A Guided Tour of Planetary Interiors
Abstract
We explore the gravitational dynamics of falling through planetary interiors. Two trajectory classes are considered: a straight cord between two surface points, and the brachistochrone path that minimizes the falling time between two points. The times taken to fall along these paths, and the shapes of the brachistochrone paths, are examined for the Moon, Mars, Earth, Saturn, and the Sun, based on models of their interiors. A toy model of the internal structure, a powerlaw gravitational field, characterizes the dynamics with one parameter, the exponent of the powerlaw, with values from 2 for a pointmass to +1 for a uniform sphere. Smaller celestial bodies behave like a uniform sphere, while larger bodies begin to approximate pointmasses, consistent with an effective exponent describing their interior gravity.
 Publication:

arXiv eprints
 Pub Date:
 May 2015
 DOI:
 10.48550/arXiv.1505.05894
 arXiv:
 arXiv:1505.05894
 Bibcode:
 2015arXiv150505894K
 Keywords:

 Physics  Popular Physics
 EPrint:
 6 pages, 5 figures