Meteors and momentum

[pavelcherepan]

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?

 

On one hand I'm tempted to think that all the energy goes into heat and viscous deformation of the atmosphere, but on the other hand if we had billions of those burning up every second , this should cause some drag and change momentum of the planet. In that case what would be the mechanism of it?

[Robittybob1]

Is there any preferred direction or are they evenly spread? If there was the same amount (in momentum terms) striking the western side as the eastern side it feels like any effect would balance each other out.

When I had considered this problem before I thought that much of the momentum a meteor has would have been gained by the gravitational attraction to the Earth so momentum gained is partly balanced by the momentum lost earlier, but if it was possible to isolate the momentum it would have had had it not struck the Earth (its momentum from orbiting the Sun) that component would add/subtract to the momentum of the Earth depending on the position it entered the atmosphere.

Edited February 24, 2016 by Robittybob1

[Mordred]

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?

 

On one hand I'm tempted to think that all the energy goes into heat and viscous deformation of the atmosphere, but on the other hand if we had billions of those burning up every second , this should cause some drag and change momentum of the planet. In that case what would be the mechanism of it?

An asteroid passing by can change the rotational speed of the planet via conservation of angular momentum. Doesn't even need to interact with the atmosphere. Usually though the effect is too small to be measurable.

[Robittybob1]

An asteroid passing by can change the rotational speed of the planet via conservation of angular momentum. Doesn't even need to interact with the atmosphere. Usually though the effect is too small to be measurable.

Is that via the slingshot effect?

[Mordred]

Yes

[Robittybob1]

That gravity assist would affect a planet's orbital speed, its orbital angular momentum, rather than its rotational angular momentum. So there are two components to the angular momentum but it sounded like Pavelcherepan was looking more to the rotational angular momentum rather than the orbital component.

[pavelcherepan]

 

 

An asteroid passing by can change the rotational speed of the planet via conservation of angular momentum. Doesn't even need to interact with the atmosphere. Usually though the effect is too small to be measurable.

 

OK, but what about linear momentum? Will it also change because of gravitational interaction or some other mechanism is also possible?

 

I was thinking that if meteor burns in the atmosphere it increases average temperature of said atmosphere and increases the rate at which gases escape. That could also lead to a decrease in linear momentum.

Edited February 24, 2016 by pavelcherepan

[Robittybob1]

 

OK, but what about linear momentum? Will it also change because of gravitational interaction or some other mechanism is also possible?

 

I was thinking that if meteor burns in the atmosphere it increases average temperature of said atmosphere and increases the rate at which gases escape. That could also lead to a decrease in linear momentum.

What is the linear momentum you are talking about?

 

Would that be like the DDE we've been discussing? Like if any effect heating the atmosphere means more atoms escape, are the atoms escaping in the prograde direction taking more momentum than the retrograde ones? I think that would be the case. Loss of atmosphere, if that logic is correct, will tend to slow the planet, and is probably unrelated to the impact direction of the meteor.

There would be other factors to consider as well particularly the Sun.

Edited February 24, 2016 by Robittybob1

[pavelcherepan]

Robitty, this is not your discussion so please stop derailing it. You're at a computer, open a new tab in the browser and search for linear momentum. Very easy, nay?

[Mordred]

Impacts can change Earths orbit though in extremely small amounts depending on size of impact. This in turn changes the orbital velocity.

 

Theoretically outgassing in a particular direction could also do the same. Again the amount of change would be immeasurable.

 

Quite frankly the physics that can change a meteor momentum and orbit apply to any mass. It's just a matter of scale

Edited February 24, 2016 by Mordred

[pavelcherepan]

So what I was wondering about is whether the impact of a meteorite or a meteor into earth's atmosphere will change it's linear momentum apart from potential increase in atmospheric escape?

 

So to put it short, is the impact onto the atmosphere somehow passed onto the solid Earth itself?

[Mordred]

Yes via pressure waves

[pavelcherepan]

So just through sound waves? Thanks, that helps a lot!

Ok, so here's the main problem I'm having. So say we have a meteor that impacts atmosphere from prograde direction. At infinity it's velocity is v and then it has an inherent momentum of mv that it has to transfer to Earth.

 

I don't take into consideration acceleration due to gravity interaction with earth, because both bodies will be accelerated proportionally to mass and hence this momentum is already conserved.

 

So it hits atmosphere and burns up. From what I know now the following effects will account for that original momentum: degassing in a preferred direction, mass loss of earth due to increased escape of gases, sound waves, but in fact escaping gases will preferrentially escape in prograde direction and hence will in fact result in thrust on retrograde vector. Then is this relation correct?

 

[latex]mv = m_2*v_e - m_g*v_p + sound-wave-momentum[/latex]

 

Sorry it's ugly, I'm typing from my phone. Here m2*ve is mass of all gas that wouldn't have escaped without the impact times velocity of earth, mg*vp is mass of the gas that's escaped in prograde direction times vp - average velocity of escaped particles.

Edited February 24, 2016 by pavelcherepan

[Mordred]

I'll have to give the relationship some thought. Sound wave influences can get tricky. It's been awhile since I last looked at shockwave metrics it's an interesting question though. One factor I can see is.

