(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

"If Ganymede, one of Jupiter's moons, has a pariod of 7.15 days, how many uits are there in it's orbital radius? Use the information given in Example Problem 1."

Example Problem:

"Galileo measured the orbital sizes of Jupiter's moons using the diameter of Jupiter as a unit of measure. He found that Io, the closest moon to Jupiter, had a period of 1.8 days and was 4.2 units from the center of Jupiter. Callisto, the fourth moon from Jupiter, had a period of 16.7 days. Using the same units that Galileo used, predict Callisto's distance from Jupiter."

2. Relevant equations

(Ta/Tb)^2=(Ra/Rb)^3

3. The attempt at a solution

My solution to the example problem:

Ta = 1.8

Tb = 16.7

Ra = 4.2

(1.8/16.7)^2 = (4.2/Rb)^3

.0116 = 74.088(Rb^3) (Dividing 1.8 by 16.2 and squaring, and cubing 4.2 and Rb)

.2264Rb=4.2 (Multiplying by Rb^3 and then taking the cubed root of everything)

Rb=18.5512 (Dividing by .2264)

I considered that since the book gave an answer of 19, that I was close enough, considering the book's want to round everything.

For the problem I'm having difficulty with, I did this:

Ta = 1.8

Tb = 7.15

Ra = 4.2

(1.8/7.15)^2 = (4.2/Rb)^3

.2517^2=4.2^3/Rb^3 (1.8 divided by 7.15)

.0634=4.2^3/Rb^3 (Squaring previous answer)

.0634(Rb^3)=4.2^3 (Multiplying by Rb^3)

.3987Rb=4.2 (Taking the cubed root of both sides)

Rb=10.5342 (Dividing by .3987)

The book, however, lists an answer of exactly 4. I can't figure out where I messed up.

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# Orbit physics homework

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