I have averaged together all of your measurements to get the following values:

• Period of inner moon = 44 hours (1.8 days)
• Period of outer moon = 398 hours (16.6 days)
• Ratio of periods = 9.2 (actual value is 9.47)

• Ratio of orbital distance = 4.5 (but wide variation in data with some measurements nonsense - actual value = 4.47)

Is there a relation between orbital period and orbital distance when quantities are measured in ratios? (Galileo uses ratios in all his physics experiments).

Hypothesis:

D^x = P^y

(4.5)^x = 9.2^y

where X and Y are integers

Let's try different values for X,Y and plug in.

X=1; Y=1 --> 4.5 = 9.2 (NO)

X=2; Y=1 --> 20 = 9 (NO)

X=2; Y=2 --> 20 = 81 (NO)

X=3; Y=2 --> 91 = 84 (Pretty close)

Suppose we then got more accurate measurements:

D = 4.47; P = 9.47

4.47³ = 89.31

9.47² = 89.78

What about eclipse times?

Most noticed that the inner most moon eclipse time is less than the outermost moon. During eclipse of either moon, the physical difference traveled is approximately equal.

Since the inner most eclipse time is shorter than the outer one, what does this tell you about orbital speeds?

Week 5