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# Orbital Inclination Change

Transfer from a LEO 350 km circular orbit with 53.4 deg inclination to a Geostationary Equatorial Orbit(GEO)

```clear all; clc;
close all;```

## Input

```R_LEO = 6378 + 350;      % km
R_GEO = 42164;           % km
mu    = 398600;          % km^3/s^2
incl  = 53.4;            % deg```

## Method 1: Hohman transfer from LEO to GEO and after inclination change

```Rp  = R_LEO;
Ra  = R_GEO;
e   = (Ra - Rp)/(Ra + Rp);  % transfer orbit eccentricity
a   = (Ra + Rp)/2;          % transfer orbit semimajor axis
V_LEO   = (mu/R_LEO)^0.5;
Vp      = (2*mu/R_LEO - mu/a)^0.5;
Va      = (2*mu/R_GEO - mu/a)^0.5;
V_GEO   = (mu/R_GEO)^0.5;
dV_LEO  = abs(Vp - V_LEO);
dV_GEO  = abs(V_GEO - Va);
dV_Hoff = dV_GEO + dV_LEO;

% Inclination change at GEO
dV_incl = 2*V_GEO*sind(incl/2);
dV_total1 = dV_incl + dV_Hoff;

fprintf('Method 1: Hohman transfer from LEO to GEO and after inclination change\n');
fprintf('dV_Hoff  = %6.2f [km/s] \n',dV_Hoff);
fprintf('dV_incl  = %6.2f [km/s] \n',dV_incl);
fprintf('dV_total = %6.2f [km/s] \n',dV_total1);```
```Method 1: Hohman transfer from LEO to GEO and after inclination change
dV_Hoff  =   3.87 [km/s]
dV_incl  =   2.76 [km/s]
dV_total =   6.64 [km/s]```

## Method 2: Inclination change in LEO and after Hohman transfer to GEO

```dV_incl   = 2*V_LEO*sind(incl/2);
dV_total2 = dV_incl + dV_Hoff;

fprintf('\nMethod 2: Inclination change in LEO and after Hohman transfer to GEO\n');
fprintf('dV_incl  = %6.2f [km/s] \n',dV_incl);
fprintf('dV_Hoff  = %6.2f [km/s] \n',dV_Hoff);
fprintf('dV_total = %6.2f [km/s] \n\n',dV_total2);
fprintf('Method 2/Method 1 = %6.2f \n',dV_total2/dV_total1);```
```Method 2: Inclination change in LEO and after Hohman transfer to GEO
dV_incl  =   6.92 [km/s]
dV_Hoff  =   3.87 [km/s]
dV_total =  10.79 [km/s]

Method 2/Method 1 =   1.63```