Superbird A sun-sat-obs angle

Jim Varney (jvarney@mail2.quiknet.com)
Sun, 29 Sep 1996 11:26:32 -0700

Last night (09/29 UT) I observed Superbird A.  Saw flashes begin 
at 0321 UT and end at 0329 UT.

There are tabs in here.  Hope they don't mess up everyone's mail
readers :)

Superbird A from Sacramento
Date,Time,Az,El,Slant Range(mi)
29-Sep-96 3:21:00 226.1775 31.7232 23960.6
r(s),r(e),r(z) vector: 14112.2621 -14704.5674 12598.8910

29-Sep-96 3:29:00 226.0861 31.5760 23969.1
r(s),r(e),r(z) vector: 14163.1316 -14710.5269 12550.9434

Sun from Sacramento (no refraction)
Date,Time,Az,El,Slant Range(mi)
29-Sep-96 3:21:00 281.6167 -18.1167 93004755
r(s),r(e),r(z) vector: -17799288.2 -86583470.5 -28920104.4

29-Sep-96 3:29:00 282.9833 -19.6500 93004859
r(s),r(e),r(z) vector: -19678330.4 -85349498.6 -31275073.4

Flash begins - sat/obs/sun angle

	cos angle = A dot B / mag A * mag B
	A dot B	657623016442.7
	mag A	23960.64059	check
	mag B	93004755.1	check
	cos angle	0.295102866
	angle(rad)	1.27123315
	angle(deg)	72.83629426

Flash ends - sat/obs/sun angle

	cos angle = A dot B / mag A * mag B

	A dot B	584297633230.8
	mag A	23969.14849	check
	mag B	93004859.1	check
	cos angle	0.262105348
	angle(r)	1.305593149
	angle(deg)	74.80497721

Use law of sines to calculate obs/sat/sun angles

a / sin A = b / sin B
cos B = (c^2 + a^2 - b^2) / 2ca


Flash begin			
	a^2	8.64857E+15
	a	92997687.04	Sun-sat distance
	cos B	-0.294867646
	B(r)	1.87011333
>>>>    B(deg)	107.149601	obs-sat-sun angle

Flash end
	a^2	8.64874E+15
	a	92998579.51	Sun-sat distance
	cos B	-0.299102134
	B(r)	1.874547901
>>>>    B(deg)	107.4036832	obs-sat-sun angle

-----------------------------------------

These numbers "feel" right: flashing starts at 107.15 degrees
and ends at 107.40 degress.  This shows that the glinting is very
sensitive to the observer-sat-sun angle, which is what we would
expect.

The next step would be to calculate the angle between r-bar
(the sat-geocenter vector) and the vector normal to the reflecting
solar panels.  This would generate some ideas about the orientation
of the satellite with respect to the orbit.

Thanks to Robert Sheaffer for sharing this object with SeeSat.
It's been a great source of (fun) time-wasting on exercises
like this :)

 -- Jim


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Jim Varney       | 121^ 23' 54" W,  38^ 27' 28" N   |           Sacramento, CA
Member, SeeSat-L |           Elev. 31 ft.           |                         
Member, Sacramento Valley Astronomical Society      |jvarney@mail2.quiknet.com
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