How big is a meteor? (shooting star)
After that brief flash as a meteor (a shooting star) traces a short line across the night sky, have you ever asked your self how big it is?
The meteor burns up before it reaches Earth – otherwise it would be a meteorite, so it seems to be a difficult question. But scientists love questions like this. A car-ful of UNSW physicists (Anna Gribakin, Gleb Gribakin and Joe Wolfe), returning from watching the annual Leonid meteor shower, enjoyed making an estimate based on what we had seen. Traditionally, such calculations are done on the back of an envelope, but it was dark. And of course we had to rely on data that we could remember.
A quirky game for passing time in the car, you might think, but it's actually typical of 'order-of-magnitude' calculations that are required often in science. 'Is this effect big enough to be important?' 'Is it large enough to be measured?' 'Could it be dangerous?' The answers to such questions often do not need precision: if it turns out to be so small that we cannot measure it, we may not need a better answer. And of course if the rough answer is interesting, we can then take the time to do a more serious calculation.
We reproduce the arguments here as an example of using simple physical arguments and plausible values to estimate unknown quantities.
The intensity of sunlight – solar power received per square metre – is 1.4 kW/m2. (This constant is well known because one needs it for solar energy, ecology, architecture etc). The Sun is 8 light minutes away. If it were 10 light years away, then its intensity, I, would be given by the inverse square law:
Another rough assumption (justified in an appendix calculation below) is that this energy is roughly equal to the initial kinetic energy of the meteor.
Now Earth is 8 light minutes from the Sun, so it travels 3000 light seconds per year around the sun = 30 km/s. The meteor has 'fallen' from the outer solar system, so it is going faster than the Earth, and we strike it at an angle. We put the collision speed at 60 km/s, which is no rougher than some of the other approximations. So
m ~ 0.3 mg
This gives a radius of 0.3 mm – about the size of a grain of sand. On our return, we were happy to see that this was broadly in line with information from other sources, such as satellite measurements.
The intensity of radiation it emits is proportional to its radius squared, and inversely proportional to the square of distance to it. So:
= approximately 1 mm
An order of magnitude is as good as one can hope for in such calculations: for more precision, one needs better data, more careful calculations – and a calculator!
Wolfe / J.Wolfe@unsw.edu.au, phone 61-
2-9385 4954 (UT + 10, +11 Oct-Mar).|