The Moon who Fell to Earth?

[Southwind17]

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?

 

[jaydeehess]

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?

As the mass increased and gravitational attraction increased, it also sped up in its orbit balancing the equation.

 

[Ziggurat]

As the mass increased and gravitational attraction increased, it also sped up in its orbit balancing the equation.

No. As the mass increases, the force needed to make the moon accelerate at the same rate increases as well. Because inertia and gravitational force are both proportional to mass, gravity creates a constant acceleration, and acceleration determines stable orbit. It doesn't matter that the mass increases, the orbit would remain the same. If it changed its speed, it would change its orbit.

As a side note, the orbital distance of the moon has increased over time because of tidal acceleration. But that's completely separate from the change in mass of the moon.

 

[Southwind17]

No. As the mass increases, the force needed to make the moon accelerate at the same rate increases as well. Because inertia and gravitational force are both proportional to mass, gravity creates a constant acceleration, and acceleration determines stable orbit. It doesn't matter that the mass increases, the orbit would remain the same. If it changed its speed, it would change its orbit.

As a side note, the orbital distance of the moon has increased over time because of tidal acceleration. But that's completely separate from the change in mass of the moon.

Thanks for that Ziggurat. I don't quite follow, though:

1. How can something travelling in an orbit at a constant speed be accelerating?
2. If gravitational force is proportional to mass, and "it doesn't matter that the mass increases", then how can gravity create a constant acceleration, as you say?

 

[xtifr]

Remember, the moon is falling. It's just going so fast that it constantly misses the Earth.

If heavy objects fell faster than light objects (as we used to think before Galileo came along), then the accumulation of particles would make the moon go faster, which would mean that it would go farther, and would miss the Earth by even more, and would eventually escape Earth completely.

And really, if you think about it, the question boils down to: why don't heavy objects fall slower, since it takes more energy to accelerate them? Kind of the opposite of pre-Galilean thinking. But the answer's the same: gravitational energy is perfectly proportional to mass, since it is, in fact, determined by mass.

 

[MG1962]

Thanks for that Ziggurat. I don't quite follow, though:

1. How can something travelling in an orbit at a constant speed be accelerating?
2. If gravitational force is proportional to mass, and "it doesn't matter that the mass increases", then how can gravity create a constant acceleration, as you say?

Rather than traveling think of the Moon as falling...in a curve....that becomes an orbit

 

[Southwind17]

Remember, the moon is falling. It's just going so fast that it constantly misses the Earth.

Rather than traveling think of the Moon as falling...in a curve....that becomes an orbit

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?

 

[Brian-M]

, 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?

If all the particles were already in orbit to begin with, then there isn't any increase in mass. You've got just as much mass in orbit as you started with, it's just that all the mass has merged together into one place.

How can an object of increasing mass orbiting the Earth settle into a static orbit?

The orbit of an object is determined by speed, not mass. If the added mass already has orbital speed, then the orbit of the object is unchanged.

Most likely some of the particles which made up the moon had a faster speed and others had a slower speed, and the moon ended up moving at their average speed and orbit.

 

[Southwind17]

As a side note, the orbital distance of the moon has increased over time because of tidal acceleration. But that's completely separate from the change in mass of the moon.

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?!

 

[xtifr]

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 constantly accelerating and decelerating, and the two balance out to provide a constant speed.

Remember, when an object falls, it goes faster and faster. But when an object is thrown upwards, it slows The slowing happens because gravity is accelerating it in the opposite direction!

The moon is falling, so it should be accelerating, but if it accelerates, it will be moving away from the earth, so the gravitational acceleration causes it to go slower. At exactly the same rate it makes it go faster.

eta: in other words, every time it misses the Earth in its fall (which it does constantly), the Earth pulls it back so it doesn't escape.

 

[Southwind17]

If all the particles were already in orbit to begin with, then there isn't any increase in mass. You've got just as much mass in orbit as you started with, it's just that all the mass has merged together into one place.

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?

The orbit of an object is determined by speed, not mass. If the added mass already has orbital speed, then the orbit of the object is unchanged.

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

 

[Reality Check]

Thanks for that Ziggurat. I don't quite follow, though:

1. How can something travelling in an orbit at a constant speed be accelerating?
2. If gravitational force is proportional to mass, and "it doesn't matter that the mass increases", then how can gravity create a constant acceleration, as you say?

