Approaches of the Parabolic Comets to the Outer Planets
Abstract
Formulae for computing the minimum distances between two heliocentric orbits are derived. Then, applying these formulae to cometary and planetary orbits the parabolic and near-parabolic comets were examined in two aspects: 1) the possibility of approach to the four outer planets and 2) the real approaches. It appears that 50% of comets (what is in agreement with the approximate theoretical estimate) have a possibility to approach the outer planets closer than to 1 a.u. The possibility of approach for 494 comets is distributed as follows: 180 to Jupiter, 98 to Saturn, 52 to Uranus and 32 to Neptune. The list of 139 comets which could pass through the sphere of predominance of the outer planets is given. There are known 62 real approaches closer than to 2 a.u. The cases of 14 approaches closer than to 1 a.u. (12 to Jupiter and 2 to Uranus) were investigated in detail by numerical integration of the equations of motion of those comets; tables showing the evolution of the heliocentric orbit of each comet during the approach are given. The closest approach occurred in the case of Parisian Comet (1759 III) which in 1758 approached Jupiter to within 0.054 a.u. Even such a deep penetration in the sphere of predominance of Jupiter does not cause any radical changes in the comet's orbit. The problem of capture is also considered. It is shown by numerical integration that a fictitious parabolic comet whose perihelion lies almost on the orbit of Jupiter, can be captured by Jupiter and may become a short-period comet. Even a highly hyperbolic orbit (with an eccentricity equal to 1.5) can be also changed into a short-period one. Tales and diagrams showing the evolution of heliocentric orbits of these fictitious comets during the approach to Jupiter are enclosed. All the computations were carried out on the GIER digital computer.
- Publication:
-
Acta Astronomica
- Pub Date:
- 1968
- Bibcode:
- 1968AcA....18..171S