The moon and loosing mass to earth

[alan2here]

According to this:

 

If the moon got too close to the earth, some mass would fall off into the earth. Iv'e been thinking about orbits as being somewhat to do with chance, things in non less stable orbits fell into or away from the things they were orbiting long ago and every orbit today is just a spiral.

 

However does this mean that there is some relationship reguarding distance and orbit appart from the obvious?

 

I'm thinking that if the moon gradually got closer and lost some of it's rocks to earth then it would become lighter it's orbit size would then increase again.

Edited February 27, 2012 by alan2here

[ajb]

The moon is moving away from us at the rate of 3.78cm (1.48in) per year. This is understood in terms of the tidal bungle and energy conservation (if I recall right).

[swansont]

According to this:

 

If the moon got too close to the earth, some mass would fall off into the earth. Iv'e been thinking about orbits as being somewhat to do with chance, things in non less stable orbits fell into or away from the things they were orbiting long ago and every orbit today is just a spiral.

 

However does this mean that there is some relationship reguarding distance and orbit appart from the obvious?

 

I'm thinking that if the moon gradually got closer and lost some of it's rocks to earth then it would become lighter it's orbit size would then increase again.

 

The moon would tend to fall apart as it did this, and the rocks would also be in orbit so they wouldn't fall into the earth. The orbit size can only change if there is some kind of energy and angular momentum transfer. Currently the moon is receding from us as the video states.

[alan2here]

So the moons orbit is expanding anyway. But if a similar body exists around a larger one that wasn't, the loss of mass wouldn't cause the orbit to expand but would have no effect on the orbits size.

Edited February 27, 2012 by alan2here

[D H]

According to this: [youtube link elided; it's already in two posts] If the moon got too close to the earth, some mass would fall off into the earth.

That video was alluding to something called the Roche limit (wikipedia: http://en.wikipedia.org/wiki/Roche_limit) and in the extreme case of a black hole, something called spaghettification (wikipedia: http://en.wikipedia.org/wiki/Spaghettification). These tidal forces are exactly what broke Comet Shoemaker–Levy 9 into pieces a couple of years before it collided with Jupiter.

 

Iv'e been thinking about orbits as being somewhat to do with chance, things in non less stable orbits fell into or away from the things they were orbiting long ago and every orbit today is just a spiral.

Orbits aren't spirals. They are better looked at as perturbed ellipses. This Star Trek notion of unstable orbits is bad sci-fi nonsense. If you want to study orbits, you should start with understanding Keplerian orbits and then work your way up the ladder of complexity.

[MigL]

I would have to disagree Swansont. Since the moon is quite large compared to earth, it would experience tidal forces, ie greater on the close face compared to the far face, while all of its fragments would be moving at the same orbital speed. So a lot of the closer fragmenys would sppiral to earth and a lot of the farther fragments would spiral out or even escape (?).

But maybe the portion closer to the moon's centre of mass would form some nice rings.

[D H]

So a lot of the closer fragmenys would sppiral to earth and a lot of the farther fragments would spiral out or even escape (?).

Spiral in, how? Ignoring relativistic effects, gravitation alone does not make things "spiral".

 

The Roche limit for the Moon is between 2.5 and 3.0 Earth radii. Using the 2.5 Earth radiui value, those fragments closest to the Earth would be in a 1450×7800 km orbit (perigee altitude by apogee altitude). Those furthest from the Earth, a 11300×31200 km orbit. The outer ones wouldn't even get to geosynchronous altitude. Those inner ones would eventually collide with the Earth due to atmospheric drag, but it would take a long time. At 3 Earth radii, that 1450 km becomes 4150 km, meaning it would take a long, long time for atmospheric drag to have any kind of effect at all.

[MigL]

Last time I checked, a decaying orbit is a spiral.

The moon's centre of gravity is in a somewhat stable orbit at a given orbital speed. If you break apart the moon such that there is little cohesion between the pieces, then the close face fragments are closer by a moon radius than the centre of mass, but are not orbiting any faster than the centre of mass, By Newton's law then, those pieces are in a less stable orbit will experience a decaying orbit.

[D H]

What do you mean by "stable orbit"?

 

There's nothing magical about circular orbits. So long as an orbit lies well within the primary body's sphere of influence the object will remain bound to the primary. For example, the Earth's sphere of influence reaches out to the Sun-Earth L1 point, about 1.5 million kilometers from the Earth. Ignoring perturbations by the Moon, objects orbiting at 500,000 to 750,000 km or less will remain bound to the Earth. At periapsis (closest approach), so long as the orbit doesn't intersect the primary body or its atmosphere the orbit will remain stable.

 

Objects don't spiral into planets (or even into our Sun) due to gravitation. You have to look at a couple of very big objects orbiting very close to one another before you start seeing that happen.

[MigL]

At no time did I mention circular orbits.

But if you know your Kepler as you say, then you know that for any orbit there is a well defined orbital speed associated with the distance, whether we are talking circular elliptic or even parabolic orbits. Deviations from this relationship makes for unstable, ie not sustainable, orbits.

