Question

Europa, a moon of Jupiter has an orbital diameter of 1.34x10^9m and a period of 3.55 days. What is the mass of Jupiter?
d=1.34x10^9m
T=3.55days = 30672s
M=?
r=71492000m
rm=6.7x10^8
r-total=7414492000m

r^3/t^2=GM/4pi^2
741492000^3/306720^2=6.67X10^-11(M)/4pi^2
I got m=2.56x10^27
But I don't think this is correct when I looked up the mass of jupiter it was actually 1898.6x10^24kg. What did i do wrong? I can't figure it out. Thanks in advance for your help.

Answer 1

kuiperbelt2003 gave an excellent explanation on Yahoo:

you will equate gravitational force with centripetal force:
GMm/r^2=mv^2/r
or
M=v^2 r/G
G=newtonian grav cst = 6.67x10^(-11)
M=mass of jupiter
m=mass of Europa
r=radius of orbit=1.34x10^9m/2=6.7x10^8m
v=velocity
knowing that europa has a period of 3.55days=3.07x10^5 secs, we can find the velocity by knowing
velocity=circumference of orbit/time = 2 pi r /period
velocity = 2 pi 6.7x10^8m/3.07x10^5 s
velocity = 1.37x10^4 m/s
so, we have:
M= v^2 r/G =
(1.37x10^4)^2(6.7x10^8)/ 6.67x10^(-11))
M=1.8x10^27kg

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