Meteors and momentum

[pavelcherepan]

 

Firstly be careful talking about a wave.

Waves have no net momentum to transfer.

You mean a pulse.

 

Yeah, that's what I read on many sources. I was just confused by the Acoustic Theory article on wiki, which says that waves do have momentum.

 

 

 

This force appears as a result of the destruction of its linear momentum in that direction.

This is similar to the destruction of forward momentum when a liquid jet impacts upon a wall.

 

But doesn't the jet transfer it's momentum to the wall? I can't see similarities between those.

 

 

Transport Phenomenon

 

Bird, Stewart and Lightfoot

 

Thanks! Found it on Google books. I'll see what kind of exciting stuff I can find there!

 

@ Studiot - How do you handle linear momentum for a proportion of the momentum would have been gained by the Earth attracting the meteor to itself.

How do you determine its natural speed? [The one it would have if it passed the Earth's orbit unassisted by Earth's gravity]

 

I have been thinking this one through maybe you could treat the meteor as coming from infinity and work out its velocity gained in the free fall to the Earth, also compare that to the free fall speed towards the Sun at the height of the Earth's orbit.

Would the final speed be the addition of both of these?

 

Robittybob1, gravitational interaction doesn't matter as that momentum is already conserved. Look at this:

 

Force acting upon a meteor: [latex]F = G \frac{Mm}{R^2}[/latex] , where m is the mass of meteor and M is the mass of the Earth.

 

And by Newton's third law the force acting on Earth will be the same but with an opposite sign. Then meteor will be accelerated by that amount:

 

[latex]a_m = F/m = G \frac{Mm}{R^2} * \frac{1}{m} = \frac{GM}{R^2}[/latex]

 

and similarly Earth will be accelerated by:

 

[latex]a_E = -F/M = -G \frac{Mm}{R^2} * \frac{1}{M} = - \frac{Gm}{R^2}[/latex]

 

Then if we take a small amount of time [latex]\Delta t[/latex] during this period meteor and Earth will change their velocities by:

 

[latex]\Delta v_m = a \Delta t = \frac{GM \Delta t}{R^2} [/latex] and

 

[latex]\Delta v_E = a \Delta t = - \frac{Gm \Delta t}{R^2} [/latex]

 

And, finally, momentum change during this time will be:

 

[latex]\Delta p_m = \Delta v_m *m = \frac{GMm \Delta t}{R^2} [/latex] for meteor, and

 

[latex]\Delta p_E = \Delta v_E *M = - \frac{GMm \Delta t}{R^2} [/latex], which are obviously the same but with opposite sign. As a result there's really no need to consider gravitational influence in momentum conservation calculations.

 

[studiot]

 

Robbitybob

How do you handle linear momentum for a proportion of the momentum would have been gained by the Earth attracting the meteor to itself.

How do you determine its natural speed?

 

Pavelcherepan

But doesn't the jet transfer it's momentum to the wall? I can't see similarities between those.

 

Answer to both,

Yes, of course, but the wall velocity remains at zero and the force developed is rate of change of momentum.

 

 

Edit

 

Remember also that a speeding solid body (meteor) striking a (relatively) stationary fluid is the same as a speeding fluid striking a (relatively) stationary solid body (wall).

Edited February 25, 2016 by studiot

[Robittybob1]

 

Answer to both,

Yes, of course, but the wall velocity remains at zero and the force developed is rate of change of momentum.

 

 

Edit

 

Remember also that a speeding solid body (meteor) striking a (relatively) stationary fluid is the same as a speeding fluid striking a (relatively) stationary solid body (wall).

I think we misunderstand each other. The Earth is ever so little attracted toward the meteor but since the mass is extremely large the relationship of momentum gained by the meteor is balanced by the momentum gained (opposite direction) by the Earth. Does that imply a meteor can not change the Earth's momentum? No because it would have had momentum due to the fall towards the Sun as well. Whether that will change the spin rate will depend on the position of impact on the surface i.e. leading side or trailing side.

[studiot]

 

So let's say we have a meteor that's burned up in the upper atmosphere like they normally would. Does that meteor change the overall momentum of the Earth, regardless of how small the change may be?

 

Remember your meteor burns up.

 

I suggest you are getting the scenario a little muddled up.

 

If the meteor burns up it adds gas to the atmosphere.

Momentum is very quickly distributed within gases.

So the atmosphere as a whole then possesses the momentum originally owned by the meteor as well as the very much larger momentum it already had due to its attachment to the Earth system.

Due to that attachment the momentum finally finds its way into the solid part of the Earth system.

 

So yes, all the meteor's original momentum is transferred to the Earth system in the same way as when two bodies coalesce on impact.

[Robittybob1]

 

 

....

So yes, all the meteor's original momentum is transferred to the Earth system in the same way as when two bodies coalesce on impact.

How did you define "original" in this case? Where was this "original momentum" measurement taken?

