I'm trying to propagate the orbit of an Earth satellite. I've tried my calculation with gravity only (no drag), and also with drag only (no gravity).

The gravity-only calculations work fine and results in an expected orbit, but the atmospheric drag-only (gravity "turned off") show that satellite’s height above the Earth rises; the satellite just flies away!

I have tried other propogators in Matlab like HPOP and also cowell. For these I've also commented-out all perturbation effects as well as gravity, leaving only atmospheric drag, and I get the same results where the satellite also flies away.

Has anyone else tried to calculate atmospheric drag without gravity and get results where satellite fly away or its just me?

Here's some representative MatLab code for acceleration:

Vector Acceleration(double const &t, Satellite &y) {
    // Gravity
    Satellite sat;
    sat.loc = y.vel;
    double p = Magnitude(y.loc);
    // GM – Earth gravity parameter = 398602
    sat.vel = y.loc * -GM /(p*p*p);

    // Atmospheric drag
    QMatrix3x3 T = NutationMatrix(t) * PreccessionMatrix(MJD_J2000, t);
    sat.vel += AccelDrag(t, y.loc, y.vel, T, y.size, y.mass, Cd);
    return sat;
  • $\begingroup$ I've adjusted the wording of your question to make it easier to understand. I've also removed the additional questions which should be asked as separate question. If you want to see your original wording, click edited above and you can scroll down to view previous versions (nothing has been lost). $\endgroup$
    – uhoh
    Jun 25, 2018 at 17:30
  • $\begingroup$ @Heopps provides the correct explanation below. However, I'll note that your GM value is incorrect/outdated. It should be 398600.4415 . $\endgroup$
    – ChrisR
    Jun 26, 2018 at 3:22

1 Answer 1


Forget for a minute about math and coding, think of physics :) Try to imagine the picture.

If you turn off gravity, you have "a puff of air" with density quickly decreasing with distance from the center. Air drag force is in opposite direction to velocity vector in your program, I suppose. So there is no forces that change direction of motion. Your spacecraft will have straight line trajectory. It will be slowing until will reached atmosphere rarified enough, and then will be moving by inertia only.

So, your result is correct.


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