|MadSci Network: Astronomy|
Don-- Well, the masses and diameters (actually, radii) do play a role in the length of time a moon takes to revolve around a planet. The only problem with your question is that it takes the moon closer to 27 days to orbit the earth. This is where we get our months from. Let's see if I can explain a little more in-depth than that now. First, I'll push some numbers up here for you. mass of Mars: 6.42 x 10^23 kg mass of Phobos: 1.08 x 10^16 kg mass of earth: 5.97 x 10^24 kg mass of Moon: 7.35 x 10^22 kg radius of Mars: 3397 km radius of Phobos: 11 km radius of earth: 6378 km radius of Moon: 1738 km Time Phobos takes to orbit Mars: 0.318910 days Time Moon takes to orbit earth: 27.321582 days The average distance from the center of Mars to the (approximate, as it is not spherical) center of Phobos is 9378 km. The distance from the center of earth to the center of the Moon is 384400 km. Now that that's out of the way, the fun part comes in...the equations. You probably saw this coming. =) Fg = G (m1 x m2)/d^2 where Fg is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the objects. Using this equation (I'll spare you the number crunching) the force of attraction between Mars and Phobos is 5.26 x 10^15 N, and between earth and the Moon is 1.98 x 10^20 N. Next equation: v = sqrt(rg) where v is the velocity of the satellite, r is the radius of its orbit (or distance between the centers) and g is the acceleration of gravity. The velocity of Phobos is 2137 m/s and the velocity of the Moon is 1017 m/s. Now we're beginning to see why Phobos orbits in less time... The last value we'd need to find the time of orbit is the length of the orbit. This one's C = 2(pi)r, where C is the circumference of the orbit (true, the orbits aren't circular, but we're working with rough averages here anyway). Therefore, the length of Phobos's orbit is 58900 km, and of the Moon's orbit, 2420000 km. Using these (this has been long enough, hasn't it? heh), we can find the time it takes each body to orbit. Note that the numbers won't be perfect, because there's been quite a bit of rounding involved, and these numbers can't necessarily be trusted with as many decimals as they've been taken out to. t = d/v, where t is time, d is distance, and v is velocity. Plug the numbers into this equation, and the time it takes Phobos to orbit Mars is 7.66 h (0.3190046622 days...looks pretty close to the accepted value), and the time it takes the Moon to orbit the earth is 661 h (27.54106122 days, again close enough to be within an acceptable margin of error). Hope that answers your question! I got my information here from http://seds.lpl.arizona.edu/nineplanets/nineplanets/data1.html and from telnet://ssd.jpl.nasa.gov:6775. Your browser may or may not be able to view the second address. You may instead need a telnet client to get the information there. Justin Miller email@example.com
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