Using Clohessy-Wi;tshire equations to demonstrate the projected circular orbit trajectory base on the initial conditions defined by parameters of Chief Satellite and Deputy Satellite Initial condition

When given a set of parameters for the Chief Satellite with an altitude of 847 km, Eccentricity, e = 0 Orbit inclination, I = 10 degrees Right Ascenscion of Ascending node,Arguement of Perigee,mean anomaly = 0 degrees respectively

The Parameters of the deputy satellite condition (Chief centered frame) x = 0.0 km y = 1.0 km z = 0.0 km v(x) = 0.5785.10^-3 km/s v(y) = 0 v(z) = 1.157.10^-3

how can I simulate all of these parameters into CW equations via MATLAB and have an illustration of the projected trajectory of the circular orbit ? What are the neccessary commands I need to use in doing this? Please advise. Thank you in advance

Best regards, Aaron Aw

Answer 1

[James Tursa]

1) Google "Clohessy Wiltshire"

2) Look at the first link

3) Look at the closed form solution on the first page of this link

4) Code up the closed form solution

5) Plug in a t vector

6) Plot the results

[Aaron]

Hi James, thanks for that wonderful suggestion , I've been to that site and tried keying it in MATLAB , everything is alright except for the t-vector ..Im not sure what values should I input it so as to have a smooth circular plot . Any suggestions ?

Perhaps you can show me how to input the code for t vector . Thanks a lot bro , hope to hear from you soon.

[James Tursa]

To get one orbit's worth, make the final t value equal to 1 period. So for n = sqrt(mu/a^3) the period will be 2*pi/n. Then it is just a matter of how often you want the points. e.g., for every second do this:

n = sqrt(mu/a^3);

T = 2*pi/n;

t = 0:1:T;

For points every 1 minute (60 seconds):

t = 0:60:T;

etc.

Just be sure that your CW coded equations use the element-wise operators (.* , ./ , .^ , etc) instead of the matrix operators (* , / , ^, etc).

[James Tursa]

Follow-up: Where are you getting your initial conditions from? In order to fly circles around the target (chief) the initial condition on xdot is xdot = y * n / 2, which I calculate to be about 0.514e-3 using earth parameters and y = 1km. Also, the geometric relationship between the crosstrack motion initial velocity and radial velocity is zdot = sqrt(3) * xdot, but I see a factor of 2 in your numbers instead of a factor of sqrt(3). So I doubt your numbers will produce circular motion about the target (chief).