Why Don't All Moons Orbit Retrograde?

[Elen Sila]

During the infancy of a planetary system, it usually consists of a young star, surrounded by a disc of spinning gas and dust. Eventually, turbulence in the disc results in the accumulation of clumps of matter, which over time grow into massive objects, which can eventually become planets, if they become so great as to achieve hydrostatic equilibrium and clear their orbits.

 

Now, early on, before the planetlets have come into their own as rulers of a Hill sphere, the matter passing by them in adjacent orbits would be travelling faster if closer to the primary, and slower if farther out; thus, from a corotating reference frame, outer dust particles should be moving backwards, and inner dust particles should be speeding ahead. So, logically, per the diagram below, matter should, as it is accreting to the orbiting object, be imparting retrograde angular momentum to the object.

 

Then, after the orbiting object has grown to the mass of a full-fledged planet, collisions and interactions with passing asteroids should destroy or eject all moons from the system, except those orbiting at approximately a certain ideal distance from the primary.

 

Thus, every planet should, 1, rotate retrograde, and 2, have only one or two large moons, both of which should, 3, orbit retrograde. So why are none of these three things true?

 

(In case you can't read my handwriting, here's a transcript of the diagram.)

 

FIGURE A – sidereal reference frame.

Inner dust particles move faster than the object.

Outer dust particles move slower.

 

FIGURE B – corotating reference frame.

Inner dust particles pass ahead of the object.

Outer dust particles fall behind the object.

 

FIGURE C.

Accreting particles impart retrograde angular momentum to the object.

 

FIGURE D – after the planet has grown more massive.

Objects orbiting the planet closer to the planet move faster than objects orbiting the planet farther out; but objects orbiting the star closer to the planet move slower' date=' relative to the planet, than objects orbiting the star farther from the planet.

 

Inset 1. Close to the planet, fast-moving moons collide with slow-moving asteroids, lose their orbital velocity, and break up under the tidal forces of the planet.

Inset 2. Farther out from the planet, slow-moving moons are struck from behind by fast-moving asteroids, which fling them out of the planet's orbit.

Inset 3. Midway out from the planet, moons and asteroids are moving at approximately the same speeds. They rarely impact each other, instead tending to accumulate in orbit until one gravitationally dominates, sucking up or flinging out the other moons from the system.[/quote']

[Janus]

You have to take into account the effect of the material moving outward or inward with respect to the planet's gravitational field and the effect that this has on the material's orbital velocity as it approaches the moon's orbit.

 

As the moon accumulates mass via gravitational collapse, it begins to draw in mass from higher and lower orbits. But when it draws in an object from a higher orbit, that object has to lose potential energy with respect to the planet, and has to increase its kinetic energy and thus its speed, to compensate. By the time it reaches the orbit of the Moon is will be moving faster than the orbital velocity of the moon.

 

Going from the other direction, pulling the object from lower orbit causes it to gain potential energy and lose kinetic energy speed, and it will be moving slower than the moon.

 

Thus material coming in from the planet side is moving slower and material coming in from the other side is moving faster. This tends to give the forming moon a pro-grade rotation.

[Elen Sila]

As the moon accumulates mass via gravitational collapse, it begins to draw in mass from higher and lower orbits. But when it draws in an object from a higher orbit, that object has to lose potential energy with respect to the planet, and has to increase its kinetic energy and thus its speed, to compensate. By the time it reaches the orbit of the Moon is will be moving faster than the orbital velocity of the moon.

 

Why don't the moons always fall into the planet, as they lose kinetic energy to head-on collisions with dust particles, micrometeors, and asteroids? Is it because the angular momentum they steal from their primary's rotation makes up for it? Shouldn't one force or the other dominate the interaction, causing all moons to either break up or fly off, given enough time?

[TonyMcC]

I was surprised when I heard that the moon is increasing its distance from the earth by more than 3cm per year. The link sets out to explain why. http://curious.astro.cornell.edu/question.php?number=124

[Janus]

Why don't the moons always fall into the planet, as they lose kinetic energy to head-on collisions with dust particles, micrometeors, and asteroids? Is it because the angular momentum they steal from their primary's rotation makes up for it? Shouldn't one force or the other dominate the interaction, causing all moons to either break up or fly off, given enough time?

 

What makes you think that all those collisions are head-on? Just look at our own Moon, are all the craters on its leading side?. Some collisions come from bodies traveling in the same direction as the moon and actually add orbital energy.

