From: wgw@vax.oxford.ac.uk
Newsgroups: sci.astro
Subject: Swift_tuttle's orbit
Date: 11 Nov 92 16:51:26 GMT
Organization: Oxford University VAX 6620


          The following should put all of the recent hoo-hah over 
          comet P/Swift-Tuttle's next apparition into perspective.


The 2126 apparition of P/Swift-Tuttle
=====================================

   As a result of the uncertainty in deriving the nongravitational 
parameters (A1 and A2) and their possible time-dependence, much has been
made of the possibility that P/Swift-Tuttle represents a threat to the
Earth at its next apparition in 2126.   The intersection of the comet's
orbit and that of the Earth at the former's descending node gives rise
to the annual Perseid meteor shower.  In 2126 the Earth will intersect
the shower maximum on August 14.3, when it will have  r = 1.01338 au.
For the comet to be at its descending node ( r = 1.01001 au ) at the
same time requires that it have a perihelion passage time of July 26.43.
Thus, to represent a collison threat to the Earth, the comet's time of
perihelion passage has to be delayed by 20 days with respect to the 
purely gravitational integration (details below).  An integration including
the effects of the nongravitational (outgassing) terms, which is a better 
fit to the previous two apparitions, brings the time of perihelion passage 
forward.  From the A2 = -0.035 integration below we see that the comet will
be at its descending node on 2126 July 18.5, at which time it will be 0.45au
from the Earth.



Details of RADAU integrations of P/Swift-Tuttle's orbit
=======================================================

Starting elements taken from IAUC 5636  (epoch 1992 Dec. 4.0).

J2000 throughout.   Planetary starting positions and velocities from DE200.
Perturbations by Venus -> Neptune included ; mass of Mercury added to that
of the Sun  (other runs including all nine planets explicitly show that the
error in time of perihelion passage in 2126 does not exceed  0.1 day  when
using this approximation).

All runs were done on the VAX 6000/620 of Oxford University Computer Service.

For the nongrav run no attempt was made to optimise the values of A1 and A2, 
the values used being chosen to approximate the probable times of perihelion 
passage in 1737 and 1862.


N-body results  ( no outgassing effects considered )
==============

     epoch          q          e         w         asc         i         nu

  2308960.500   0.976371   0.962033   152.8388   139.5157   113.5590   254.7898
  2355360.500   0.979797   0.961454   152.6993   139.4771   113.6880   235.7157
  2401760.500   0.962661   0.962659   152.7805   139.3815   113.5693   129.3062
* 2448960.500   0.958120   0.963590   153.0130   139.4560   113.4300   347.8336
  2497760.500   0.956312   0.963880   153.1270   139.6201   113.4081    12.4523



Nongrav results   ( outgassing effects included : A1 = 0 , A2 = -0.035 )
===============

     epoch          q          e         w         asc         i         nu

  2308960.500   0.976695   0.962003   152.8302   139.5090   113.5599   253.4023
  2355360.500   0.980095   0.961423   152.6924   139.4716   113.6843   238.4297
  2401760.500   0.962645   0.962661   152.7804   139.3821   113.5691   129.5740
* 2448960.500   0.958120   0.963590   153.0130   139.4560   113.4300   347.8336
  2497760.500   0.956460   0.963875   153.1236   139.6194   113.4039    22.1289

    ( * indicates starting values )
    (    nu is the true anomaly   )


Thus, for these osculating epochs, we find the following times of successive 
perihelion passages (Gregorian calendar) for the comet,

                epoch             T (n-body)         T (non-grav)

           1609 Aug. 14.0      1610 Jan. 20.98     1610 Jan. 27.94    
           1736 Aug. 28.0      1737 July  7.12     1737 June  5.00
           1863 Sept 12.0      1862 Aug. 28.33     1862 Aug. 23.66
        *  1992 Dec.  4.0                1992 Dec. 12.32
           2126 July 15.0      2126 July 6.50      2126 June 29.64


By way of comparison, Brian Marsden (A.J. vol 78, p.654-662; 1973) gives 
the time of perihelion passage for 1862 as August 23.41.    For 1737 he 
gives a range of solutions with perihelion passage times varying in the 
range June 3.5 to June 16.4.


NOTE
====
   It should be stressed that all of the foregoing is based entirely on
the osculating elements given on IAUC 5636 (dated 1992 October 15) which
have presumably already been improved upon.



        Graeme Waddington                        wgw @ vax.ox.ac.uk