Mass of Jupiter In 1610 Galileo used his telescope to discover the four prominen
ID: 1466432 • Letter: M
Question
Mass of Jupiter In 1610 Galileo used his telescope to discover the four prominent moons of Jupiter. Their mean orbital radii, a, and periods, T are given in this table.
Use these data and Kepler’s third law to find the mass of Jupiter (take the average of the four values). Compare to Jupiter’s actual mass.
Name
a (×108 m)
T (days)
Io
4.2170
1.769
Europa
6.7103
3.551
Ganymede
10.704
7.155
Callisto
18.827
16.69
Name
a (×108 m)
T (days)
Io
4.2170
1.769
Europa
6.7103
3.551
Ganymede
10.704
7.155
Callisto
18.827
16.69
Explanation / Answer
According to Kepler’s third law , M = (4^2 r^3)/Gp^2
Where r =
Taking Average of Values ,
r = (4.2170 + 6.7103 + 10.704 + 18.827) /4 * 10^8 m
r = 10.1145 * 10^8 m
G = 6.67 x 10-11 m3/kg-sec2.
p = (1.769 + 3.551 + 7.155 + 16.69) / 4 * 24 *3600 s
p = 7.29125 * 24 *3600 s
p = 629964 s
Substituing Values -
M = 4^2 r^3)/Gp^2
M = (4 * 3.14^2 * (10.1145 * 10^8)^3 )/ (6.67 * 10^-11 * (629964)^2)
M = 1.542 * 10^27 Kg
Actual Mass of Jupiter = 1.898 * 10^27 Kg