function ydot = hel_eqm (t, y)
% heliocentric equations of motion
% with planetary perturbations
% Battin's f(q) formulation
% input
% t = current simulation time (days)
% output
% ydot = first order equations of motion
% Orbital Mechanics with Matlab
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global xmu jdtcm
% current julian date (relative to tcm event)
jdate = jdtcm + t;
% distance from sun to spacecraft
rsun2sc = norm(y(1:3));
rrsun2sc = -xmu(1) / rsun2sc^3;
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% calculate planetary position vectors
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nplanets = 6;
for i = 1:1:nplanets
svplanet = jplephem(jdate, i, 11);
rplanet = svplanet(1:3);
for j = 1:1:3
rp(i, j) = rplanet(j);
end
end
% compute planet-centered position vector of spacecraft
for i = 1:1:nplanets
rp2sc(i, 1) = y(1) - rp(i, 1);
rp2sc(i, 2) = y(2) - rp(i, 2);
rp2sc(i, 3) = y(3) - rp(i, 3);
end
% compute f(q) functions for each planet
for k = 1:1:nplanets
q(k) = dot(y(1:3), y(1:3) - 2.0 * rp(k, :)') / dot(rp(k, :), rp(k, :));
f(k) = q(k) * ((3.0 + 3.0 * q(k) + q(k) * q(k)) / (1.0 + (1.0 + q(k))^1.5));
d3(k) = norm(rp2sc(k, :)) * norm(rp2sc(k, :)) * norm(rp2sc(k, :));
end
% compute planetary perturbations
for j = 1:1:3
accp(j) = 0.0;
for k = 1:1:nplanets
accp(j) = accp(j) - xmu(k + 1) * (y(j) + f(k) * rp(k, j)) / d3(k);
end
end
% compute integration vector
ydot = [ y(4)
y(5)
y(6)
accp(1) + y(1) * rrsun2sc
accp(2) + y(2) * rrsun2sc
accp(3) + y(3) * rrsun2sc];