[studiot]

Before it burned up of course.

 

[Robittybob1]

Before it burned up of course.

 

In the post before you said "So the atmosphere as a whole then possesses the momentum originally owned by the meteor as well as the very much larger momentum it already had due to its attachment to the Earth system".

There seemed to be two components to the momentum and one of them was called "momentum originally owned by the meteor" Is that the same as it "original momentum" Can you define this term please?

"Before it is burning up" it will have the combination of both sources of momentum (acceleration gained from the Sun (+Solar system) and the Earth), I'd imagine, so how do you measure the "original momentum"? For that sounds like the final momentum rather than the original.

Edited February 26, 2016 by Robittybob1

[pavelcherepan]

 

Remember your meteor burns up.

 

I suggest you are getting the scenario a little muddled up.

 

If the meteor burns up it adds gas to the atmosphere.

Momentum is very quickly distributed within gases.

So the atmosphere as a whole then possesses the momentum originally owned by the meteor as well as the very much larger momentum it already had due to its attachment to the Earth system.

Due to that attachment the momentum finally finds its way into the solid part of the Earth system.

 

So yes, all the meteor's original momentum is transferred to the Earth system in the same way as when two bodies coalesce on impact.

 

Thanks studiot, it was a really good explanation.

[Robittybob1]

I tried to find science papers discussing meteors etc and the only fact that seemed logical was that comets, asteroids and near Earth objects go past Earth faster if they come from further out in the Solar System (longer orbits) ranging from 20 - 30 km/sec. I couldn't find any that detailed the impact speed with the Earth but there was a site on the internet where you could enter masses and trajectory into it and it would give a resulting impact speed. Does anyone have that site?

[Robittybob1]

Search for that calculator http://impact.ese.ic.ac.uk/ImpactEffects/ is one like what I was remembering. It had this comment beside the entry box for "Impact Velocity" - "This is the velocity of the projectile before it enters the atmosphere. The minimum impact velocity on Earth is 11 km/s. Typical impact velocities are 17 km/s for asteroids and 51 km/s for comets. The maximum Earth impact velocity for objects orbiting the sun is 72 km/s"

So that seems to give some indication that the speed the meteor had prior to being drawn by the Earth will have a major bearing on the momentum. From the above file search this will be indicative of it source.

[studiot]

I tried to find science papers discussing meteors etc and the only fact that seemed logical was that comets, asteroids and near Earth objects go past Earth faster if they come from further out in the Solar System (longer orbits) ranging from 20 - 30 km/sec. I couldn't find any that detailed the impact speed with the Earth but there was a site on the internet where you could enter masses and trajectory into it and it would give a resulting impact speed. Does anyone have that site?

 

Here are some facts, figures and terminology.

 

Source: Strahler, The Earth Sciences

 

Meteoriods are tiny particles ravelling through space at high velocity.

When they enter the Earth's atmosphere they become meteors. These are characterised by their luminous trails in the sky.

They range in mass from .000001 to .001 kg and enter tha atmosphere at 25 to 80 km / second

Nearly all burn up to gas in the upper atmosphere, 90 to 200 km above the surface.

Because they are so small and so high, their destruction is accompanied by their luminous trails (50 to 100 km in length) , but no sound.

 

Larger particles can make it all the way to the surface.

These are called meteorites.

These are accompanied by brilliant light and explosive sounds, especially upon impact.

 

 

@Pavel another book you might find interesting

 

http://www.amazon.co.uk/Atmosphere-Ocean-Our-Fluid-Environments/dp/0851412955

[Robittybob1]

 

Here are some facts, figures and terminology.

 

Source: Strahler, The Earth Sciences

 

Meteoriods are tiny particles ravelling through space at high velocity.

When they enter the Earth's atmosphere they become meteors. These are characterised by their luminous trails in the sky.

They range in mass from .000001 to .001 kg and enter tha atmosphere at 25 to 80 km / second

Nearly all burn up to gas in the upper atmosphere, 90 to 200 km above the surface.

Because they are so small and so high, their destruction is accompanied by their luminous trails (50 to 100 km in length) , but no sound.

 

Larger particles can make it all the way to the surface.

These are called meteorites.

These are accompanied by brilliant light and explosive sounds, especially upon impact.

 

 

@Pavel another book you might find interesting

 

http://www.amazon.co.uk/Atmosphere-Ocean-Our-Fluid-Environments/dp/0851412955

OK but all things fall at similar speeds don't they? Hammer and feather on the moon fell at the same rate, so what difference does it matter about the size. A comet could be the source of those meteorites, but they don't slow down just because the comet broke up.

I was using the speeds of other objects to get a indication of the speed of these meteors.

So some are very small and some make it all the way to the ground and they are called meteorites. There was no indication in the OP on the maximum size of a meteor as long as it burned up.

Edited February 27, 2016 by Robittybob1