The New Cosmos by Albrecht Unsöld, Bodo Baschek, R. C. Smith, Carl A. Hein

By Albrecht Unsöld, Bodo Baschek, R. C. Smith, Carl A. Hein (auth.)

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Consider a particle of mass m taken to infinity (r ~ 00) from rest at distance r from the Sun (mt ) under the action of the gravitational force -Gmtmlr2. The work done is equal to its potential energy Epolr), where Epot(r) = -G Joomtm dr r -2- r = mtm r -G - - . 28) Since no work is done in any trans verse motion, we see that the expression is independent of the choiee of integration path. Referred to unit mass, we call cp(r) = -Gmt/r the potential at distance r from the Sun. This is one of the fundamental concepts of celestial mechanics as weIl as of theoretical physies.

With the Sun as origin (heliocentric) let r p, rEbe the position vectors of a planet and of the Earth. 38) - rE. Let us look back from here for a moment to the geocentric view of Ptolemy: (1) In the case of the outer planets, for example Mars ct , we begin by drawing the vector r p out from the Earth and letting it rotate in the same way as it originally rotated about the Sun. 7. Motion of an outer planet (Mars) and an inner planet (Venus) on the celestial sphere, represented heliocentrically and geocentrically.

2) Elliptic paths of shortperiod comets. The aphelia are concentrated near the orbits of the major UJupiter ? ) Uranus WNeptune B Pluto Symbol W. 1. 5. Mean orbital radii (semimajor axes) 01 the planets. The lengths of the ares eorrespond to the mean motion in one (terrestrial) year. 15. planets, particularly Jupiter. Such cometary families may have arisen by the "capture" of long-period comets by Jupiter or some other planet. 6 AU almost equal to a? 2 AU) and i = 15°. 30 years. The comets 30 5.

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