I pulled this stuff together and deposit it here mostly for the sake
of future reference. However, if any of Ye Gentle Readership would
care to check through the calculations, I'd appreciate any feedback.
Note that the SM-3 traveled about as far horizontally as it did
vertically to reach USA-193. Does this imply it has sufficient
propulsive oomph to reach significantly higher altitudes than 250 km
if fired on a more vertical trajectory?
++++++++++++++++++++
Data
++++++++++++++++++++
Annotations on DoD video frame showing flame coming from launcher on
Lake Erie but no missile visible as yet. Missile visibly out of
launcher a few frames later. Video apparently shot from an airplane.
(http://www.youtube.com/watch?v=OhdHkoal31o)
052:03:36:47.36 [Presumably Zulu time on Day 52 of 2008, February 21
2008]
Alt 26463 FT [Aircraft altitude]
N 23 35.30 [Aircraft latitude, apparently degrees and decimal
minutes]
W 163 06.30 [Aircraft longitude]
GSPD 263 KTS [Aircraft ground speed]
HDG 152 [Aircraft heading]
TGT_BR 236.9 [Bearing of target (i.e., the Lake Erie) from the
aircraft]
TGT_EL -20.5 [Target elevation (depression) from the aircraft]
====================
http://www.omaha.com/index.php?u_page=2798&u_sid=10272556
Published Sunday | March 2, 2008
Weeks of intense work paved way for StratCom's direct hit
BY TIM ELFRINK
© 2008 OMAHA WORLD-HERALD
[EXCERPT]
Following the missile's telemetry [after launch], the graphic showed
the SM-3 arcing gracefully toward the satellite. A clock ticked down
the approximately 170 seconds from launch to impact.
====================
Satellite orbital elements for about three hours before the intercept
from http://www.satobs.org/seesat/Feb-2008/0441.html:
USA-193
1 29651U 06057A 08052.01700749 .00286558 00000-0 31619-3 0 04
2 29651 58.4796 26.1000 0011038 100.0855 260.1493 16.08904727 04
++++++++++++++++++++
Calculations
++++++++++++++++++++
Range to cruiser from sub-aircraft point = 26,463/tan(20.5) = 70,779
ft = 21,573 meters.
====================
Cruiser is at 21.573 km from 23d 35.30m N, 163d 06.30m W on a bearing
of 236.9 degrees, giving the coordinates of the launch point: 23d 28m
56s N, 163d 16m 56s W (23.4822 N, 163.2822 W) using
http://www.movable-type.co.uk/scripts/latlong.html
====================
Intercept time is approximately 170 seconds after 03:26:47.5Z, or
03:29:37.5 .
====================
From the orbital elements of the satellite and the time of intercept:
Approximate sub-intercept point: 21.15 N, 163.76 W
Intercept altitude: 249 km.
