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Mean Local Time of the Ascending Node
by David Eagle
Determines the relationship between mean local time of the ascending node and RAAN.
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| gast2 (tjdh, tjdl, k)
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function gst = gast2 (tjdh, tjdl, k)
% this function computes the greenwich sidereal time
% (either mean or apparent) at julian date tjdh + tjdl
% nutation parameters from function nod
% input
% tjdh = julian date, high-order part
% tjdl = julian date, low-order part
% julian date may be split at any point, but for
% highest precision, set tjdh to be the integral part of
% the julian date, and set tjdl to be the fractional part
% k = time selection code
% set k=0 for greenwich mean sidereal time
% set k=1 for greenwich apparent sidereal time
% output
% gst = greenwich (mean or apparent) sidereal time in hours
% Orbital Mechanics with Matlab
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
seccon = 206264.8062470964;
t0 = 2451545.0;
tjd = tjdh + tjdl;
th = (tjdh - t0) / 36525;
tl = tjdl / 36525.0;
t = th + tl;
t2 = t * t;
t3 = t2 * t;
% for apparent sidereal time, obtain equation of the equinoxes
eqeq = 0.0;
if (k == 1)
% obtain nutation parameters in seconds of arc
[psi, eps] = nod(tjd);
% compute mean obliquity of the ecliptic in seconds of arc
obm = 84381.4480 - 46.8150 * t - 0.00059 * t2 + 0.001813 * t3;
% compute true obliquity of the ecliptic in seconds of arc
obt = obm + eps;
% compute equation of the equinoxes in seconds of time
eqeq = psi / 15.0 * cos (obt / seccon);
end
st = eqeq - 6.2e-6 * t3 + 0.093104 * t2 + 67310.54841 ...
+ 8640184.812866 * tl + 3155760000 * tl ...
+ 8640184.812866 * th + 3155760000 * th;
gst = mod(st / 3600.0, 24.0);
if (gst < 0.0)
gst = gst + 24;
end
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