Gravity gradient analysis of Gateway orbit

See also: Constant, Date2JD, RPRA2AE, Period, RVOrbGen, PltOrbit, UMinGG, U2Q, QForm, Cross, TimeHistory, DeltaQToRate, PrintFig

Contents

%--------------------------------------------------------------------------
%   Copyright (c) 2022 Princeton Satellite Systems, Inc.
%   All rights reserved.
%--------------------------------------------------------------------------
%   Since 2023.1
%--------------------------------------------------------------------------

User inputs

Constants

mu = Constant('mu moon');
rM = Constant('equatorial radius moon');

% Gateway
rA = 70000; % apogee
rP =  3000; % perigee

% The body inertia is used for gravity gradient
inertia = [1.6406e+06  -8.6764e+04  -4.7583e+03;...
          -8.6764e+04   9.9031e+05  -8.5474e+02;...
          -4.7583e+03  -8.5474e+02   1.8093e+06];

cM = [ -3.1182e-04; 4.2778e-05; -1.5026e-05];

% Script control
nOrbits = 4;
nSamp   = 400;
jD0     = Date2JD([2024 2 2]);

% Plot
printPlots = false;

Calculate

if( printPlots )
  close all
end

% Orbit
[a, e] = RPRA2AE( rP, rA );
el     = [a pi/2 0 0 e 0];
period = Period( a, mu );
t      = linspace(0,nOrbits*period,nSamp);
dT     = t(2);
[r,v]  = RVOrbGen(el,t,[],mu);
PltOrbit( el, jD0, [], 'moon' );

u  = UMinGG(inertia );
q  = zeros(4,nSamp);
m  = zeros(3,nSamp);

for k = 1:nSamp
  q(:,k) = U2Q(Unit(r(:,k)),u);
  rB     = QForm(q(:,k),r(:,k));
  m(:,k) = 3*mu*Cross( rB, inertia*rB )/Mag(rB)^5;
end

Plot

TimeHistory(t,q,{'q_s' 'q_x' 'q_y' 'q_z'},'Quaternion for Minimum GG');
yL = {'r_x (km)' 'r_y (km)' 'r_z (km)' 't_x \muNm' 't_y \muNm' 't_z \muNm'};
TimeHistory(t,[r;m],yL,'Orbit and Gravity Gradient Torque');

Delta rates and torques

omega = DeltaQToRate(q,dT);

yL = {'\omega_x (rad/s)' '\omega_y (rad/s)' '\omega_z (rad/s)'};
TimeHistory(t(2:end),omega,yL, 'Angular Rate');

torque = inertia*(omega(:,2:end)-omega(:,1:end-1))/dT;
yL = {'T_x (Nm)' 'T_y (Nm)' 'T_z (Nm)'};
TimeHistory(t(3:end),torque,yL, 'Control Torque');

Print to file

if( printPlots )
  PrintFig(1,4,2,'GG1')
  PrintFig(1,4,3,'GG2')
  PrintFig(1,4,4,'GG3')
  PrintFig(1,4,5,'GG4')
end


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% $Id: c62d3d3f1d7c01c77f05f4d656f15ba329e86462 $

Published with MATLAB® R2023b