# Doing Math for Fun and Science

The girlfriend of one of my fellow physics students works on the Lunar Reconnaissance Orbiter project.
Tonight as a bunch of us physics folks were sitting around my apartment chatting (the girlfriend was up in the Phoenix area), my friend noticed her status message on Skype posed a practical question which I paraphrase as, “If a spacecraft 20km away from the LRO vents ~100g of hydrazine, what’s the probability of hydrazine impacting the LRO’s optical elements? You have 20 minutes.”
Taking this is as a challenge, we started calculating the answer. We knew very little details, so we made some assumptions: the hydrazine is in a spherically-symmetric expanding shell, both spacecraft are stationary relative to each other, and gravity is not a factor. In a few minutes we came up with a quick, dirty, back-of-the-envelope calculation that indicated that it would be very unlikely for any hydrazine to contact the optics and, if any did, it would be a very small amount (on the order of a few molecules).
My friend relayed our calculations and results to his girlfriend, who was surprised: she didn’t actually expect anyone to bother working stuff out. After a short while, she informed us that our calculations had been passed upstream to NASA for their consideration.
Very cool.
Of course, our calculations were almost certainly unrealistic. Even so, they provide a starting point.
Yes, physics students actually do this sort of thing in their spare time.