Astronomy Lab. Problem: How can you calculate the mass of Uranus using 3-5 of its moons? . General information.
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Problem: How can you calculate the mass of Uranus using 3-5 of its moons?
Where R=radius from the planet using a2 +b2=c2
a is the distance on the x-axis and b is the distance on the y-axis.
P is the rotational period. You are given how many degrees the moon travels per second and need to find how many seconds in 360o.
G is a constant. 6.67x 1011
M or mass is going to be in kg X1025
Measure the distance from the center of Uranus to a moon in the North or south direction using it orbital path.
For my example, I got 8.4cm . Measure the distance from the center of Uranus to a moon in the east or west direction using its orbital path. For my example I have 5.9cm.
R therefore = 10.26 cm
Let say the moon moves at 2.23 degrees per second. How many seconds does it take to get around Uranus?
P therefore = 161.4349776 sec
7.21E14m3 = 6.67E11m3/s2 x MkgE25
2.61 E4 s2 4Π2
(2.76E10 m3/s2 )(39.48)= 6.67E11m3/s2 xMkgE25
MkgE25 =(1.090719348E12 m3/s2 )/ (6.67E11 m3/s2 )
M= 1.64 E25 (Now do this for four moon. Get an average and then check to see how close you are to the actual mass of Uranus. Do % error only if you are off by magnitude of 10.