\magnification = 1095
\vsize = 9.0 true in
\hsize = 6.7 true in
\voffset = .5 true in
\baselineskip = 1 pc
\parskip = 1 pc
\parindent = 2 pc
\font\large = cmr10 scaled\magstep2
\setbox0 =\hbox{"\kern-.15cm{.}\kern.04cm}
\def\qd{\copy0\/}


\write 0 {10.  RADIATION PRESSURE REFLECTANCE MODEL 
\noexpand\dotfill\the\pageno\noexpand\break}
\noindent{\large CHAPTER 10}  {\bf RADIATION PRESSURE REFLECTANCE MODEL}
\bigskip

     For a near-Earth satellite the solar radiation pressure
acceleration,  is given by:
$$\ddot{\bar{r}}=\kappa\biggl[{A\over R}\biggr]^2C_R{a\over m}
{\vec{R}\over R},$$
where 

\item{$\kappa$}= $4.560\times 10^{-6}$ newtons/m$^2$ (1367 watts/m$^2$),
\vskip-1pc
\item{$A$} = astronomical unit in meters,
\vskip-1pc
\item{$R$} = heliocentric radius vector to the satellite,
\vskip-1pc
\item{$a$} = cross-sectional area (m$^2$) of the satellite
              perpendicular to $\vec{R}$,
\vskip-1pc
\item{$ m$} = satellite mass,
\vskip-1pc
\item{$C_R$} = reflectivity coefficient, usually an adjusted       
             parameter.


     The radiation pressure due to backscatter from the Earth is
ignored.  The model for the Earth's and Moon's shadows should
include the umbra and the penumbra (Haley, 1973).

\halign{\kern4pc#\hfil&\kern1pc\hfil#\cr\cr
                         Earth Radius&    6402 km\cr
                         Moon Radius &    1738 km\cr
                         Solar Radius&  696000 km\cr}


\write 0 {\indent Global Positioning System \noexpand\dotfill\the
\pageno\noexpand\break}
\noindent {\bf Global Positioning System}

\nobreak

     For GPS satellites, the solar radiation pressure models T10
(for Block I) and T20 (for Block II and IIA) of Fliegel {\it et al}.
(1992), Gallini and Fliegel (1995) and Fliegel and Gallini (1996)
are recommended.  These models include thermal reradiation. A
preliminary model for the forthcoming Block IIR satellites,
which may begin to replace Block II/IIA as early as January 1997,
is given here as T30.

     Those models provide the $X$ and $Z$
components of the total nominal solar pressure force as functions 
of the angle $B$ between the Sun and the $+Z$ axis of the satellite.
For Block I, II, and IIA, 0 $<$ B $<$ 180 degrees, but Block IIR,
0 $<$ B $<$ 360 degrees (no ``noon turn").

\noindent The model formulae for T10 are (angles in radians): 
$$X = -4.55\sin B + 0.08\sin(2B + 0.9) - 0.06\cos(4B +0.08) + 0.08,$$
$$Z = -4.54 \cos B + 0.20 \sin (2B - 0.3) - 0.03 \sin 4B.$$
The model formulae for T20 are:
$$X = -8.96 \sin B + 0.16 \sin 3B + 0.10 \sin 5B - 0.07 \sin 7B,$$
$$Z = -8.43 \cos B.$$
The model formulae for T30 (Fliegel, 1995) are:
$$X = -11.0 \sin B - 0.2  \sin 3B + 0.2 \sin 5B,$$
$$Z = -11.3 \cos B +0.1 \cos 3B + 0.2 \cos 5B.$$
In both cases the units are $10^{-5}$ N.

\noindent{\bf References}

\nobreak

\item{}\kern-2pc
Fliegel, H. F., Gallini, T. E., and Swift, E., 1992, ``Global
     Positioning System Radiation Force Models for Geodetic
     Applications," {\it J. Geophys. Res.}, {\bf 97}, No. B1, pp. 
     559--568. 

\item{}\kern-2pc
Fliegel, H. F. and Gallini, T. E., 1996, ``Solar Force Modelling of
     Block IIR Global Positioning System Satellites," {\it J. of 
     Spacecraft and Rockets}, {\bf 33}, No. 6, pp. 863--866.

\item{}\kern-2pc
Gallini, T. E. and Fliegel, H. F., 1995, {\it The Generalized Solar
      Force Model}, Aerospace Report No. TOR-95(5473)-2, The Aerospace
      Corporation, El Segundo, CA.

\item{}\kern-2pc
Haley, D., 1973, {\it Solar Radiation Pressure Calculations in the
     Geodyn Program}, EG\&G Report 008-73, Prepared for NASA Goddard 
     Space Flight Center.

\vfil\eject
