Jupiter\'s satellite Europa orbits Jupiter with a period of 3.55 C at an average
ID: 1265388 • Letter: J
Question
Jupiter's satellite Europa orbits Jupiter with a period of 3.55 C at an average orbital radius of 6.71 X 10^8 m. (a) Assuming that the orbit Is circular, determine the mass of Jupiter from the data given. (b) Another satellite of Jupiter, Callisto, orbits at an average radius of 1.88 x 10^9 m with an orbital period of 16.7 d. Show that these data are consistent with an inverse-square force law for gravity (Note: Do NOT use the value of G anywhere In Part (b)). (Do this on paper. Your instructor may ask you to turn in this work.)Explanation / Answer
a) T = 3.55 days = 3.55*24*60*60 = 306720 s
Apply,time periode T = 2*pi*r^(3/2)/sqrt(G*M)
T^2 = 4*pi^2*r^3/(G*M)
M = 4*pi^2*r^3/(G*T^2)
= 4*pi*(6.71*10^8)^3/(6.67*10^-11*(306720)^2)
= 6.05*10^26 kg
b)
in the first case, r1^3/T1^2 = (6.71*10^8)^3/(306720)^2
= 3.21*10^15
in the second case, T2 = 16.7 days = 16.7*24*60*60 = 1442880 s
r2^3/T^2 = (1.88*10^9)^3/(1442880)^2
= 3.19*10^15
in both cases the ratios r^3/T^2 is approximately a constnt. Hence, inverse square law is proved.
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