FSW-1 / 93-63H / 22870 decay
Mike McCants (mike@comshare.com)
Thu, 29 Feb 1996 21:35:22 -0600
Bjorn writes:
>If this is correct, I would be interested to know where
>more accurate atmospheric model parameters for predictions
>are available!
That's a good question. It would seem that NPOE does have a good
atmospheric model if we knew what parameters to give it.
I have copied atmospheric density values for 105Km to 350Km from the
book "Satellite Environment Handbook" from the page titled "Atmospheric
Parameters as a Function of Altitude for a Low-Density Atmosphere
(Nighttime Near Sunspot Minimum)" (Stanford University Press, 1965).
Then I carefully "fit" 4 pieces of the atmosphere (105-130Km), (130-160Km),
(160-220Km), (220-350Km) to polynomials. Here is a simple Fortran
program that shows the density and the fitting polynomials:
DIMENSION BASE(4),REFDEN(4),A(4),B(4),C(4)
DIMENSION IHGT(15), DENS(15)
DATA IHGT/105,110,120,130,140,150,160,180,200,220,240,
1 260,280,300,350/
DATA DENS/2.14E-10,9.86E-11,2.47E-11,7.64E-12,2.87E-12,1.30E-12,
1 6.70E-13,2.30E-13,9.71E-14,4.57E-14,2.33E-14,1.26E-14,7.02E-15,
2 4.02E-15,1.09E-15/
DATA BASE/105.0,130.0,160.0,220.0/
DATA REFDEN/2.14E-10,7.64E-12,6.70E-13,4.57E-14/
DATA A/0.16062,0.10925,0.06023,0.0355/
DATA B/-.001139,-.001231,-.0003796,-.000098/
DATA C/0.00000185,0.0000098,0.000002027,0.00000038/
CC
DO 100 I=1,15
HGT=IHGT(I)
IF (HGT .LT. BASE(2)) THEN
J=1
ELSE IF (HGT .LT. BASE(3)) THEN
J=2
ELSE IF (HGT .LT. BASE(4)) THEN
J=3
ELSE
J=4
ENDIF
DHGT=HGT-BASE(J)
PRDDNS=REFDEN(J)*EXP(-((C(J)*DHGT+B(J))*DHGT+A(J))*DHGT)
100 WRITE(6,102) IHGT(I),DENS(I),PRDDNS
102 FORMAT(I4,2E11.3)
END
Here is the output from the program:
Hgt(Km) G/cm3 Predicted
105 0.214E-09 0.214E-09
110 0.986E-10 0.986E-10
120 0.247E-10 0.247E-10
130 0.764E-11 0.764E-11
140 0.287E-11 0.287E-11
150 0.130E-11 0.130E-11
160 0.670E-12 0.670E-12
180 0.230E-12 0.230E-12
200 0.971E-13 0.971E-13
220 0.457E-13 0.457E-13
240 0.233E-13 0.233E-13
260 0.126E-13 0.126E-13
280 0.702E-14 0.712E-14
300 0.402E-14 0.412E-14
350 0.109E-14 0.103E-14
Bjorn writes:
>According to this integration, the decay would occcur on Mar.11 (96071.6)
>If adjusted for the 96054-96058 ndot2 factor, I get Mar.10 at noon.
I have put this density model into my numerical integration (of the X,Y,Z
coordinates and velocities) and come up with re-entry about March 11.3.
(But then the orbit plane does go over my head in darkness at March 11.3,
so my program would naturally generate a re-entry prediction for that time.)
The part of the orbit in darkness goes from +56 to -56, so it looks like
almost everyone has a chance.
Since this is an eccentric orbit until March 10 and the perigee does not
decrease very much until then, I cannot see how it can possibly re-enter
before then. As usual, March 9/10/11 is a weekend, so we will not get
any updated elements from OIG unless they enter them by hand. The
last regular elset should be about 68.5 or so. But after re-entry on
March 11, we should get the last elset (71.3) on Monday afternoon.
This program generates south-north equator crossing times and a "pseudo-
mean motion" based on those times. (There is no variation of density
from daytime to nighttime or from equator to pole (except height above
the elipsoid).)
