Nongravitational Forces and C/2002 C1 Graeme Waddington

As a result of normalization errors all the values for the nongravitational parameters given in my April TA note are incorrect. This unfortunate state of affairs was a result of transcription and editing errors incurred when incorporating the nongravitational force expressions from a mediaeval Fortran version of the n-body integrator program into the current C version. Fortunately, these errors do not adversely affect the idle speculations presented in the last note.

By way of example, the values for the extreme and middle columns of the first table in the last TA note should be replaced by the following correct values,

As in the last note, these are based on integrations of the MPEC 2002-F55 (March 25) orbit. For comparison, the latest orbit solutions derived from the current apparition alone - by MPC, JPL and Nakano - all give values for the nongravitational parameters around A1 = 3 and A2 = 1. Extrapolating these solutions backwards results in a previous apparition in 1667. By including nongravitational effects in his 1661-2002 linked solution Nakano (April 15) initially found A1 = 1.76 and A2 = -0.0129, leading to perihelion passages of 1661 Jan 29, 1273 Feb 23, 877 July 7 and 452 Oct 23. A recent revision of this by Nakano (April 26) gives A1 = 1.64 and A2 = -0.0163 - resulting in a sequence of previous perihelia of 1661 Jan 29, 1273 Feb 7, 877 Feb 23, and 458 July 31.

So what exactly are these nongravitational parameters A1 and A2 ?

When dealing with cometary nongravitational accelerations it is now standard practice to follow the precepts laid down by Marsden, Sekanina and Yeomans in 1973 (AJ 78, 211-225) by adding to the equations of motion an additional acceleration of

A1 * g(r) * R + A2 * g(r) * T + A3 * g(r) * N

where R, T and N are unit vectors outward along the heliocentric radius vector, tangential to the orbit in the direction of motion and normal to the orbit respectively. A simplification is usually made by setting the component normal to the orbital plane to zero since the uncertainty in any derived average value of A3 tends to be larger than its actual value. The unit for the parameters A1, A2, and A3 is taken to be 10^-8 AU.day^-2 unless otherwise specified.

The function g(r) is based on the expected vaporization of water-ice from an isothermal sphere and depends only on the distance of the comet from the Sun (and so is symmetrical around perihelion). This obviously has limitations when the outgassing rate, as indicated by the light curve, peaks away from perihelion. Even so, the values of the nongravitational parameters derived from using this expresssion can give us an indication of the precession of the nucleus; a notable case being that of 22P/Kopff, whose A2 values from apparition to apparition show a trend indicating that its rotation axis lay in its orbital plane in the early 1930’s.