Expert: Tom Whiting - 10/6/2009

Question
when you look at jupiter through a telescope why do the moons orbit so fast around  jupiter(my thinking is jupiter is a large planet so why wouldn't the orbit be slower) . I was told this is an optical illusion of distance but this does not satify my understanding.

Answer
Hi Sean,
According to Kepler's laws of motion, orbital time is based on distance from the primary planet, (or more specifically, a baricenter point)... and take into account the high mass of Jupiter.  Since Jupiter is many times more massive than the Earth, the Galilean moons are actually further from their primary then our moon is from the Earth, because Jupiter's more mass gives Jupiter a much deeper 'gravitational well' that the Galilean moons have to orbit in, so they have to travel much faster (much shorter period than our moon)  to maintain orbit around Jupiter.

There is no optical illusion or trick here, simply obeying Kepler's laws of motion.  If Io were even closer to Jupiter, it would have to travel even faster around it's orbit, and thus have an even shorter period than 1.77 days.  If it were more distant, than it would have a longer period and travel even slower around Jupiter.
So each Galilean moon has it's own period relative to the distance from Jupiter.  But in the case of Jupiter's moons, there is an orbital resonance that's been established over the millenia...one to two to four, for the 3 closest moons, see
http://www.deepfly.org/TheNeighborhood/GalileanMoons.html

When our moon first formed up some 4 billion years ago, it was closer, so it had a period
shorter than 29.6 days, which it has today. As the moon slowly migrates farther from the
Earth over the millenia, it's period will also grow longer too.  So this is all natural
occurances.
In binary stars, if they are close, they might orbit each other in just several years...in fact
with contact binaries, the star's might orbit each other in a matter of a few days.
Then there are binary stars so far apart that it takes thousands of years to perform one orbit.
So it's actually a distance thingy in a given gravitational field. (It's all based on Kepler's third law where the period squared is proportional to the distance cubed...just like the planets going around the sun).
Clear Skies,
Tom Whiting
Erie, PA