Problem Set 5 ASTR 502 F1

Points: Nominal 8

(6 pt) 1. Use "log-log" paper (given out in class or you can download below) to plot the Periods versus Distances of at least 6 satellites of Jupiter, Uranus, Neptune, and/or Saturn (choose two different host planets!). In Space Update, the data can be gotten from selecting "Solar System" and then choosing a planet. Then click on "Moons" - that will give you a list of moons. Once you click on a moon in the list of moons, the data will show at the bottom. Use "Orbital Period" (in earth days) for the period (y axis). For the Y-axis (distance) use the "orbit scale" (in planetary radii) and then multiply by the radius of the host planet.
PLAN AHEAD - some of the orbits are fractional earth days, so you'll probably need to start your y-axis label at 0.1 instead of 1. If you use a satellite list from the book or elsewhere, that's OK, but be sure to label your axes!

You can use this log-log paper to plot on. "Titan" for Saturn is plotted as a sample.

Be sure that you have enough "cycles" on the log paper to cover all your selected satellites. You probably want a page that is taller than it is wide, if you put the period on the y-axis.

Once you have plotted each satellite as a point, see if you can draw a line through the points. Is it a good line (it should be)? If not, go back and check to see if you've used the same units for all points.

What's the value of the period for distance = 1 km? This can be used to find the mass of the host planet. How does the slope differ between the two planets you chose? The intercept?

(2 pt) 2. Use the value of the intercept above to calculate from your data, the ratio of the masses of the two planets you chose. How does this compare to the accepted value? Hint: use Kepler's 3rd law and Newton's Law of Gravitation. What does the value of the intercept correspond to? See the "topics and terms" notes #28.

Law of Gravitation: F = -GMm/r2
Kepler's third law P2 = K a3
P = Period = 2 pi a / v
So, if r = a, solve for K = ? ________________
here is the value for G but it will divide out so you don't need it...
G = gravitation constant = = 6.67 E-11 (N-m2/kg2)

Last revised: 10/5/2015