Deriving the Approach Velocity of Meteorites

[Jimmy87]

Hi,

I’m interested to understand some of the mechanics involved in meteorites that originate from the asteroid belt. I have researched several including the Barringer and the one in Northern Canada in 2008 that was caught on multiple CCTV cameras. They all have very similar velocities before impact (20km/s).

Using the GPE calculation of E = GMm/R with R as the surface of the Earth and equating it to kinetic energy I get 11km/s impact speed. This assumes the meteorite started at rest when entering Earth’s gravitational field (and assumes it started at the edge of it as apprise to the asteroid belt). So this shortfall of 9km/s I’m assuming it starts off at 9km/s before heading to the Earth.

I understand that if they were assumed to start at rest then the impact velocity will be independent of the mass since the starting GPE will be equal to the final KE (conservation of mechanical energy).

So my main question- is it a coincidence that all these meteorites start off at 9km/s before heading to Earth? Is there a mechanism to explain this starting velocity when they get deflected out of the asteroid belt from Jupiter’s gravity?

Thanks for any insights offered.

 

[Orodruin]

There are several effects at work here, not only the Earth’s gravitational potential. On top of that you have the initial orbital motion of the Earth itself (30 km/s) as well as the original orbital velocity of the asteroid belt. There is also the potential difference im the solar potential between the asteroid belt and Earth. See https://xkcd.com/681/

 

[Jimmy87]

There are several effects at work here, not only the Earth’s gravitational potential. On top of that you have the initial orbital motion of the Earth itself (30 km/s) as well as the original orbital velocity of the asteroid belt. There is also the potential difference im the solar potential between the asteroid belt and Earth. See https://xkcd.com/681/

Thanks! Could there be a situation then where an asteroid heads directly towards Earth’s orbital motion then you could get impact speeds greater than 30km/s?

Is it a coincidence that all the impacts I’ve looked at are all pretty much 20km/s impact speed?

 

[anorlunda]

There object could intercept Earth's orbit at a tangent in the same direction or in opposing directions or anything in between

I'm assuming that the asteroid was knocked out of it's solar orbit by collision or interaction with some other object.

 

[Jimmy87]

This is the one from the 2008 Canada meteorite:

https://www.sciencedaily.com/releases/2008/11/081125141602.htm

They quote:

“Hildebrand estimates that hundreds of meteorites larger than 50 grams could have landed since the rock was large and its entry velocity was lower than average. The object's speed is calculated to be only roughly 14 km/sec when it entered the atmosphere versus the average of around 20 km/sec.”

I watched a documentary on it where Hildebrand featured in it as he was the lead scientist investigating this impact. Again he quotes this average 20km/s for meteorites in general. With all the many parameters we discussed seems strange they all end up with roughly the same entry velocities.

 

[davenn]

I have researched several including the Barringer and the one in Northern Canada in 2008 that was caught on multiple CCTV cameras. They all have very similar velocities before impact (20km/s).

That should be clarified .... 2 very different situations. The Barringer Crater (Meteor Crater - Arizona) impactor was huge and heavy compared to that Canadian example.
The Barringer impactor could well have hit the ground at between 14 and 20 km/s, where as the stones from the Canadian (and most resulting meteorites) hit the ground at terminal velocity ~ 100+ km / hour ( NOT per second). It is only the very large, crater forming objects, that hit the ground at very high speeds. This is because they are so big and travelling so fast that the atmosphere does little to slow their velocity.
Also, the Barringer impactor was Nickel-Iron and they more commonly survive atmospheric entry reasonably intact.
It is the stony meteors that tend to more commonly break up in flight resulting in more smaller rocks reaching the
ground to become meteorites.

Using the GPE calculation of E = GMm/R with R as the surface of the Earth and equating it to kinetic energy I get 11km/s impact speed.

Reasonably irrelevant, can't be used, as per my previous comments. Yes, many get "captured " by the Earth's gravity field
most are just coming straight in and would do so regardless of if there was a gravity field or not. For the most part,
the substantial slowing by atmospheric friction negates any additional speed caused by gravity.
The main things determining the resulting velocity of the object is the relative velocities of the rock and the Earth.
Head-on and for some degrees off that centre line are going to have the highest velocities. Those perpendicular to the direction
of travel of the Earth much slower and finally those coming from behind the Earth ie. travelling the same direction as the Earth's
orbit will have the slowest velocities.

I understand that if they were assumed to start at rest then the impact velocity will be independent of the mass since the starting GPE will be equal to the final KE (conservation of mechanical energy).

A bad assumption = bad answers .... they don't start at rest, they are all moving through space at high velocities relative to other objects.

I’m assuming it starts off at 9km/s before heading to the Earth.

Again, another bad assumption, they have varied velocities in their travels through the solar system.

(and assumes it started at the edge of it as apprise to the asteroid belt). So this shortfall of 9km/s

I don't even know what that is supposed to mean ??

I understand that if they were assumed to start at rest then the impact velocity will be independent of the mass since the starting GPE will be equal to the final KE (conservation of mechanical energy).

Again all bad assumptions that will lead you to false answers

I understand that if they were assumed to start at rest then the impact velocity will be independent of the mass since the starting GPE will be equal to the final KE (conservation of mechanical energy).

See my comments above re bad assumptions

Thanks! Could there be a situation then where an asteroid heads directly towards Earth’s orbital motion then you could get impact speeds greater than 30km/s?

Of course ... there are many recorded at up to 70km/s, readings tell me that, so far, 77km/s is the highest recorded velocity.
As I stated above, the entry velocity depends on the angle/direction that the meteoroid/asteroid enters the Earth's atmosphere.

So my main question- is it a coincidence that all these meteorites start off at 9km/s before heading to Earth?

I have already answered that Regards
Dave

 

[Jimmy87]

@davenn thank you for taking the time to write such a detailed response!

So it is bad to think of meteoroids having high speeds from the conversion of GPE to KE within Earth’s gravitational field? Their high speeds are from their orbital speeds around the Sun and the direction they strike the Earth (head on, from behind Earth etc)?

The new DART technology seems promising.