Perturbing Accelerations in Satellite Orbit Determination

[TheRock123321]

Hi, first time posting here.
I'm working on satellite orbit determination and wish to add in perturbing accelearations in addition to the Earth's graviatational field. I will be adding in acceleration due to the moon, sun, atmospheric drag, etc... The acceleration due to the Earth's graviational field at the specefic satellite altitude is about 7 m/s and the acceleration from the sun, for example is on the order of 10^-7 m/s. I have an initial state vector, I would like to incorporate these accelerations and produce a state vector at a later time. I am working in MATLAB and having difficulties mainly with units and integration. A short example of MATLAB code would be handy. Right now I am getting an ever increasing velocity and this is happening because I am doing the integration as if it were a linera problem. How to integrate so that it is orbital. Thanks!

 

[BobG]

David Vallado's "Fundamentals of Astrodynamics and Applications" talks about orbital perturbations. While a lot of the book does have software available, the book doesn't have a lot of coded algorithms for perturbations. What it does have is available in Fortran, Pascal, or C.

By the way, I'm curious how you came up with acceleration from the Sun being around 10^-7 m/sec^2. It should be around 6 x 10^-3 m/sec^2 (plus or minus .005% depending on where you're at in your orbit).

You're almost high enough to disregard atmospheric drag (you have density around the 10^-15 kg/m^3 range) and that's good. You can't model atmospheric drag very well when it varies so much - especially between solar min and solar max. You'd need to creat a user input variable that they obtain from NOAA or some other space weather agency (they'll actually get values for the last few days, but can use that to guess the current or future value).

The most efficient way of propagating your initial state vectors into the future is to reduce as many perturbations as possible to algebraic equations that reflect long period or secular perturbations, while disregarding the perturbations that cycle over short periods of time (for example, the Earth's oblateness would increase the orbit's inclination as the satellite approached the equator from either pole, but it would decrease it at exactly the same rate when the satellite is approaching its max latitude from the equator; but, in doing so, the Earth's oblateness would the shift the right ascension of the ascending node the same direction regardless of the satellite's position in the orbit).

That's not the most accurate way. Two line mean element sets are accurate enough to find a satellite since even seemingly large errors turn into small angles when the distance is hundreds to thousands of kilometers. If you're looking for precision, such as what's needed for GPS, then try the numerical solutions in Vallado as a starting point.

 

[oswaler]

Hi there, it's great to hear that you are working on satellite orbit determination and incorporating perturbing accelerations into your analysis. This is an important aspect to consider when studying the motion of satellites in orbit.

Firstly, it's important to understand that the Earth's gravitational field is the dominant force in determining the orbit of a satellite. However, as you mentioned, there are other factors such as the gravitational pull from the moon and sun, atmospheric drag, and solar radiation pressure that also play a role in the satellite's motion.

To incorporate these perturbing accelerations into your analysis, you will need to use numerical integration techniques in MATLAB. This will allow you to solve the equations of motion for the satellite's position and velocity over time. You will also need to ensure that your units are consistent throughout your calculations.

One approach to solving this problem is to use the Runge-Kutta method, which is a numerical integration technique commonly used for solving differential equations. In this method, the equations of motion are discretized into smaller time steps, and the satellite's position and velocity are updated at each time step. This will allow you to accurately capture the effects of the perturbing accelerations on the satellite's motion.

Here is a short example of how you could implement this in MATLAB:

% Define initial state vector
X0 = [x0; y0; z0; vx0; vy0; vz0]; % where x0, y0, z0 are initial position coordinates and vx0, vy0, vz0 are initial velocity components

% Define constants
mu = 3.986e14; % Earth's gravitational parameter
m = 1000; % satellite mass
Cd = 2.2; % drag coefficient
A = 10; % satellite cross-sectional area
rho = 1.2; % atmospheric density
R = 6378e3; % Earth's radius
J2 = 1.0826e-3; % Earth's second gravitational harmonic

% Define time span
tspan = [0 3600]; % 1 hour time span

% Define perturbing accelerations as functions of time
a_sun = @(t) -mu*(X0(1:3)./norm(X0(1:3))^3) + mu*(X0(1:3) - [149.6e9; 0; 0])./norm(X0(