Acceleration is a change in velocity which is speed + direction. Something in an orbit is constantly changing direction and so accelerating.
Gravity creates a constant acceleration basically because the mass cancels out.
The force on a body of mass m due to a body of mass M is

F=ma=GmM/r^2​

so

a = GM/r^2​

which is constant for a constant M and r.

 

[Southwind17]

It's constantly accelerating and decelerating, and the two balance out to provide a constant speed.

Remember, when an object falls, it goes faster and faster. But when an object is thrown upwards, it slows The slowing happens because gravity is accelerating it in the opposite direction!

The moon is falling, so it should be accelerating, but if it accelerates, it will be moving away from the earth, so the gravitational acceleration causes it to go slower. At exactly the same rate it makes it go faster.

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

I think part of the 'problem' is reconciling the notion of acceleration with something that's not actually changing speed. Are we talking about a different kind of acceleration from what we see with, say, motor cars?

Anybody?

 

[BowlOfRed]

Thanks for that Ziggurat. I don't quite follow, though:

1. How can something travelling in an orbit at a constant speed be accelerating?

Circular motion involves acceleration because a change in velocity is an acceleration. Since velocity is both speed and direction, simply changing direction counts as acceleration.

Ignoring the fact that the moon isn't in a circular orbit (it's elliptical), there is an additional thing going on. That is a slight coupling between the orbit of the moon and the rotation of the earth. Since the earth spins faster than the moon and it's not a perfectly rigid body, then it sets up gravitation forces that *slightly* speed up the moon and *slightly* slow down the earth's spin. Over time, this causes the orbit of the moon to get larger (and the earth's day to get longer). This will continue until the two match and the moon stays over one spot on the earth many billions of years later.

• If gravitational force is proportional to mass, and "it doesn't matter that the mass increases", then how can gravity create a constant acceleration, as you say?

Because two things go up as mass goes up: the pull of gravity, and the resistance (inertia) against that pull.

Imagine you have a length of heavy pipe, and you work hard to get it rolling over the ground. If we double the length of pipe and give you a second person to push, you'd expect you could accelerate it at about the same rate. That's what happens here. Twice the mass, twice as hard to move, but twice the gravitational pull. The two cancel out, and it accelerates at the same rate.

 

[Southwind17]

Acceleration is a change in velocity which is speed + direction. Something in an orbit is constantly changing direction and so accelerating.

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

 

[Southwind17]

Circular motion involves acceleration because a change in velocity is an acceleration. Since velocity is both speed and direction, simply changing direction counts as acceleration.

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

 

[BowlOfRed]

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

I think part of the 'problem' is reconciling the notion of acceleration with something that's not actually changing speed. Are we talking about a different kind of acceleration from what we see with, say, motor cars?

Anybody?

It depends on which acceleration you're asking about.

Over short periods of time, the speed of the moon is mostly constant because the acceleration of the earth's gravity mainly serves to change the direction, not speed it up or slow it down. (Again, I'm ignoring the elliptical nature of the orbit here which complicates this statement).

However, over long periods of time, the speed does change. The earth is able to put a force on it that causes the orbit to elongate and therefore slow down the orbital speed as well.

 

[Turgor]

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, you are accelerating if you zig-zag

ETA: as previously pointed out, a change in direction is a change in velocity and therefore requires an accelaration

 

[BowlOfRed]

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

Yup.

F = m * a

Because there are so many forces that we use just to walk at a constant speed, this is difficult to see in everyday life. But maybe if you imagine instead being on ice skates.

If you want to make a right turn on skates, you have to dig your skates in and push against the ice (a force). That force accelerates you (either speeding you up, slowing you down, or changing your direction).

There you can see there's a lot more work to changing direction (even while keeping a constant speed) than there is when you're just gliding along.

 

[xtifr]

I think part of the 'problem' is reconciling the notion of acceleration with something that's not actually changing speed.

But it is changing velocity. Remember, velocity has a directional component. And yes, if you zig-zag through the streets, you always have to stop your movement in one direction and add it in another. That's why race cars have to slow down for corners. You have to remove the velocity in the direction you don't want, and add it in the direction you do.

Try this. Imagine a spaceship traveling in a straight line past the Earth. (A spaceship so that it's engines can compensate for the effects of gravity.) As it's getting closer to the point of closest approach, the Earth's gravity will be accelerating it. And after it's past the point of closest approach, the Earth's gravity will be decelerating it. Thus, at the point of closest approach, the acceleration and deceleration will be perfectly balanced.

But the moon doesn't travel in straight line (although it wants to, which is why this all works). It's always at (approximately) the point of closest approach, so the forces of acceleration and deceleration are always in balance.