- #1
trekkie1701c
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Homework Statement
"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."
Homework Equations
(Ta/Tb)^2=(Ra/Rb)^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.