Kepler's third law predicts for a planet of orbital semi-major axis and period

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Data analysis and model fitting in the laboratory · Data analysis and model fitting in the laboratory

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Problem

Kepler's third law predicts

T^2 \propto a^3

for a planet of orbital semi-major axis

a

and period

T

. The table gives

a

in astronomical units (AU) and

T

in years for four planets. Mercury:

a=0.39

T=0.241

. Earth:

a=1.00

T=1.00

. Jupiter:

a=5.20

T=11.86

. Neptune:

a=30.07

T=164.8

. ((a)) State which combination of linear, semi-logarithmic and log-log axes will turn this expected relation into a straight line, and justify the choice from the functional form of Kepler's third law. ((b)) Predict the slope that a straight line through the plotted data would have on those axes.

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