Re: HST close approaches

Bjoern Gimle (b_gimle@algonet.se)
Mon, 24 Mar 1997 07:16:36 +0100

Russell Eberst <eberst@cableinet.co.uk> wrote:
...
>>HST
>>1 20580U 90037B   97080.05727574 +.00000377 +00000-0 +25237-4 0 09658
>>2 20580 028.4675 240.1986 0014574 358.9811 001.0726 14.86427821179933
...
>With the revs/day for Cosmos1666 being very similar to the figure for HST,
>this indicates that if there is one close approach between the two objects
>as calculated for 3/24/97 at 04:42, then there must be other close approaches
>every half-orbit (that's about every 48 minutes). It would be interesting to 
>see calculation of the 2 series of close approaches which occur at the two
>orbinodes. (I just invented that word, for the point where two orbits cross)

I used these two elsets:
Cosmos 1666                                      623 x 596 km
1 15889U 85058A   97079.11427531  .00000278  00000-0  28772-4 0  4669
2 15889  82.5246 290.8691 0019773 314.0859  45.8729 14.86283170632244
Cosmos 1666                                      623 x 596 km
1 15889U 85058A   97080.12412792  .00000252  00000-0  25809-4 0  4733
2 15889  82.5247 289.9198 0019748 310.7573  49.1928 14.86283453632392

MM differs from HST's by about 0.0014 revs/day, or 9 seconds, but the
inclinations, and hence the progression of the perigees and the ascending
nodes differ much more. 

MM is the inverse of the anomalistic(perigee-perigee) period, which has
little to do with the 'orbinodes'. Since HST's perigee advances by
about 9.5 degrees/day, and C*1666's regresses by 3.6 degrees/day,
the nodal periods differ by an additional 3+ minutes, making the total
difference 228.3 seconds/day.

The orbinodes are located near the northern and southern apex of HST's
orbit, and since the ascending nodes regress by 6.5 and 1.0 degrees/day,
this effectively moves the orbinodes 5.5 degrees East each day, or
about 4.5 degrees along HST's orbit, adding another minute to the 
separation. These are the reasons you see the minimum separations
increase so quickly :

 3/24/1997 11:05:06.9 15889 Cosmos 1666   64.7     +4.35
 3/24/1997 11:53:29.6 15889 Cosmos 1666   39.4     +4.38
 3/24/1997 12:41:59.1 15889 Cosmos 1666    2.4     +4.41
 3/24/1997 13:30:21.7 15889 Cosmos 1666   30.8     +4.45
 3/24/1997 14:18:51.2 15889 Cosmos 1666   66.3     +4.48
 3/24/1997 15:07:13.8 15889 Cosmos 1666   94.3     +4.52
(from the first elset)

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