Question

Planet	Period (days)	Mean distance (x 106km)
Mercury	88	57.9
Venus	225	108.2
Earth	365	149.6
Mars	687	227.9
Jupiter	4,329	778.1
Saturn	10,753	1428.2
Uranus	30,660	2837.9
Neptune	60,150	4488.9

Plot the period T verses the mean distance r using these data.

Assuming a relationship of the form T=Cr^a, determine the parameters C and a using the given data and the transformed data r' = ln(r). Are these models the same? Do they seem reasonable?

Answer 1

The plot of period versus distance is shown below.

The heading of the plot shows a curve fit equation for the best fit.

The equation is in the form

Here, C = 0.1982

a = 1.5015

Now, the data is plotted in logarithmic scale for distance and period.

The plot is found to be linear with slope = 0.979.

The relation between period and radius, given by Kepler's law is

So,

So, the graph 1 is reasonable.

Taking logarithm on both sides,

So, this graph should be linear.