The Europan Day Problem

[fenderzilla]

I’ve got a math problem of sorts that I was wondering about and unable to solve. Maybe some seasoned math major can give me a hand.

Imagine I’m colonizing a moon of some planet – let’s say, oh, Europa. Europa orbits once every 3.5 days and is tidally locked to Jupiter, which means a day on Europa is 3.5 days long from dawn to dawn, with the odd Jovian eclipse. Jupiter won’t move in the sky because Europa is tidally locked to it, so a Jovian eclipse would only happen once a Europan day. Jupiter takes up 1/15th of the Europan sky (just assume the surface is flat, not too far-fetched on Europa), and so Jovian eclipses would last about 2.8 hours ((3.5*12)/15=2.8).

Now let’s suppose, by some sort of magic, I managed to “tidally unlock†Europa and speed its day up to the same approximate speed of an earth day – this would mean making it turn 3.5 times per orbit. The sun would move across the sky once every 24 earth hours, but how fast would Jupiter move? How often would Jovian eclipses be then? How long would they be? That is my question.

To help you answer it, I have made this table which better states the above data.

Give it your best shot! I actually haven’t figured this out myself, so I’m not just testing you. I’m relying on you.

Edited October 23, 2013 by fenderzilla