 

During the early stages of formation there were likely a great many more collisions and some of those might have resulted in a moon getting too close to the planet or being ejected. But you have to remember, in order to be ejected from orbit the moon would have to increase its velocity by over 40%. ( For our own Moon that would work out to be around 400 m/sec)

Conversely, for our Moon to lose enough orbital speed to crash into the Earth it would have to lose over 80% of its velocity. In addition, over time the moons and planets sweep their orbits clean of most of the debris. So any moons left over after the initial dust up are pretty stable.

 

For example: Every day the Earth collides with some 100,000 kg of meteorites. Even if all of these robbed the Earth of orbital speed, is in significant to Earth mass. It would take trillions of years before this could reduce Earth's orbital velocity by even 1%

[Elen Sila]

What makes you think that all those collisions are head-on?

 

They don't all have to be, they just have to mostly be. Since head-on collisions would be statistically more common, the moon would have a net loss of angular momentum.

 

Just look at our own Moon, are all the craters on its leading side?

 

Our moon is a poor example, because it's so far out, and its orbital velocity is so low compared to the earth's (1.023 KPS versus 29.785 KPS), that it's actually usually moving approximately parallel to the earth around the sun, regardless of which way it's facing relative to the earth. Thus, it gets peppered on all sides roughly evenly.

 

A better example would be, say, Jupiter's moon Io (17.334 KPS), or Saturn's moon Mimas (14.323 KPS), which both move around their primaries faster than they move about the sun (13.068 KPS for Jupiter, and 9.689 KPS for Saturn).

Edited September 6, 2011 by Elen Sila

[Janus]

They don't all have to be, they just have to mostly be. Since head-on collisions would be statistically more common, the moon would have a net loss of angular momentum.

 

Based on what? Anything that come within the vicinity of the moon is subject to the same orbital mechanic as the moon. So you have four possibilities:

 

Objects that pretty much have the same orbit as the moon which will have very little velocity with respect to the moon and just will fall in on the moon due to its gravity. The moon will pull this stuff in equally from all directions and clear it out pretty quickly.

 

Objects in orbit around the Planet which cross the moon's orbit but have an average distance closer to the planet. These objects will be moving slower than the moon and will more likely collide with its leading edge.

 

Objects in orbit around the planet which cross the moon's orbit but have an average distance further from the planet. These objects will be moving slower that the moon and are more likely to hit from behind.

 

Of the last two, whether or not there are more of one that than the other depends on the Moon's own position in orbit. If it is near the planet, there will be more of the later and it will get hit from behind more often, pushing to a higher orbit. If it in a high orbit, there will be more of the former which will push it into a lower orbit. Generally the action of these two will tend to move the planet towards a medium orbit. But as in the first case, these types of objects get cleared out fairly early on.

 

Last we have objects that come from outside the planetary system. All of these will have fallen through the planet's gravity and picked up quite a bit of speed.

 

They also fall into the first three categories as above with their orbits being with respect to the Sun. They will have various speeds and trajectories with respect to the planet and can hi the moon at any point of its orbit. A faster moving body coming from one direction is just as likely to hit the moon when it is on any side of the planet and add or subtract from the moon's velocity, the same can be said for a slower moving moving object. There is no strong statistical preference for one over the other.

 

You have to look at things from a orbital mechanical view.

 

 

Our moon is a poor example, because it's so far out, and its orbital velocity is so low compared to the earth's (1.023 KPS versus 29.785 KPS), that it's actually usually moving approximately parallel to the earth around the sun, regardless of which way it's facing relative to the earth. Thus, it gets peppered on all sides roughly evenly.

Look at any moon for which we have a picture that shows cratering. None of them show preferential cratering on their leading edge.

 

A better example would be, say, Jupiter's moon Io (17.334 KPS), or Saturn's moon Mimas (14.323 KPS), which both move around their primaries faster than they move about the sun (13.068 KPS for Jupiter, and 9.689 KPS for Saturn).

 

This would have nothing to do the likelyhood of direction of impact. Objects coming in from behind or from ahead of the Planet are just as like to pass inward of the planet as outward, and the moon is just as likely to be inward or outward of the planet during a collision.

