Planetary orbital changes

The Flartree-Fock model represents only a very minute improvement over the independent orbit model for the solar system, since the planetary orbits do not cross. The effect of a planet inside the Earth s orbit corresponds to adding its mass to the Sun, while the effect of the spread-out mass of a planet outside the Earth s orbit is zero. The Flartree-Fock model for the Earth thus consists of increasing the Sun s effective mass with that of Mercury and Venus, i.e. a change of only 0.0003%. For the solar system there is thus very little difference between totally neglecting the planetary interactions and taking the average effect into account. 

The orbits of double stars, where the sizes of the orbits have been determined, provide the only information we have about the masses of stars other than the Sun. Close doublestars will become decidedly non-spherical because of tidal distortion and/or rapid rotation, which produces effects analogous to those described above for close artificial planetary satellites. Also, such stars often have gas streaming from their tidal and equatorial bulges, which can transfer mass from one star to the other, or can even eject it completely out of the system. Such effects are suspected to be present in close doublestars where their period of revolution is found to be changing. 

In 1930, Tombaugh discovered Pluto, the outermost known planet (Reaves, 1997 Marcialis, 1997). Several authors have derived the radius of Pluto with very small uncertainties unfortunately, the derived values do not overlap. Consequently, only a broad range can be quoted (1145 to 1200 km) within which the true radius of Pluto may fall (Tholen Buie, 1997). Pluto is by far the smallest planet of our Solar System it is even smaller than many planetary satellites. Pluto s orbit is highly eccentric and inclined by more than 17° to the ecliptic plane (Malhotra Williams, 1997). At perihelion (29.7 AU), Pluto is closer to the Sun than Neptune (30.1 AU), and at aphelion it reaches a heliocentric distance of almost 50 AU. Pluto s orbital period, 248.35 sidereal years, is locked in a 3 2 ratio with that of Neptune (Cohen Hubbard, 1965). The axis of rotation is nearly in the orbital plane therefore, this small planet undergoes rather complex seasonal changes (Spencer et al., 1997). Malhotra (1993, 1999) provides interesting discussions of the possible evolution of Pluto s orbit and that of other planets (see also Stem etai, 1997). 

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