The Moon who Fell to Earth?

[fuelair]

Fast high school version: Acceleration is a change in velocity (negative or positive). Velocity has a speed component and a direction component (that is, to fully state velocity you must have a speed `and a direction).

If the speed changes but the direction doesn't, you have a change in acceleration.

If the direction changes but the speed doesn't, you have a change in acceleration.

If the speed and the direction change, you have a change in acceleration.

In the case of an orbiting body it is constantly changing acceleration since it is constantly changing direction.

As a side note, to cause a change in direction or speed a force is needed. In the case of orbiting things that force is gravity.

Hope this helps!!

You might find it a great idea - if interested but not mathematically inclined - to pick up a used copy of Paul Hewitt's Conceptual Physics. It is a textbook that is marvelous at using examples and very little math to get over the important principles.



Edit to replace acceleration (wrong) with direction (right!!).

 

[Loss Leader]

I don't think the moon slowly gained mass as it picked up debris, in any case. The moon appears to have been formed through one sudden collision.

 

[fuelair]

Best immediate bet as basics, not wild constant updates...buy USED!!!: http://www.amazon.com/Conceptual-Ph...F8&qid=1402011424&sr=1-4&keywords=Paul+Hewitt

 

[BowlOfRed]

I don't think the moon slowly gained mass as it picked up debris, in any case. The moon appears to have been formed through one sudden collision.

I think the idea behind the question was that the collision didn't create a solid body suddenly. It created a debris field that took some time to coalesce into the moon. (Where "some time" means "much longer than one orbit").

 

[Molinaro]

As I zig-zag my way through city streets am I accelerating then, even though I'm walking at a constant speed (well trying!)?

If you are sitting in a car that goes around a sharp turn in the road and the car stays at 50km/h the whole time you feel the acceleration as you go around the corner. What you feel there, during the constant velocity and changing direction is exactly the same as what you feel during changing velocity and constant direction.

They are both acceleration.

 

[Reality Check]

As I zig-zag my way through city streets am I accelerating then, even though I'm walking at a constant speed (well trying!)?

Yes - every time you zig you apply a force to change direction, every time you zag you apply a force to change directions. And F=ma.

Also by definition a = dv/dt where a = the acceleration vector, v = the velocity vector (vectors have both magnitude and direction).

 

[xtifr]

(A spaceship so that it's engines can compensate for the effects of gravity.)

Argh, obviously I meant "its engines", not "it's engines". I do know the difference, but sometimes my fingers get ahead of my brain, and that's a hard typo to spot.

 

[Ziggurat]

I was aware of tidal acceleration, and having read the explanation the you link to, never fail to be fascinated by the physics and mechanics that come into play by the interaction of the Earth and the Moon.

It seems such a shame that the majority of people either aren't remotely aware of the effects of this interaction, other than knowing that the Moon generates tides, or don't care to understand it to any appreciable degree?!

If you like that, then you'll probably also like knowing that if the moon were orbiting much closer to earth (below geosynchronous orbit), then tidal forces would act to suck the moon towards us instead of push it away, eventually causing it to crash into earth. In fact, that's what's slowly happening to Phobos, one of the moons of mars. We won't live to see it crash, though: it's got an estimated 50 million years left. But that's not really very long by geological standards.

 

[Brian-M]

Hence the gravitational force of the collective particles is focused at a point (the centre of the Moon), thereby increasing its acceleration towards the earth, no?

No. Gravitational attraction is proportional to the product of the masses divided by the square of the distance.

The total mass hasn't changed, and the average distance hasn't changed, so why should gravitational attraction change?

Doesn't inertia increase with mass, hence the orbit increases too, or does the body slow down to compensate?

Twice the mass means twice the inertia resisting gravitational attraction and twice the gravitational attraction pulling at it. They cancel each-other out exactly.

That's why objects fall to the earth at the same speed in a vacuum, regardless of differences in the weight of the objects. The inertia from the extra mass and the extra gravitational attraction from the extra mass cancel each-other out exactly.

 

[Brian-M]

This makes no sense, other than the second paragraph. You might be correct, but it doesn't help my understanding.

Here's an easy way to understand it...

