If your answer is similar to mine, then is wrong. Each one is graded individuall
ID: 1600784 • Letter: I
Question
If your answer is similar to mine, then is wrong. Each one is graded individually.
In 1610, Galileo used his telescope to discover four prominent moons around Jupiter. Their mean orbital radii a and periods T are as follows: (a) Io has a mean orbital radius of 4.22 times 10^8 m and a period of 1.77 days. Find the mass of Jupiter from this information. (b) Europa has a mean orbital radius of 6.71 times 10^8 m and a period of 3.55 days. Find the mass of Jupiter from this information. (c) Ganymede has a mean orbital radius of 10.7 times 10^8 m and a period of 7.16 days. Find the mass of Jupiter from this information. (d) Callisto has a mean orbital radius of 18.8 times 10^8 m and a period of 16.7 days. Find the mass of Jupiter from this information.Explanation / Answer
Time period T = (2*pi*r^3/2)/sqrt(GM)
(a)
T = 1.77 days = 1.77*24*60*60 s
G = 6.67*10^-11 N m^2/kg^2
r = 4.22*10^8 m
1.77*24*60*60 = (2*pi*(4.22*10^8)^(3/2)/sqrt(6.67*10^-11*M)
M = 1.9*10^27 kg
(b)
T = 3.55 days = 3.55*24*60*60 s
G = 6.67*10^-11 N m^2/kg^2
r = 6.71*10^8 m
3.55*24*60*60 = (2*pi*(6.71*10^8)^(3/2)/sqrt(6.67*10^-11*M)
M = 1.9*10^27 kg
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(c)
T = 7.16 days = 7.16*24*60*60 s
G = 6.67*10^-11 N m^2/kg^2
r = 10.7*10^8 m
7.16*24*60*60 = (2*pi*(10.7*10^8)^(3/2)/sqrt(6.67*10^-11*M)
M = 1.9*10^27 kg
(d)
T = 16.7 days = 16.7*24*60*60 s
G = 6.67*10^-11 N m^2/kg^2
r = 18.8*10^8 m
16.7*24*60*60 = (2*pi*(18.8*10^8)^(3/2)/sqrt(6.67*10^-11*M)
M = 1.9*10^27 kg