The following pages are from the book
"Solar System Dynamics" by C.D. Murray and S.F. Dermott.
In the homework you have done some datafitting to derive
a Kepler law. Here is an other example of a data fitting
problem in astronomy:
the Titius-Brade Law:
Brade's law was that the distance d from the sun in astronimical
units from the sun to each of the six known planets is
d = 0.4 + 0.3 wn, n=-infinity, 0,1,2,4,5
The law predicted an other planet for n=3 and 6 etc.
brode claimed a planet at n=3. After Uranus was found
close to n=6, the law was considered a success and called
Titius Bode law.
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