An invariant relation in the elliptic restricted problem of three bodies. III - Asteroids

Details An invariant relation in the elliptic restricted problem of three bodies. III - Asteroids An invariant relation in the elliptic restricted problem of three bodies. III - Asteroids

Jul 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979aj.....84.1072v&link_type=abstract

Astronomical Journal, vol. 84, July 1979, p. 1072-1078.

Mathematics

Asteroid Belts, Elliptical Orbits, Jupiter (Planet), Mass Ratios, Planetary Mass, Three Body Problem, Eccentric Orbits, Functions (Mathematics), Orbital Elements, Planet Ephemerides, Planetary Orbits, Solar System, Sun, Jupiter, Asteroids, Kirkwood Gaps, Mass, Mars, Perturbations, Orbits, Ephemeris, Eccentricity, Period, Three Body Problem, Trojan Asteroids, Ceres Asteroid, Pallas Asteroid, Juno Asteroid, Vesta Asteroid

Scientific paper

An invariant relation is reduced to a simpler form valid in the case of the Sun-Jupiter-asteroid system. The terms neglected contain the Jupiter-Sun mass ratio as a factor and are of the second order in eccentricities, or linear in the eccentricities and of the second order in the relative inclination. The relation contains a nonintegrated part reducible to elementary functions only at certain commensurabilities of mean motions, the analysis of which leads to the well-known ratios corresponding to the gaps in the asteroidal distribution. All calculations are carried out with respect to the ecliptic and equinox of 1950, taking the time of Jupiter's perihelion passage on 1 March 1928 as the initial epoch. The Jacobi constants of the asteroids Ceres, Palas, Juno, and Vesta are found to be 3.3196, 3.0521, 3.3048, and 3.5427, respectively, with an error of + or - 0.0002.

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