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3. In Starry Messenger (Sidereus Nuncius 1610), Galileo reported his discoveries of four moons around Jupiter with their mean orbital radii $a$ and period $T$ given in Table 1. (a) (5 marks) Plot $\log a$ (y-axis) vs $\log T$ (x-axis) and show that you can fit a straight line to the data. (b) (5 marks) Measure the slope of the line and compare it with the value that you expected from Kepler's 3rd law. (c) (5 marks) Find the mass of Jupiter from the intercept of this line with y-axis. Name $a$ ($10^8$ m) $T$ (days) Io 4.22 1.77 Europa 6.71 3.55 Ganymede 10.7 7.16 Callisto 18.8 16.7 Table 1

          3. In Starry Messenger (Sidereus Nuncius 1610), Galileo reported his discoveries of four moons around Jupiter with their mean orbital radii $a$ and period $T$ given in Table 1.
(a) (5 marks) Plot $\log a$ (y-axis) vs $\log T$ (x-axis) and show that you can fit a straight line to the data.
(b) (5 marks) Measure the slope of the line and compare it with the value that you expected from Kepler's 3rd law.
(c) (5 marks) Find the mass of Jupiter from the intercept of this line with y-axis.
Name
$a$ ($10^8$ m)
$T$ (days)
Io
4.22
1.77
Europa
6.71
3.55
Ganymede
10.7
7.16
Callisto
18.8
16.7
Table 1

3. In Starry Messenger (Sidereus Nuncius 1610), Galileo reported his discoveries of four moons around Jupiter with their mean orbital radii a and period T given in Table 1.
(a) (5 marks) Plot log a (y-axis) vs log T (x-axis) and show that you can fit a straight line to the data.
(b) (5 marks) Measure the slope of the line and compare it with the value that you expected from Kepler's 3rd law.
(c) (5 marks) Find the mass of Jupiter from the intercept of this line with y-axis.
Name
a (10^8 m)
T (days)
Io
4.22
1.77
Europa
6.71
3.55
Ganymede
10.7
7.16
Callisto
18.8
16.7
Table 1

Added by Anna C.

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