Place a large rock on the ground to represent the earth.
Draw a circle around the rock to represent the orbit of the moon.
Place a pebble on the line of the circle to represent the moon.

Now move the pebble moon clockwise around the circle, and take notes on what direction the rock's earth's gravity is pulling at the moon.

When the moon is north of the earth, the moon is traveling east and the earth is pulling it south.

So the moon starts to move towards the south-east, but as the moon start to get east of the earth, the earth starts it pull it south-west, so the moon starts to move less and less east until by the time it's completely east of the earth it's going straight south.

When the moon is east of the earth, the moon is traveling south and the earth is pulling it west.

So the moon starts to move toward the south-west, but as soon as the moon ... well, you can figure out the rest. It's the same as when the earth was north of the moon, but with different directions.

When the moon is "north" of the earth, the earth is accelerating it "south".
When the moon is "south" of the earth, the earth is accelerating is "north".
When the moon is "east" of the earth, the earth is accelerating it "west".
When the moon is "west" of the earth, the earth is accelerating is "east".

This acceleration in opposite directions cancels out, so the moon ends up accelerating in a circle without speeding up or slowing down.

(Note, these directions are purely metaphorical, to indicate the position of the pebble on the circle. The actual moon can't ever be said to be "north" or "east" of the earth.)

 

[Southwind17]

No. Gravitational attraction is proportional to the product of the masses divided by the square of the distance.

The total mass hasn't changed, and the average distance hasn't changed, so why should gravitational attraction change?

Because the mass is concentrated into a smaller space as opposed to being scattered within various orbits. Imagine Saturn's rings gradually transforming into a solid moon (which I understand they will do over time?!?) - the resultant effect on Saturn will be somewhat different from the current effect of the rings (which I suspect is largely neutral given it's relative uniformity).

 

[Brian-M]

Because the mass is concentrated into a smaller space as opposed to being scattered within various orbits. Imagine Saturn's rings gradually transforming into a solid moon (which I understand they will do over time?!?) - the resultant effect on Saturn will be somewhat different from the current effect of the rings (which I suspect is largely neutral given it's relative uniformity).

The only effect on Saturn would be tidal forces, because it would all be pulling on one side of the gas-giant at the same time instead of being evenly distributed.

But the newly formed moon wouldn't be any more inclined to crash into Saturn than the debris that make up the rings currently is.

How concentrated the mass is doesn't affect how strong the pull of gravity from it is. If the sun were to suddenly collapse into a blackhole (possibly due to some mad-science experiment gone wrong), and all that mass were squeezed into an area the size of a grapefruit instead of being billions of times the size of our planet, the earth and other planets would continue to orbit it just the same, without the slightest disturbance.

(Of course, we'd all die as the earth slowly froze, but that's beside the point.)

Think of it this way, before forming into a moon each particle was being pulled to earth by a force of X. After gathering together to form a moon, each particle is still being pulled to earth by a force of X.

No difference.

 

[Southwind17]

Think of it this way, before forming into a moon each particle was being pulled to earth by a force of X. After gathering together to form a moon, each particle is still being pulled to earth by a force of X.

No difference.

Except that the pull exerted on the Earth by the formed Moon will be different - being along a singularly focused axis - thereby drawing the two together more than the individually scattered particles would (as their collective gravitational forces as felt by the Earth would act in different directions).

And that's my point - as the Moon gradually forms the combined gravitational force between the Earth and the Moon will increase along an increasingly narrowing axis.

So unless the forming Moon accelerates tangentially to the Earth to increase it's orbital radius it will tend to fall towards the Earth as it's mass increases.

 

[Delvo]

I think the problem here is similar to the one that makes it hard for people to anticipate how powerfully magnetizable objects are drawn toward the electromagnet in an MRI machine. Even things that feel really heavy to us, so we'd expect them to be hard for a magnet to move, get sucked up at unimaginable speeds if they're brought into the room or even too close to the door.

We're generally used to forces that are relatively restricted in magnitude, not forces that keep scaling up as long as mass does. For example, it's easy to push a bicycle, hard to push a motorcycle, and harder to push a car, because our pushing ability doesn't increase with the mass of the thing we're trying to push.