Or was Newton wrong ?

[D H]

But if you know your Kepler as you say, then you know that for any orbit there is a well defined orbital speed associated with the distance, whether we are talking circular elliptic or even parabolic orbits. Deviations from this relationship makes for unstable, ie not sustainable, orbits.

Or was Newton wrong ?

No!

 

Imagine some object, call it object A, orbiting some primary. Now imagine some other object, call it object B, at the same distance from the primary as object A with a velocity that differs from that of object A. Does this mean that this object B is an "unstable, or unsustainable, orbit"? Of course not. It just means that it is in a different orbit.

 

Pick up almost any text on orbital mechanics and it will go through excruciating detail on how to go from Keplerian elements to position and velocity, or from position and velocity to Keplerian elements. Any position, any velocity. There is no such thing as an unstable orbit in the Newtonian two body problem.

[MigL]

I know that a lower orbital speed will usually just drop you down into a lower orbit. But did you miss the part in the OP where the moon has moved a LOT closer to the earth and is torn apart by tidal forces ( wouldn;t be a day in the park for the earth either ) ? Do you know at what distance this would happen ? I don't. But I base my reasoning on observation of similar situations.

Have you seen pictures of Saturn's rings ? Have you ever wondered why there are no 'stragglers' below or above some very clearly defined orbits ?

Does your book on orbital mechanics explain that ?

Maybe my choice of words was wrong and I shouldn't have used unstable. But pick up a rock and throw it. It is now in an orbit. Unfortunately its orbit passes through the earth, ie IT HITS THE GROUND !

[alan2here]

Are you sure orbits due to gravity arn't spirals D H, or elliptical spirals.

 

The moons orbit for example is increasing in distance from the earth.

 

It's star trek that two bodies instead of being held together orbiting at exactly the same distance appart in an elliptical orbit are instead always just a very tight spiral?

Edited March 1, 2012 by alan2here

[Janus]

I know that a lower orbital speed will usually just drop you down into a lower orbit. But did you miss the part in the OP where the moon has moved a LOT closer to the earth and is torn apart by tidal forces ( wouldn;t be a day in the park for the earth either ) ? Do you know at what distance this would happen ?

 

 

He gave the distance in the post where he talked about the Roche Limit for the Moon. That is where the Moon is torn apart by tidal forces. As the video states, it is when the tidal forces overcome the gravity holding the object together. But note here its says "overcomes", not "eliminates completely". Even when the Moon reaches its Roche limit, the Moon's gravity will still be fighting to hold the Moon together.

 

Here's what I mean. Assume you are standing on the Moon with the Earth overhead as the Moon reaches the Roche limit given by DH above. Would you suddenly enter the elliptical orbit around the Earth as described? No, Because that orbit is for an object moving at that speed and altitude and not under the gravitational influence of a third body. But there is third body to consider, the remaining mass of the Moon. It is fighting to hold on to you, it may not win the battle in the end, but it certainly will influence what final orbit you will enter into.

 

It isn't like the Moon reaches the Roche limit and explodes into pieces throwing shrapnel in all directions. (note that in the Video the narrator only says that the Moon will be torn apart; he never says anything about parts of it hitting the Earth.)

[alan2here]

From the video I interpreted it more as because the earth has so much more mass than the moon then there would be a point, if the orbit of the moon was closer to the earth, where rocks on the surface of the moon fell downwards towards the earth instead of downwards towards the moon, causing the moon to loose mass. I didn't originally imagine that this lost mass would remain in orbit.

[Janus]

From the video I interpreted it more as because the earth has so much more mass than the moon then there would be a point, if the orbit of the moon was closer to the earth, where rocks on the surface of the moon fell downwards towards the earth instead of downwards towards the moon, causing the moon to loose mass. I didn't originally imagine that this lost mass would remain in orbit.

 

It more of a matter of reaching a point where the gravity of the Moon is unable to prevent those rocks from entering their own independent orbit around the Earth.

[MigL]

Appreciate your imput Janus.

I guess if you are also of the opinion that none of the disintgrating moon's pieces will impact the Earth, then my thinking must be at fault and I obviously need to re-examine the situation.

[Ophiolite]

Appreciate your imput Janus.

I guess if you are also of the opinion that none of the disintgrating moon's pieces will impact the Earth, then my thinking must be at fault and I obviously need to re-examine the situation.

We probably have to modify the none to few. Perturbations could arise form one or more of the following:

Collision between objects

Atmospheric drag

Influence of other system bodies

[MigL]

Well atmospheric drag was my thinking also but the Roche limit given by D.H. is well beyond the atmosphere.

 

I still don't uderstand why the rings of Saturn have such a well defined inner and outer orbit. They are attributed to a fragmenting satellite, but their density is almost constant from inner to outer circumference, with none of the decrease in density and straggler particles you would expect from a chaotic event, almost as if they had been swept clean by some effect.