In 1610, Galileo used his telescope to discover four prominent moons around Jupi
ID: 1468819 • Letter: I
Question
In 1610, Galileo used his telescope to discover four prominent moons around Jupiter. Their mean orbital radii a and periods T are as follows 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. 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. 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. 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
According to kepler's third law
T^2 =4*pi^2*a^3/(GM)
A) given that a = 4.22*10^8 m
G is the universal gravitational constant
M is the mass of the planet = ?
T = 1.77 days = 1.77*24*60*60 = 152928 S
mass of the Jupiter is M = 4*pi^2*a^3/(G*T^2) = (4*3.142*3.142*4.22*4.22*4.22*10^24)/(6.67*10^-11*152928*152928) = 1.902*10^27 kg
B) similarly M = 4*pi^2*a^3/(G*T^2) = (4*3.142*3.142*6.71^3*10^24)/(6.67*10^-11*(3.55*24*60*60)^2) = 1.902*10^27 kg
C) M = 4*pi^2*a^3/(G*T^2) = (4*3.142*3.142*10.7^3*10^24)/(6.67*10^-11*(7.16*24*60*60)^2) = 1.902*10^27 kg
D) M = 4*pi^2*a^3/(G*T^2) = (4*3.142*3.142*18.8^3*10^24)/(6.67*10^-11*(16.7*24*60*60)^2) = 1.902*10^27 kg