Source https://smallsat.wordpress.com

% TT&C satellite used to monitor pacific coast battle has failed
% NACSOC has decided to transfer the functions of a spare
% Atlantic battle group satellite to the pacific until a replacement
% can be launched

Design an Orbital phasing Maneuver that Allows Transfer of a

GEO Synchronous Communication Satellite from 40.40’ west Longitude to 118.15’ west longitude

clc;
fprintf('Phasing Orbital Maneuver from 40.40’ west to 118.15’ west Long\n\n');
R_GEO   = 42164;        %km
we      = 7.292e-5;     %rad/s
mu      = 398600;
V_GEO   = we*R_GEO;      %km/s
%fprintf('Velocity in GEO orbit = %4.2f  km/s\n',V_GEO);
% Period of Geocentric orbit
T_GEO = 2*pi/we;
%fprintf('Period of Geocentric orbit = %6.2f  s\n\n',T_GEO);
%Number of orbits
N = 1:1:5;
%fprintf('Number of orbits = %d  \n',N);
% New orbital period needed
dLon = (77+35/60)/180*pi;       %deg
T_ph = (2*pi + dLon./N)/we ;
%fprintf('Period of Phasing orbit = %6.2f  s\n',T_ph);
% New Semimajor Axis needed
a_ph = (mu*(T_ph/(2*pi)).^2).^(1/3);
%fprintf('New Semimajor Axis  = %6.2f  km\n',a_ph);
% New apogee
R_pha =   2*a_ph - R_GEO;
%fprintf('Apogee Radius  = %6.2f  km\n',R_pha);
% New velocity to achieve this orbit
V_ph = ( mu*(2/R_GEO - 1./a_ph)).^0.5;
%fprintf('Velocity to achieve this orbit = %4.2f  km/s\n',V_ph);
% Total Delta V required;
dV = 2*abs( V_ph - V_GEO);
%fprintf('Total delta V required = %4.3f  km/s\n\n',dV);

fprintf('N     T period      R_GEO      R apogee     Ph.Vel     dV   \n');
for i = 1:5
fprintf('%d      %6.2f      %6.2f   %6.2f    %4.2f     %4.3f  \n',...
    N(i),T_ph(i),R_GEO,R_pha(i),V_ph(i),dV(i));
end

Phasing Orbital Maneuver from 40.40’ west to 118.15’ west Long

N     T period      R_GEO      R apogee     Ph.Vel     dV   
1      104734.91      42164.00   53882.93    3.26     0.364  
2      95450.19      42164.00   48119.22    3.17     0.200  
3      92355.28      42164.00   46156.94    3.14     0.138  
4      90807.82      42164.00   45167.59    3.13     0.105  
5      89879.35      42164.00   44571.28    3.12     0.085

Design a Reverse Orbital Maneuver that Puts the Satellite Back to the

Original Longitude after Mission has been accomplished

fprintf('\nReverse Orbital Maneuver\n\n');
%fprintf('Number of orbits = %d  \n',N);
% New orbital period needed
dLon = (77+35/60)/180*pi;       %deg
T_ph = (2*pi - dLon./N)/we ;
%fprintf('Period of Phasing orbit = %6.2f  s\n',T_ph);
% New Semimajor Axis needed
a_ph = (mu*(T_ph/(2*pi)).^2).^(1/3);
%fprintf('New Semimajor Axis  = %6.2f  km\n',a_ph);
% Perigee Radius
R_php =   2*a_ph -R_GEO;
%fprintf('Perigee Radius  = %6.2f  km\n',R_php);
% New velocity to achieve this orbit
V_ph = ( mu*(2/R_GEO - 1./a_ph)).^0.5;
%fprintf('Velocity to achieve this orbit = %4.2f  km/s\n',V_ph);
% Total Delta V required;
dVr = 2*abs( V_ph - V_GEO);
%fprintf('Total delta V required = %4.3f  km/s\n\n',dV);
fprintf('N     T period      R_GEO      R apogee     Ph.Vel     dV   \n');
for i = 1:5
fprintf('%d      %6.2f      %6.2f   %6.2f    %4.2f     %4.3f  \n',...
    N(i),T_ph(i),R_GEO,R_php(i),V_ph(i),dVr(i));
end

Reverse Orbital Maneuver

N     T period      R_GEO      R apogee     Ph.Vel     dV   
1      67596.01      42164.00   29566.39    2.79     0.566  
2      76880.73      42164.00   35992.94    2.95     0.248  
3      79975.64      42164.00   38076.63    3.00     0.159  
4      81523.10      42164.00   39108.38    3.02     0.117  
5      82451.57      42164.00   39724.29    3.03     0.092

Parametres of the Thruster

F_th = 500;         % N
m_dry =1000;        % kg
ISP = 310;
g0 = 9.81;          %km/s;
% Burn time for Transfer Orbit Insertion
% Burn Time for Final Orbit Insertion
% Required  Budget for !V1, !V2
m_fin = m_dry;
m_prop = m_fin*(exp(dVr*1000/(g0*ISP)) - 1) ;
dt = m_prop*ISP*g0/F_th;
m_fin = m_dry + m_prop;
fprintf('\nN    dV2[km/s]    m_dry[kg] m_prop[kg]  m_fin[kg]   dt[s]   \n\n');
for i = 1:5
fprintf('%d      %4.3f      %4.2f    %4.2f    %4.2f       %4.3f  \n',...
    N(i),dVr(i),m_dry,m_prop(i),m_fin(i),dt(i));
end
fprintf('Phasing Orbit \n\n');
m_dry = m_fin;
m_prop = m_dry.*(exp(dV*1000/(g0*ISP)) - 1) ;
dt = m_prop.*ISP*g0/F_th;
m_fin = m_fin + m_prop;
fprintf('\nN    dV1[km/s]    m_dry[kg] m_prop[kg]  m_fin[kg]   dt[s]   \n\n');
for i = 1:5
fprintf('%d      %4.3f      %4.2f    %4.2f    %4.2f       %4.3f  \n',...
    N(i),dV(i),m_dry(i),m_prop(i),m_fin(i),dt(i));
end

N    dV2[km/s]    m_dry[kg] m_prop[kg]  m_fin[kg]   dt[s]   

1      0.566      1000.00    204.53    1204.53       1243.967  
2      0.248      1000.00    84.83    1084.83       515.976  
3      0.159      1000.00    53.51    1053.51       325.481  
4      0.117      1000.00    39.08    1039.08       237.677  
5      0.092      1000.00    30.77    1030.77       187.152  
Phasing Orbit 

N    dV1[km/s]    m_dry[kg] m_prop[kg]  m_fin[kg]   dt[s]   

1      0.364      1204.53    153.37    1357.90       932.849  
2      0.200      1084.83    73.63    1158.46       447.831  
3      0.138      1053.51    48.76    1102.28       296.583  
4      0.105      1039.08    36.50    1075.57       221.983  
5      0.085      1030.77    29.18    1059.95       177.454

Published with MATLAB® 7.10