 

What the orbital velocity of the Moon does determine is how much of a velocity change it would take to significantly change the orbit. For Io it would take a 7 km/sec change to kick it out of orbit and a 9 km/sec change to get it to fall in to Jupiter.

[Elen Sila]

Look at any moon for which we have a picture that shows cratering. None of them show preferential cratering on their leading edge.

 

I'm aware that my conclusions are wrong. I am asking for an explanation of why they are wrong.

 

Here were my two questions, originally, which I admit I did not enunciate very clearly.

1. Why do proto-planetary discs form in a prograde, rather than a retrograde, direction?

2. Once a prograde moon system has formed, why don't all of the moons fall into the planet due to head-on collisions with dust and rocks?

 

My understand of your initial response, in terms of its practical application, is that objects being gravitationally captured do not follow the simple curves I described in my diagram, but rather perform a sort of "zig-zag" manoeuvre, where their motion relative to the planet reverses direction as they approach, due to some switch involving kinetic and potential energy that I don't really understand. Far moons would thus generally be hit in the face, dropping them in orbit, while near moons would generally be hit from behind, raising them in orbit, and resulting in the equilibrium you described. Is this a correct description of the mechanism of gravitational capture?

 

Here's my attempt at a diagram.

It shows the actual path of captured objects, as described in this thread, in a bold line, and and the logical path of captured objects, as described in my diagram, in a dotted line.

 

If this diagram accurately expresses the system you've described, why does it work that way? What causes the reversal of direction?

[matterdoc]

"During the infancy of a planetary system, it usually consists of a young star, surrounded by a disc of spinning gas and dust. Eventually, turbulence in the disc results in the accumulation of clumps of matter, which over time grow into massive objects, which can eventually become planets, if they become so great as to achieve hydrostatic equilibrium and clear their orbits."

 

Try to visualize above scenario with the young star moving at definite speed, as it happens in a galaxy. Formation of planets as envisaged in 'Nebular hypothesis' will be an impossibility.

[Ophiolite]

"During the infancy of a planetary system, it usually consists of a young star, surrounded by a disc of spinning gas and dust. Eventually, turbulence in the disc results in the accumulation of clumps of matter, which over time grow into massive objects, which can eventually become planets, if they become so great as to achieve hydrostatic equilibrium and clear their orbits."

 

Try to visualize above scenario with the young star moving at definite speed, as it happens in a galaxy. Formation of planets as envisaged in 'Nebular hypothesis' will be an impossibility.

You seem to be hung up on the invalidity (alleged) of the nebular hypothesis. You have given absolutely no explanation of why the speed of the star is significant. The star and the accretion disc both condense from the same cloud and so their relative velocity is small. There is simply no problem. what do you think the problem is?

[baric]

Let's also keep in mind that there is only one mechanism known for moons forming around their host planet, and those planets are all giants. These planets are all large enough to gravitationally disrupt the protoplanetary disk as they pass through it, which may provide enough "breathing room" for their moons to form without as much disruption from the eddys leading and trailing the planet's orbit.

 

There are no known instances of smaller, terrestrial-sized planets forming moons as part of their development process, so the mechanism that the OP suggests could very well be playing a part in this.

[matterdoc]

You seem to be hung up on the invalidity (alleged) of the nebular hypothesis. You have given absolutely no explanation of why the speed of the star is significant. The star and the accretion disc both condense from the same cloud and so their relative velocity is small. There is simply no problem. what do you think the problem is?

 

May be my mechanics is stale. But I reason it as shown in the attached figure.

 

Figure shows the star at the centre and a planet being formed in the condensing part of accretion disc at certain distance from the star. Black arrows show linear speed of whole system. Red arrows show relative speed and blue arrows show resultant speeds of condensing part of gas.

 

If the star is static in space: the condensing part of accretion disc will move around the star at (say) constant angular speed and form into a planet. (We may ignore non-circular orbit, for the time being). This is the scenario envisaged in nebular hypothesis.

 

Let us now consider real status of the central star. The central star along with surrounding gas-disc, being a part of a rotating galaxy, moves at certain linear speed, V, along a circular path around the galactic centre. Linear motion is represented by black arrows. As seen from the figure, at different locations, relative to the star, the condensing part of accretion disc will have different resultant speeds, R. Irrespective of the magnitude of relative speeds, v, different resultant speeds will not suit a circular path around the central star at all. In fact, a planetary orbit will not form any type of closed geometrical path around its central star.

 

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