Most of you were able to measure the orbital period of the outermost moon to pretty high accuracy. Measurements of the inner moon were a little less accurate.

Average results for those that actually made the measurement on the simulation rather than looking up the answer (what possible point is there to that?) in terms of ratios

• Moon 4 to Moon 1: 9.4
• Moon 3 to Moon 1: 4.0

The accuracy of the orbital radius was determined mostly by your measuring device. In this case, looking up the answers wouldn't have helped since even I know you don't have a kilometer measuring device in class. Measurements using "jupiter widths" were less accurate than those that used ruled paper. Approximate ratios are

• Moon 4 to Moon 1: 4.5
• Moon 3 to Moon 1: 2.5

Notice the ratios are different between orbital periods and orbital distances but the ratio of orbital periods is almost twice the ratio of orbital distances.

More precisely:

We would like to satisfy this relation.

P ^x = D ^y

Let's try random combination of x = 1,2,3 and y = 1,2,3

We already know that x=y=1 doesn't work.

Let's try x=1; y = 2

9.4 = (4.5)² nope

What about x = 2 y = 3

(9.4)² = 88
(4.5)³ = 91 wow, pretty close: let's try this for the other system.

(4.0)² = 16
(2.5)³ = 15.6 close enough

The square of the ratio of orbital periods equals the cube of the ratio of orbital distances This is Kepler's Third Law !!!