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## Homework Statement

Finally, develop models for only the four innermost planets and the four Galilean moons by reducing all the orbital radii by a factor that makes the orbital radius of the first planet or moon equal to one. Give possible reasons for the similarities and/or differences in two models.

## Homework Equations

x = position of planets relative to sun

y = orbital radii

Mercury Venus Earth Mars Asteriod Jupiter Saturn Uranus Neptune Pluto

x 1 2 3 4 5 6 7 8 9 10

y 57.9 108.2 149.6 227.9 T 778.3 1249 2871 4504 5914

x = position of galilean moons relative to jupiter

y = orbital radii

Lo Europa Ganymede Callisto

X 5 6 7 8

Y 422 670.9 1070 1883

## The Attempt at a Solution

This math portfolio asks us to find an equation relating x and y. I find this by plotting the points, and the best fit line. The equation is exponential. I solve for T (the orbital raidus of asteriod), T = 469 millions of kilometers.

For this last question, I don't understand what they mean by the four "innermost" planets...And finding a factor (a common factor?)....

The model for case A is: 1.19x^3.71

The model for case B is: 1.18^3.54

Also, is there another way, other than the graphical method, to find the equation relating x and y??