Question

The data of the 2 moons of Earth and Saturn are shown below. If possible, then find the mean orbital radius of the moon of Saturn; if not possible, then explain why.
Period Mean Orbital Radius
EArth's moon 1 unit 3 units
Saturn's moon 2 units ???

Answer 1

@theEric can you help me please? I know you're good :)

Answer 2

I actually don't know this stuff, sorry! I could only make an educated guess. Do you have any thoughts at the moment?

Answer 3

Have you learned about Kepler's Third law?

Answer 4

It's about Kepler's 3rd Law \(\Large \frac{T^2}{R^3}\), the part where I'm confused is when my teacher said that "sometimes this is law is not applicable if the central object is different". I really don't what it means. So for this problem I'm not sure if this is possible or not.

Answer 5

yeah!

*know

Answer 6

Okay! :)

Answer 7

If i'll apply Kepler's law, i'll get \[\sqrt[3]{108}\]

Answer 8

Okay! Based on what your teacher said, it sounds like it's not applicable. I can't be sure, of course, but that's what it seems like. Our moon is orbiting Earth, and the other moon is orbiting Saturn, and they're very different.. So maybe it doesn't apply!

Answer 9

that's what i've been thinking :)
BUT according to the law, the ratio between the period of a planet and it's radius will be the same for all the planets...?

:/

Answer 10

Like I said, I don't know these things. But, based on what your teacher said, that ratio will hold for all the planets in the solar system because they are all orbitting the same thing - the sun.

Answer 11

orbiting*

Answer 12

And it makes sense because the mass will be different between the Earth and Saturn.

Answer 13

Ahhh , i get it!
thank you so much! (^_^)

Answer 14

If the ratio held true for everything ever, we'd have a number for it. But it's not on the Wikipedia page, so there can't be one :P

Answer 15

You're welcome! :)

Answer 16

Glad you got it!

Answer 17

Kepler's Third Law is not applicable when the orbiting bodies in question are orbiting different, uhm, bodies. Using Kepler's Third law formula to calculate the constant:\[constant=\frac{ T ^{2} }{ R ^{3} }\]for Saturn's moons, I get roughly 1.4 *10^-16. For our moon, however, the constant is approximately 0.0019. You could likewise calculate the constant for the planets of our solar system and get a third different constant.

Why is the case? Consider Kepler's 1st law which says that orbits are elliptical and as such have some ellipticity. That ellipticity is a function of the masses of the two bodies under consideration: the body being orbited and the orbiting body. Your data lacks mass information.

Answer 18

@PsiSquared thank you for the additional explanation :)