 

How much of the shockwave would get buffered and dispersed by the atmosphere. Which correlated to how much inertia is transferred to the Earth. As well as outgassing

[pavelcherepan]

I've given it a bit more thought. [latex]v_p[/latex] should be the vector sum of escaped particles velocities.

Edited February 24, 2016 by pavelcherepan

[Mordred]

You might want to look at the shockwave metrics in this article.

 

http://www.google.ca/url?sa=t&source=web&cd=17&rct=j&q=meteor%20%20moving%20Earth%20pdf&ved=0ahUKEwi1-8mc-I_LAhVMyGMKHWl5AGM4ChAWCC0wBg&url=http%3A%2F%2Fsci-ed.org%2Fdocuments%2FLCP%252011%2520%2520ASTEROID%2520May%252020.pdf&usg=AFQjCNHiZk8M0ShXIhdPiC7hnle4b4j-Vg

 

You should be able to refine your metrics as it has a formula for % forward thrust to outgassing.

Edited February 24, 2016 by Mordred

[pavelcherepan]

Thanks I'll do that once I get off a plane.

[Mordred]

Lol I know that feeling I just flew home today myself

[Robittybob1]

An asteroid passing by can change the rotational speed of the planet via conservation of angular momentum. Doesn't even need to interact with the atmosphere. Usually though the effect is too small to be measurable.

Do you have reference for this change in rotational speed as a result of the slingshot effect?

[pavelcherepan]

 

Do you have reference for this change in rotational speed as a result of the slingshot effect?

 

That's the whole idea of the slingshot effect. An object passing by a more massive object "steals" some of it's momentum to increase/decrease it's own velocity.

 

https://en.wikipedia.org/wiki/Gravity_assist

 

 

You should be able to refine your metrics as it has a formula for % forward thrust to outgassing.

 

I'm still reading the link you've sent. It was so interesting (the Tunguska part) that I didn't really skip to formulas as I planned but in the mean time I've ran into a bit of an issue.

 

A part of the relationship above was the bit cleverly titled "sound-wave-momentum" but depending on the source I look at some say that sound waves carry no momentum (but have energy and can perform work) and some (for example wiki article on Acoustic Theory) have formulas above what I can comprehend. What I was thinking in the plane is that the sound wave propagates as a cone so if we consider the surface it hits to be completely flat and we know how to express momentum transfer at any point of contact then we can express the momentum transferred to Earth in retrograde direction as [latex]x*sin(\alpha)[/latex] where x is that formula for momentum of sound wave at a point and alpha is measured from horizontal.

 

Than I could take a half of the cone and to get the entire momentum I could integrate that relationship by alpha from 0 to pi/2, since if the surface is flat every point of contact will have a different alpha, and then doubling this entire expression I could get the full momentum of sound wave. I hope I'm making some sense. Would that work? You can guess, calculus is not my strongest field.

 

And further on, since sound waves are created all along the path of the projectile, in order to get the complete momentum from the sound wave all of this above would have to be integrated either by time or distance traveled through atmosphere.

Edited February 24, 2016 by pavelcherepan

[Robittybob1]

 

That's the whole idea of the slingshot effect. An object passing by a more massive object "steals" some of it's momentum to increase/decrease it's own velocity.

 

https://en.wikipedia.org/wiki/Gravity_assist

 

 

 

from the link you provided:

To increase speed, the spacecraft flies with the movement of the planet (taking a small amount of the planet's orbital energy); to decrease speed, the spacecraft flies against the movement of the planet.

 

Mordred made it sound as if the rotational speed of the planet slowed. This is not the case as it is the orbital speed that is slowed.

That was the point I was trying to make. It steals the planet's momentum making it move closer to the Sun, it doesn't change the planet's day length.

Edited February 24, 2016 by Robittybob1

[pavelcherepan]

from the link you provided:

Mordred made it sound as if the rotational speed of the planet slowed. This is not the case as it is the orbital speed that is slowed.

That was the point I was trying to make. It steals the planet's momentum making it move closer to the Sun, it doesn't change the planet's day length.

 

That is part true and good job on noticing, but angular momentum of the planet can change due to Tidal interaction with the passing object.

[Robittybob1]

 

That is part true and good job on noticing, but angular momentum of the planet can change due to Tidal interaction with the passing object.

If it was big enough .... like the Moon. You got me there. I still want to know what object had the "linear momentum" you mentioned.

Linear momentum of the meteor was that it?

[studiot]

Hi, Pavel.

 

Firstly be careful talking about a wave.

Waves have no net momentum to transfer.

You mean a pulse.

 

Secondly as the meteor traverses the atmosphere it exerts a ffrictional force on the atmosphere (and the atmosphere on it) .

 

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.

 

The science of momentum transfer and exchange (in this context) is called transport phenomenon and the classic text is

 

Transport Phenomenon

 

Bird, Stewart and Lightfoot

 

IMHO it is one of the best textbooks ever written on any technical subject.

[Robittybob1]

@ 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?

Edited February 25, 2016 by Robittybob1