An Introduction to Modern Astrophysics · Problem 19.2

The Planetary System — Carroll & Ostlie

Physics — Astrophysics · bodes-rule-planetary-distances

Problem

A second version of Bode's rule (the Blagg--Richardson formulation) is given by

r_n = r_0 A^n,

where

n

is the number of the planet in order from the Sun outward (e.g.,

n = 1

for Mercury) and

r_0

and

A

are constants. (a) Plot the position of each planet and that of Ceres on a semilog graph of

\log_{10} r_n

vs.

n

. (b) Draw the best-fit straight line through the data on your graph and determine the constants

r_0

and

A

. (c) Compare the ``predictions'' of your fit with the actual values for each planet by calculating the relative error,

\frac{r_n - r_{\text{actual}}}{r_{\text{actual}}}.