigee will be lower), and its average distance (over time) will be less. Alternately, it’s orbit could become rounder, with a lower apogee and a higher perigee, and an average over time that is still less than it was.

I don’t know where you got the idea that the Moon is growing farther from the Earth (care to prove a cite?), but unless some other body were pulling the Moon from the Earth (none is), the average distance will decrease over time, not increase. The apogee may increase, the perigee may increase, but never both together, and whichever one increases, the other will dcrease enough to more than make up for it.

I’m fairly certain that the apogee is decreasing andf the perigee is increasing. Why? Well, in very crude terms: the earth and the moon are actually orbiting each other (equal and opposite reaction) and the Earth is losing energy due to the sloshing of the tides caused by lunar gravity. If the Earth’s orbit were becoming more eccentric, the sloshing of tides would become even more dramatic [between the highest and lowest tides) but if the orbit becomes more circular, the sloshing will become more uniform and regular. I think that tyou can see, intuitively, that the system is going totry to dcrease the sloshing. (This crude analogy could be dangerous if applied indiscriminately, but it gives the right image in this case)

Since the Earth’s orbit is becoming “rounder” (more regular) and the Earth and Moon co-orbit, the Moon’s orbit is becoming rounder, too. The moon doesn’t go as far from the Earth as it did a thousand or million years ago, but it doesn’t come as close either. The differences are small, but definite. The average orbital distance is decreasing as the Earth-Moon system loses energy… and the Moon is Falling.

KP – We hardly have the space available to teach you basic planetology. Please pull out any scientific journal and see the fact that the Moon is, in fact, steadily increasing its distance from Earth. This fact makes the rest of your lengthy explanation laughable. Serious question – Uninformed answer.

[bcampdaddy]

@snailboy

I’m interested to know where you heard/read that. If an object is in a stable orbit and slows down, it will be pulled in by the planet. It would have to speed up its orbit to be flung away.

Snailboy – You are right – My question is in error. The moon’s orbital speed is increasing because of the effect of the faster rotating Earth – That effect ‘pulls’ the moon faster, resulting in an increase of orbital distance per Keppler’s Laws. My bad.
B.C.

[bcampdaddy]

@David Simmons

The moon is being pulled along in its orbit by the gravitation resulting from the earth’s tidal pull. This causes the moon to speed up slightly in its orbit but that speeding up results in the moon’s motion going off at a tangent to its present orbit. As a result the moon retreats slightly from the earth until its orbital distance and speed in orbit match for equilibrium. The result is that the increased kinetic energy of the moon from the tidal pull is being converted to potential energy by moving the moon away from the earth against the pull of gravity. This happens on an incremental basis. That is, the moon is speeded up continually by little teeny increments of velocity. This results in little teeny incremental motions away from the earth. The process goes on all of the time.

The moon’s gravitation pulls the earth into a slightly oval shape with two very small tidal bulges one pointing toward the moon and another on the side of the earth opposite the moon. Because of friction as the earth rotates, these tidal bulges are slightly displaced from a precise line from earth to moon with the bulge on the side of the earth facing the moon being slightly advanced. Since this bulge is closer to the moon than the bulge on the opposite side of earth it exerts a stronger gravitational pull on the moon and thus pulls it along in its orbit and speeds it up slightly.

The burning up of artificial satellites as their orbits decay is an entirely different animal. Their orbits decay because they are traveling in a thin atmosphere and they burn up because the enter the thicker atmosphere at high speed and the friction with the atmosphere heats them to incandescence. Like a meteor.

Mr. David Simmons – You are 100% correct. My question was wrong. My bad.

[butler1850]

@Tripler

Oh, and I’ll submit this darned cool link from NASA that will let you real-time track satellites in orbit.

You’ll note that there are two distinct areas where the satellites (points of white) are: There’s a big band way the hell out there, on a more or less equatorial plane, and then there’s a “near earth” bunch, swarming over Earth like bees on flower garden.

The “way the hell out there” band are the geosynchronous satellites, that follow the rotation of the earth, “hovering” over one fixed point in the sky/on the globe. Their distance is way out there because their velocities are so slow. Atmospheric drag isn’t a problem with them.

<nitpick>

Geosyncronous satellites are moving much FASTER than those in LEO. </nitpick>

They appear over the same spot on earth due to the fact that one revolution “around” it, takes 24 hours. The same time it takes for the same spot to rotate once “under” it.

-Butler

[Whack-a-Mole]

@butler1850

<nitpick>

Geosyncronous satellites are moving much FASTER than those in LEO. </nitpick>

Ok…this constitutes a hijack maybe but clearing this up can be relevant to the OP so here it is.

One more time for the dopes among us (of which I think I lead the pack as I have asked this and still did not get a firm grasp on it)…

Do you speed up or slow down to go into a higher orbit?

Here is a link to the thread where I asked this once before: http://boards.straightdope.com/sdmb/showthread.php?t=189796 The following quotes are from that link:

Originally posted by Podkayne:
It’s a lovely little paradox, isn’t it? If you’re confused by it, you’re in good company. The Gemini astronauts ran smack-dab into this problem during their first attempt at an orbital rendevous. The object was ahead of them, so they tried to speed up to catch it . . . but burning their rockets moved them into a higher, and therefore slower, orbit, so they fell further behind. After quite a bit of consternation, they realized that what they had to do was turn around and fire their rockets the other way, to fall into a lower, faster orbit, get a bit ahead of the target, then return to a higher, slower orbit and drop back toward it.

The way I keep it straight in my mind is by not thinking in terms of orbital speed, but orbital energy. The higher the orbit, the higher its energy. So to get to a higher orbit, you need to do a burn that intuition would tell you would make you go faster, but really it’s just increasing your orbital energy.

Originally posted by Chronos:
Suppose you start off in a circular orbit, with radius 1 AU (a fair approximation to the Earth’s orbit). If you decrease your orbital speed suddenly, you’ll go into an elliptical orbit, with apihelion distance (furthest distance from the Sun) of 1 AU. At apihelion, you’ll be going slower than you were originally… But as you fall closer to the Sun, you’ll lose potential energy and therefore gain kinetic energy. When you hit perihelion (closest approach to the Sun), your speed will actually be greater than it was in the original circular orbit. Now, suppose that when you’re at perihelion, you again suddenly decrease your speed by the right amount. Now, you’ll be in a lower circular orbit, with a speed greater than your original speed.

In other words, if Vc1 is your speed in your original circular orbit, Ve1 is the speed of your elliptical orbit at apihelion, Ve2 is the speed of your elliptical orbit at perihelion, and Vc2 is the speed of your new, lower circular orbit, then Ve2 > Vc2 > Vc1 > Ve1 .

But back to the original question, if you’ve got some continuous drag acting on your orbit, rather than sudden changes of speed, your orbit will gradually get lower and faster.

So, from this I have lower orbit = faster orbit but higher orbit = more energy yet slower orbit. But above it is being said higher orbit = faster orbit.

Color me confused…

Say I am in orbit around the earth and I have two baseballs. I throw one ahead of me (in the direction I am orbiting) and one behind me. In effect I have sped up the ball going forward and slowed the ball down that I threw behind me (relative to me at least). Which ball goes into a higher orbit and which goes lower? (Hopefully the effect of losing the mass of the two balls I threw is too small to consider how my orbital mechanics have changed but if it is important of course include it).

[David_Simmons]

A satellite in orbit 100 miles above the surface circles the earth in about 1-1/4 hours so its orbital speed is about 10200 mph. A satellite in geosynchronous orbit is about 22000 miles above the surface and circles once in 24 hours at about 3150 mph.