# Compute and simulate a repeat ground track orbit

The repeat ground track solver is a numerical routine and notice that it is not exact. The simulation includes the J2 perturbation. See also: RepeatGroundTrack, RHSGeoJ2, GroundTrack

```%--------------------------------------------------------------------------
%   Copyright (c) 2014 Princeton Satellite Systems, Inc.
%--------------------------------------------------------------------------

% Desired characteristics of repeat track
% 15 orbits per day at 66 degrees inclination
%--------------------------------------------
g      = struct;
g.P0   = 15;
g.Q0   = 1;
g.inc  = 66*(pi/180);
g.ecc  = 0.01;
g.da   = 100;
g.PMax = 15;
g.QMax = 1;

% Call the function and create a plot
%------------------------------------
dGT = RepeatGroundTrack(g,1);

% Get the Cartesian coordinates and simulate
%-------------------------------------------
[r,v] = El2RV([dGT.a(1) g.inc 0 0 g.ecc 0]);

d     = struct;
d.j2  = 0.00108262563430956;
d.a   = 6378.137;
d.mu  = 398600.436;
d.jD0 = 2455197.5;

opts = odeset('RelTol',1e-12,'abstol',1e-12);

tEnd = dGT.nodalPeriod(1);
dOut = ode45( @(t,x) RHSGeoJ2(x,t,d), [0 tEnd], [r;v], opts );

% Plot the simulated track
%-------------------------
GroundTrack(dOut.y(1:3,:),dOut.x,d.jD0);

%--------------------------------------
% PSS internal file version information
%--------------------------------------
```