Tuesday, June 06, 2006

What is this, the Straight Dope?

Bast asks:

I have a question, with regards to the possible impact crater found in antarctica. If an asteroid 50 km in length slammed into the earth could it alter the orbit around the sun? and by alter I mean not just a little wobble but actually push the earth further away (or closer I suppose depending on whether it hit at night).
The full solution to this problem is likely to be quite complex, so forgive me if i do a bit of handwaving and back-of-the-envelope calculating here. The way i see it, at the bares bones we're talking about a collision. When it comes to collisions, at the very least we know that momentum will be conserved so, to start with, the important factors are mass and velocity. If i know the mass and velocity of the two bodies (the earth and the impactor) prior to impact, i can use those to work out the final velocity of the earth after impact. But how does knowing how fast the earth is moving help me?

Well, when it comes to orbits there is an inverse proportionality between orbital radius (the distance of the orbit from the sun) and orbital velocity. Decrease the earth's orbital radius, and it will increase it's orbital velocity. Similarly, if you decrease the earth's orbital velocity, it will increase it's orbital radius (this what makes it difficult for shuttle pilots to manoeuvre in orbit - changing your speed can have undesired effects).

Knowing the change in velocity allows us to calculate the change in radius as a result of the change in velocity, assuming conservation of momentum. This is of course the simplest way of getting an order of magnitude answer - i could go to a lot of effort calculating the exact orbital mechanics, but for this i think we just want a feel of how big a change can be made. I'm going to make assumptions like a circular orbit for earth, and a constant orbital velocity for earth, anyway.

So, we are going to need to set some bounds to the problem. How massive is a 50km wide asteroid? How fast can it be going when it hits us? How elastic is the collision. The following are the extrema i've selected for each variable:

  1. Density for observed meteoroids is between 3-8g/cc.
  2. Impact (i.e. relative) velocity of impact has been recorded in the range from 11-72km/s.
  3. The collision can range from perfectly inelastic (all impactor's energy released, final mass = earth mass), to perfectly elastic (no energy released by impactor, final mass = earth mass + impactor mass).
  4. Direction of impact can range from travelling in exactly the same direction along the orbital path, to travelling in exactly the opposite direction along the orbital path.

I calculated the range of possible values for all combinations of these extrema, and came out with a range of variance in final velocity from 0.000094% increase to 0.0000067% decrease. So on order of magnitude we're talking roughly a 0.00001% change one way or the other, depending on how the impact happened. Since orbital velocity is inversely proportional to orbital radius, this translates to a 0.00001% change in our distance from the sun.

The question is, how big a change is this, really? Is it enough to significantly affect life on earth?
One of the measures of whether life can exist on earth or not is the so-called Habitable Zone, the range of distances from a star where water is in a liquid state. For our sun, this is in the range 0.7AU to 1.5AU (one AU, or astronomical unit, is the distance from the earth to the sun). We would therefore require at least a 30% change in our orbital distance to radically affect all life on earth.

But all life on earth isn't us. We would be severely uncomfortable at temperatures that many bacteria would thrive in. How big a difference is 0.00001% to us? Another way of looking at it is to measure the change in energy we're receiving from the sun. This is usually measured in terms of the Solar Constant, the amount of energy received by 1 square meter of the atmosphere when the sun is shining directly at it. This is naturally related to the distance from the sun. Given the numbers from the previous calculation, we're looking at a variance in the solar constant on the order of 0.000002%. Again, how big is this in terms that mean something to us? Normal changes in the earth's distance from the sun due to axial tilt, precession and orbital eccentricity (the Milankovitch cyles) are thought to be a factor in the causation of ice ages, but the factors involved create changes on the order of a few percent, much larger than our variance.

In other words, any change in the earth's orbit due to a collision is going to be negligable, even for an object as large as 50km across. Even then, an object of this size impacting the earth is extremely rare (there are no measured Near Earth Asteroids greater than 25km across at present). At the end of the day, it's the dust kicked up by the impactor that has the real long term effect - it only takes a 2km meteor to throw enough ejecta into the atmosphere to result in serious environmental damage, and anything larger than that is guaranteed to cause mass extinction.

Here's a good page on meteorites, with plenty of good links.

And here's NASA's comet and asteroid impact hazard site.

Proviso: any and all calculations made in this post may be completely and utterly incorrect.


Blogger totalwaste said...

w00t! i feel like i done learnded something!

June 06, 2006 11:25 PM  
Blogger Bast said...

criminy! thanks didn't really expect that much thought into it. Just wondered if that size meteor could have made a difference. The Permian Triassic extinction is extremely puzzling because of the almost complete extinction of marine life, which mere lack of sun doesn't entirely explain. After reading the initial article I found out a bit more about this so called impact crater and the theory is extremely spurious.

June 09, 2006 3:54 PM  
Blogger moonflake said...

no problem, you got me thinking and it was fun anyway :)

June 09, 2006 4:41 PM  

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