School kids measure distance to the Moon

http://www.technologyreview.com/blog/arxiv/23205/

42 15 17 years ago

An exercise I use as the start of a math masterclass is to calculate the distance to the moon using a pendulum and a calendar. The answer is remarkably close to the one obtained by these kids using recordings from the Apollo missions.

If NASA really did fake the Moon landings, they did a bloody good job!

If you want to know how to calculate the distance, let me know and I'll write something about it.

Retric• 17 years ago

Shure, I think I could work it out, but I would still like to see your process.

PS: A pendulum and a calendar and a stopwatch or clock?

RiderOfGiraffes6• 17 years ago

Yes, pendulum and stopwatch.

More later.

gjm112• 17 years ago

Suppose the moon is in a circular orbit with radius R and angular velocity w. Then its position looks like R exp(iwt), so its acceleration is the second derivative of this = -Rw^2 exp(iwt), whose magnitude is -Rw^2. (That's a standard formula but I always have to derive it from scratch.) So GM = R^3w^2.

Now, what do we know? If we have a calendar that marks full moons, we know how often the occur and therefore we know w. What about the stuff involving GM? Well, now construct a pendulum. Standard formulae again but let's do it from scratch again. Length L, angular displacement a: vertical displacement is negligible to first order, so for small displacements the restoring force just comes from the tension in the string. To first order again, that equals the gravitational force on the mass, so the horizontal component of the acceleration is GM/r^2.La where r is the radius of the earth. So, measure the period of the pendulum (and of course its length); that tells us a and therefore GM/r^2. So provided we know r we now have GM and therefore R, and we're done.

So, one remaining question for RiderOfGiraffes: are you happy to look up r in a reference book for this exercise, or do you have a classroom-friendly way of getting that by simple observation and calculation too?

yread• 17 years ago

They should try to measure it the way Ptolemy did! Or the distance to Sun...

srveit• 17 years ago

For really accurate measurements check out http://www.physics.ucsd.edu/~tmurphy/apollo/apollo.html By bouncing a laser off several reflectors that were left on the moon, they are able to get accuracies of one millimeter.

ZeroGravitas• 17 years ago

If you've got two OLPC XO laptops you can measure the distance between them using a similar techique:

http://wiki.laptop.org/go/Acoustic_Tape_Measure

numbchuckskills• 17 years ago

REALLY smart school kids would go to wolfram alpha to get the distance to the Moon, and let the suckers analyze echo's from old NASA clips.

RiderOfGiraffes6• 17 years ago

This deserves a separate discussion.

See http://news.ycombinator.com/item?id=802856

mrduncan• 17 years ago

I'm reminded of Clifford Stoll's TED talk where he dicusses (among other things) how he teaches high schoolers to calculate the speed of sound.

http://www.ted.com/index.php/talks/clifford_stoll_on_everyth...

mhb• 17 years ago

Measuring the height of a building using a barometer:

http://www.snopes.com/college/exam/barometer.asp

School kids measure distance to the Moon

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