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: $$\begin{array}{lcc} {\text { Name }} & a\left(10^{8} \mathrm{~m}\right) & T \text { (days) } \\ \hline \text { Io } & 4.22 & 1.77 \\ \text { Europa } & 6.71 & 3.55 \\ \text { Ganymede } & 10.7 & 7.16 \\ \text { Callisto } & 18.8 & 16.7 \\ \hline \end{array}$$ (a) Plot $\log a(y$ axis $)$ against $\log T(x$ axis $)$ and show that you get a straight line. (b) Measure the slope of the line and compare it with the value that you expect from Kepler's third law. (c) Find the mass of Jupiter from the intercept of this line with the $y$ axis.

          In 1610, Galileo used his telescope to discover four prominent moons around Jupiter. Their mean orbital radii $a$ and periods $T$ are as follows:
$$\begin{array}{lcc}
{\text { Name }} & a\left(10^{8} \mathrm{~m}\right) & T \text { (days) } \\
\hline \text { Io } & 4.22 & 1.77 \\
\text { Europa } & 6.71 & 3.55 \\
\text { Ganymede } & 10.7 & 7.16 \\
\text { Callisto } & 18.8 & 16.7 \\
\hline
\end{array}$$
(a) Plot $\log a(y$ axis $)$ against $\log T(x$ axis $)$ and show that you get a straight line. (b) Measure the slope of the line and compare it with the value that you expect from Kepler's third law. (c) Find the mass of Jupiter from the intercept of this line with the $y$ axis.

Added by Alfredo D.

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