The Cause of the Residuals in the Motion of Halley's Comet

Abstract

A remarkable periodicity in the residuals in perihelion time of Halley's Comet was recently attributed by Brady to the action of a trans-plutonian planet. The main idea of this paper is that, on the contrary, this periodicity can be shown to be an inherent property of the 3-body configuration Sun–Jupiter–Halley. A second-order equation with periodic coefficients is derived, which governs the behaviour of any residual in the system. The natural period of this equation, found by Hill's (1886) method of infinite determinant, and verified by numerical integration, turns out to be nearly the same as the observed value of about 600 yr. This idea explains naturally why Brady's synthetic residuals, obtained through the omission of Pluto terms, showed the same period and not the period of Pluto. It is also shown that, (i) the residuals practically vanish when Brady's calculations incorporating his empirical term ∊ 6 are used, (ii) the latter term is mathematically equivalent to the outstanding deceleration of Halley's Comet found in a previous paper, and (iii) this deceleration corresponds to a value of +2.43 × 10 −7 for Marsden's non-gravitational parameter A2 , comparable to the known values for other comets. It is thereby inferred that what actuates the residuals is the same non-gravitational force (the jet effect) that has been the subject of much discussion in recent years. In the case of Halley, the non-gravitational force appears to have changed little over the last 22 rounds, or 1700 yr.