But gravitational force does. Yes, the more massive the moon got, the more force would be needed to change its velocity. But also, the more massive it got, the more force gravitation would apply to it.

 

[Reality Check]

And that's my point - as the Moon gradually forms the combined gravitational force between the Earth and the Moon will increase along an increasingly narrowing axis.

Not really, Southwind17.
The gravitational force between the pre-Moon debris cloud (from the collision between the Earth and a large body) and the forming Moon would change because of the change in mass distribution. It would not be a simple as changing along one axis. It would be a complex process.

See the wild stuff that happens in computer simulations of the collision (e.g. https://www.youtube.com/watch?v=Fwl_JBQtH9o).

 

[Damien Evans]

So, if the Moon really is formed from the conglomeration of debris created from the collision of another planet with Earth billions of years ago, how is it that as the particles combined, and the mass increased as a result, the orbit of the forming Moon didn't reduce increasingly to the point where it fell to Earth? How can an object of increasing mass orbiting the Earth settle into a static orbit?

Remember the mass didn't actually increase, it just went from being small particles spread over a wider area to the one big lump we see now. It's distributed differently but it didn't go up (in fact it would have gone down because some of the particles would have crashed on to the young Earth rather than the forming moon).

 

[Damien Evans]

"Counts as acceleration"? So not actually changing speed then (as opposed to "velocity")?

Yes. When you turn a corner in a car you are accelerating in the direction you're turning towards, even if your actual speed stays the same.

 

[Slowvehicle]

I understand this notion - but the Moon isn't actually accelerating, is it, in the sense that today its velocity is greater than it was yesterday?

It's a good question.

Remember that acceleration is any change in velocity, which is a vector, that is, it has both a magnitude and a direction. Changing the direction component of a velocity is, in fact, an acceleration (think about how your car slows down, in a turn, if you do not "add gas").

Since the moon is constantly changing direction, it is constantly accelerating--even as its speed remains constant.

 

[xtifr]

Except that the pull exerted on the Earth by the formed Moon will be different - being along a singularly focused axis - thereby drawing the two together more than the individually scattered particles would (as their collective gravitational forces as felt by the Earth would act in different directions).

No, it won't draw them together more strongly. It'll shift the epicenter of their common orbit (the Earth and the particles that make up the moon), very slightly. The total gravitational attraction will remain unchanged.

You can't get more gravitational attraction without more mass. (That's pre-Galilean thinking.)

Only the vectors (the direction of the pull) will change. The amount of pull won't change. And note that we're talking about the pull of the moon's mass on the Earth here, not the opposite. The pull of the Earth on the moon's particles is unchanged. So the Earth will wobble just slightly more than it used to, but the moon won't be affected at all. (Except for the incredibly tiny perturbations caused by the Earth's increased wobble.)

 

[Brian-M]

Except that the pull exerted on the Earth by the formed Moon will be different - being along a singularly focused axis - thereby drawing the two together more than the individually scattered particles would (as their collective gravitational forces as felt by the Earth would act in different directions).

Why would the pull of gravity draw them together more when the pull of gravity hasn't changed?

I think I see where your problem is, you're switching from thinking of lots of little particles separately to thinking of one giant object (the moon).

Try this... stop thinking of the moon as a single object!

Instead, think of the moon as a big cloud of particles that happen to be floating really, really close together.

Each particle gets the same pull from earth's gravity regardless of whether they're close together or far apart. So why should they be more inclined to fall towards the earth when they're close than when they're far apart?

And that's my point - as the Moon gradually forms the combined gravitational force between the Earth and the Moon will increase along an increasingly narrowing axis.

No it won't. There is no increase.

The gravitational pull between the earth and the particles which make up the moon has remained unchanged, it's no stronger than it has ever been.

The only difference in having all this mass concentrated in one direction is tidal forces, and tidal forces are slowing down the moon's orbit by a small but measurable amount, but I don't think that's what you're talking about.

So unless the forming Moon accelerates tangentially to the Earth to increase it's orbital radius it will tend to fall towards the Earth as it's mass increases.

But the mass in orbit hasn't increased. You still have exactly the same mass in orbit as you had before it became concentrated into one place.

Why should it be more inclined to fall towards the earth just because it's all neatly in one place instead of spread out?