model q gravity assist manuever in matlab

To model a gravity assist maneuver in MATLAB, you can use the following steps:

1. Define the input parameters such as the initial velocity of the spacecraft, the mass of the planet or moon that the spacecraft will use for the gravity assist, and the distance of closest approach to the planet or moon.

2. Calculate the gravitational potential energy and kinetic energy of the spacecraft before and after the gravity assist using the input parameters.

3. Calculate the change in velocity of the spacecraft as a result of the gravity assist using the conservation of energy and momentum.

Here's an example MATLAB code:

main.m
% Input parameters
v0 = 10; % Initial velocity of spacecraft
m_p = 5.97e24; % Mass of planet (Earth)
r_p = 6.37e6; % Radius of planet (Earth)
v_p = 3.986e14; % Gravitational parameter of planet (Earth)
d = 10^7; % Distance of closest approach to planet

% Calculate the gravitational potential energy and kinetic energy
% of the spacecraft before and after the gravity assist
E_before = 0.5 * v0^2 - v_p / d;
E_after = - v_p / r_p;
Delta_E = E_after - E_before;

% Calculate the change in velocity of the spacecraft
v1 = sqrt((2 * (E_after + 0.5 * v0^2)) - v_p / d);
v2 = sqrt((2 * E_after) - v_p / r_p);
Delta_v = v2 - v1;

fprintf('Change in velocity: %.2f km/s\n', Delta_v / 1000);
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This code calculates the change in velocity of a spacecraft due to a gravity assist maneuver around Earth. It assumes a circular orbit for Earth, and uses the gravitational parameter of Earth. Note that this is a simplified model, and more complex models may be needed for more accurate simulations.