as said in the title I have different results between numerical en vector approach during inclination changing maneuver.

The initial orbit :

Perigee radius : 6700 km

Eccentricity : 0.7

Inclination : 40.0 °

Ascending node : 20.0 °

Perigee Argument :10.0 °

The target orbit is the same with inclination set at 55 °, so we have a relative inclination of 15°

My vector approach:

At planes intersection I subtract final vector by initial vector and I get the following result : |delta_v| = 2608.9 m/s

And the result of my new orbit matches perfectly all expected parameters.

Now the problem comes from the numerical approach :

  1. I compute delta v magnitude |delta_v| = 2.0 * velocityAtNode * sin(relativeInclination * 0.5) = 2615,65 m/s

  2. My delta v vector is initialized on normalized velocity vector.

  3. I compute the rotation amplitude of my normalized delta v vector : rotationAngle = 90° + relativeInclination*0.5; = 97.5 °

  4. I rotate my normalized delta V vector around line of nodes axis by an angle of 97.5°

  5. Then I apply delta v computed previously to my rotated normalized vector: final delta v vector = rotated normalized vector * 2615,65

  6. I add this delta v vector to my initial velocity vector

In this numerical approach the orbits planes are perfectly aligned but I've a drift in others parameters :

perigee height becomes : 6675 km

eccentricity : 0.706

perigee argument : 12°

If I compare my delta v vector obtained by vector approach and by numerical approach. I notice an angle of 4.1° between these two vectors and a magnitude difference of 6.7 m/s

Any help is welcome to understand the difference between these two approaches. Thanks!

  • $\begingroup$ You haven’t shared how you are performing the transformation between keplerian elements and position+ velocity vectors. Are you confident you are performing that step correctly? $\endgroup$
    – cms
    Nov 10, 2021 at 12:43
  • 1
    $\begingroup$ Hi @cms, I use a routine from spice toolkit provided by JPL : naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/cspice/conics_c.html. The conversion to keplerian elements is perfect on the vector approach so I think it should be correct for the numerical approach. $\endgroup$
    – sl20
    Nov 10, 2021 at 12:57

1 Answer 1


Instead of using the normalized velocity vector, you should first project the velocity vector onto the transverse plane (i.e., take $\mathbf{v} - \frac{\mathbf{v}\cdot \mathbf{r}}{\mathbf{r}\cdot \mathbf{r}}\mathbf{r}$, where $\mathbf{r}$ is the position vector), and then normalize this projection. Similarly, you should use the magnitude of this projection to calculate the magnitude of $\Delta v$. Otherwise, your $\Delta v$ has an extra radial component.

  • $\begingroup$ Perfect it works, today you taught me very important things. I never saw this vector projection in my astrodynamics books. Thank you very much!! $\endgroup$
    – sl20
    Nov 10, 2021 at 14:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.