To Explain the World

The Discovery of Modern Science

Steven Weinberg, Bvtn 509 Wei, 2015 Harper Collins


Steven Weinberg is a theoretician who does physics with mathematics, not measurement. This book is about the development of mathematical explanations for observations, not how those observations are made or validated, nor how experimental apparatus is constructed and calibrated.

I only skimmed the book. It whetted my interest in how Tycho and Kepler performed their measurements and especially how they estimated the errors in their imprecise pre-telescope pre-photography pre-standards astronomical measurements. A companion book should be written by an experimentalist instead of a pure theoretician.


A footnote on page 168 may be result from narrow theoretical focus:

The underlined text above is incorrect. The radius r of a Keplerian orbit (with a semimajor axis of a and an eccentricity of e ) varies with angle \theta by the formula:

\Large r ~ = ~ \LARGE { { a ( 1 - e )^2 } \over { 1 + e \cos( \theta ) } }

This equation can be derived from the conservation of energy and angular momentum in an inverse-square gravity field, and is well known to astronomers and space engineers. For Mars, the semimajor axis a is 2.279392e11 meters or 1.523679 AU and the eccentricity e is 0.0934. At perihelion (closest to the Sun), \theta = 0, so the perihelion radius is:

\Large r_{p} ~ = ~ \LARGE { { a ( 1 - e )^2 } \over { 1 + e \cos( 0 ) } } \Large ~ = ~ \LARGE { { a ( 1 - e )^2 } \over { 1 + e } } \large ~ = ~ a ( 1 - e ) ~ \approx ~ 2.067e11 m or 1.3814 AU

At aphelion (farthest from the Sun), \theta = \pi, so the aphelion radius is:

\Large r_{a} ~ = ~ \LARGE { { a ( 1 - e )^2 } \over { 1 + e \cos( \pi ) } } \Large ~ = ~ \LARGE { { a ( 1 - e )^2 } \over { 1 - e } } \large ~ = ~ a ( 1 + e ) ~ \approx ~ 2.492e11 m or 1.6660 AU

The ratio of these distances is ( 1 + e ) / ( 1 - e ) \approx 1.206. About 20%, not ½%.


Page 170 has an amusing quote from page 24 of Donahue's translation of Kepler's Astronomia Nova:

Advice for Idiots.

But whoever is too stupid to understand astronomical science, or too weak to believe Copernicus without affecting his faith, I would advise him that, having dismissed astronomical studies and having damned whatever philosophical opinions he pleases, he mind his own business and betake himself home to scratch in his own dirt patch.

ExplainWorld (last edited 2016-09-04 21:07:20 by KeithLofstrom)