You might have heard the story that's been going round about the asteroid
Apophis. This is an asteroid that was, briefly, considered by NASA to be a collision risk with earth. But after more observations to gather enough data to compute its orbit more precisely, the result was that it's not a significant risk. The current NASA estimates are that it's a collision risk of about one in 45,000.
The news around it is that some German kid claims to have figured out that
NASA got it wrong, and that the real risk is 1 in 450. What was NASA's big
mistake, according to the kid?
He says that if the asteroid were to hit a satellite, that it would change the satellite's trajectory enough to make it hit the earth.
This has been reported with ridiculous credulity. Anyone with the least
bit of mathematical literacy should know, pretty much without even needing to
think about it, that this is absolutely silly.
According to the estimates that I've been able to find, the mass of
Apophosis is about 1.2×1011 kilograms. That's 120 billion kilograms.
The mass of a Boeing communication satellite (which from a few minutes of
searching around the net appears to be average) is about 1400 kilograms.
The asteroid is around 100 million times larger than a satellite.
Let's put that into perspective. A pretty average car - a Toyota Corolla - has a mass of roughly 1400 kilograms. A common housefly has a mass of 16 milligrams. That's pretty close to the same ratio of masses as the asteroid and a typical satellite. So when we talk about how much the trajectory of the
asteroid could be changed by hitting a satellite - we're talking about
roughly the same kind of thing as how much a bug can alter the trajectory of a moving car by crashing into its windshield.
Obviously, the speed of the collision matters. But still - take a fly moving at 1,000 kilometer per second, and collide it with a car, and the
change in speed of the car is going to be miniscule: the momentum
of the fly at that velocity is 1×106m/s × 1.6×10-6kg = 1.6 kg m/sec; in a perfect collision,
the maximum change in velocity of a 1400 kilogram car would be around
1 millimeter per second. If the fly were moving at one million kilometers per second - which is quite a bit faster than the speed of light! - it could change the velocity of the car by a meter per second. (Originally, I screwed up my units here, and got the speed of light wrong by a teeny little bit - like three orders of magnitude. D'oh.)
So how much could a collision with a satellite alter the orbit of an
asteroid? Not bloody much. How much would it need to alter the course of the satellite to make it hit the earth? A lot. A huge amount. A satellite impact would be occurring at a range of around 6 times the radius of the earth (based on the closest approach distance of the asteroid.) The asteroid would be following a trajectory very close to tangential to the earth's surface at this point. So to turn it to a collision would require a dramatic shift.
There's just no way to make this work. It's impossible. And anyone with a bit of common sense should be able to work this out. Not necessarily to this degree of detail - but for goodness sake, the fact that a huge rock in space isn't going to have its path altered significantly by hitting a tiny little tin can should be bloody well obvious.