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Orbital_Elem.m
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Orbital_Elem.m
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function [sm, ecc, RA, Inclination, ArgPer, TrueA, T] = Orbital_Elem(Y)
%{
This function computes the classical orbital elements (coe)
from vector Y
mu - gravitational parameter (km^3/s^2)
R - position vector in the geocentric equatorial frame (km)
V - velocity vector in the geocentric equatorial frame (km)
r, v - the magnitudes of R and V
vr - radial velocity component (km/s)
H - the angular momentum vector (km^2/s)
h - the magnitude of H (km^2/s)
incl - inclination of the orbit (rad)
N - the node line vector (km^2/s)
n - the magnitude of N
cp - cross product of N and R
RA - right ascension of the ascending node (rad)
E - eccentricity vector
e - eccentricity (magnitude of E)
eps - a small number below which the eccentricity is considered
to be zero
w - argument of perigee (rad)
TA - true anomaly (rad)
sm - semimajor axis (km)
%}
mu = 398600.4;
% i=0;
% for i = 1:1:1440
%
for k = 1:1:3
% R(k) = Eph(i, k 1)/1000;
% V(k) = Eph(i, k 4)/1000;
R(k) = Y(k)/1000;
V(k) = Y(k 3)/1000;
end
eps = 1.e-10;
r = norm(R);
v = norm(V);
vr = dot(R,V)/r;
H = cross(R,V);
h = norm(H);
�lculate Inclination
incl = acos(H(3)/h);
Inclination = rad2deg(incl);
�lculate Node Line vector
ab = [ 0 , 0, 1];
N = cross(ab,H);
n = norm(N);
�lculate right ascension
if n ~= 0
Rasc = acos(N(1)/n);
if N(2) < 0
Rasc = 2*pi - Rasc;
end
else
Rasc = 0;
end
Ra = rad2deg(Rasc);
RA = Ra;
�lculate eccentricity
E = 1/mu*((v^2 - mu/r)*R - r*vr*V);
e = norm(E);
ecc = e;
�lculate Argument of Perigee
if n ~= 0
if e > eps
w = acos(dot(N,E)/n/e);
if E(3) < 0
w = 2*pi - w;
end
else
w = 0;
end
else
w = 0;
end
W = rad2deg(w);
ArgPer = W ;
�lculate true anomaly
if e > eps
TA = acos(dot(E,R)/e/r);
if vr < 0
TA = 2*pi - TA;
end
else
cp = cross(N,R);
if cp(3) >= 0
TA = acos(dot(N,R)/n/r);
else
TA = 2*pi - acos(dot(N,R)/n/r);
end
end
TrueAnom = rad2deg(TA);
TrueA = TrueAnom;
%(sm < 0 for a hyperbola):
sm = h^2/mu/(1 - e^2);
�lculate period
T = 2*pi/sqrt(mu)*sm^1.5;
end