1 22870U 93063H 96060.44121675 .01353185 10569-4 15729-3 0 4770
2 22870 56.4201 70.8136 0250031 54.4695 307.9383 15.86450931116225
X Y Z Time R Hgt Perg EqMM
2166 6225 0 60.44122 6591.5 213.3
2198 6214 0 60.50422 6591.6 213.4 148.8 15.873
2452 6119 0 61.00795 6592.6 214.5 148.8 15.888
2948 5898 0 62.01400 6594.3 216.2 148.7 15.918
3425 5635 0 63.01809 6595.5 217.3 148.6 15.950
3880 5333 0 64.02013 6595.9 217.8 148.4 15.983
4309 4992 0 65.02004 6595.6 217.4 148.0 16.018
4709 4616 0 66.01767 6594.2 216.0 147.5 16.056
5075 4205 0 67.01284 6591.5 213.3 146.8 16.098
5406 3762 0 68.00528 6587.0 208.9 145.7 16.144
5714 3260 0 69.05630 6579.3 201.1 144.1 16.204
5958 2760 0 70.04150 6567.1 188.9 141.5 16.277
5972 2728 0 70.10292 6566.1 187.9 141.2 16.282
5999 2663 0 70.22569 6563.9 185.7 140.7 16.294
6024 2598 0 70.34836 6561.4 183.3 140.2 16.306
6049 2533 0 70.47094 6558.8 180.6 139.6 16.320
6073 2467 0 70.59341 6555.7 177.6 138.9 16.334
6096 2401 0 70.71576 6552.3 174.2 138.1 16.350
6117 2334 0 70.83799 6548.4 170.2 137.1 16.368
6138 2267 0 70.96005 6543.6 165.5 135.9 16.390
6147 2233 0 71.02102 6540.8 162.7 135.2 16.402
6156 2199 0 71.08194 6537.7 159.5 134.4 16.415
6164 2165 0 71.14280 6533.9 155.8 133.4 16.431
6171 2130 0 71.20359 6529.3 151.2 132.1 16.450
6177 2095 0 71.26430 6523.2 145.1 130.5 16.474
6179 2058 0 71.32487 6513.7 135.5 128.1 16.508
6157 2014 0 71.38516 6478.4 100.3 100.3 16.587
6089 2188 281 71.38566 6477.1 99.0 99.0
Here is output from my "other" program:
REV XNO XN1 XN2 NODE WO XM PRGEE E
0 60.440816 15.864509 0.013532 70.815 54.469 305.650 145.12 0.025003
1 60.503816 15.866215 0.013579 70.521 54.609 305.510 145.08 0.024940
9 61.007571 15.880072 0.013967 68.169 55.728 304.390 144.73 0.024424
25 62.013728 15.908978 0.014819 63.465 57.967 302.150 144.00 0.023350
41 63.017999 15.939650 0.015790 58.761 60.207 299.910 143.23 0.022211
57 64.020272 15.972340 0.016906 54.057 62.446 297.670 142.41 0.020997
73 65.020418 16.007357 0.018204 49.353 64.685 295.430 141.53 0.019699
89 66.018289 16.045091 0.019731 44.648 66.924 293.190 140.59 0.018300
105 67.013710 16.086042 0.021558 39.944 69.164 290.950 139.58 0.016783
121 68.006475 16.130863 0.023783 35.240 71.403 288.709 138.47 0.015125
137 68.996331 16.180439 0.026555 30.536 73.642 286.469 137.26 0.013292
138 69.058094 16.183721 0.026751 30.242 73.782 286.329 137.18 0.013171
154 70.044518 16.239708 0.030364 25.537 76.021 284.089 135.81 0.011104
170 71.027289 16.304177 0.036461 20.833 78.261 281.849 133.89 0.008781
171 71.088577 16.308649 0.037067 20.539 78.401 281.709 133.72 0.008625
172 71.149849 16.313194 0.037713 20.245 78.540 281.569 133.54 0.008468
About a 10 minute error at this point due to drag too small.
173 71.211103 16.317817 0.038404 19.951 78.680 281.429 133.36 0.008309
174 71.272339 16.322523 0.039145 19.657 78.820 281.289 133.16 0.008148
175 71.333557 16.327319 0.039940 19.363 78.960 281.149 132.96 0.007985
176 71.394757 16.332211 0.040795 19.069 79.100 281.009 132.74 0.007820
177 71.455938 16.337205 0.041717 18.775 79.240 280.869 132.52 0.007652
This program cannot predict the re-entry time since it cannot properly
compensate for the tremendous increase in drag when the orbit becomes
more circular around March 10. But it does give a guess at the orbital
elements before that time.
----
I also have a prediction of March 14 for the TSS tether (assuming
there is not a break which would lessen the drag).
Mike McCants
mike@comshare.com