I apologize if my question is badly formulated I know it's really specific but here what I would like to know :

I managed to compute the turning angle of the velocity for a body along a hyperbola trajectory thanks to the following equation :

$\delta = 2 \arcsin(1/e)$

This equation give me the turning angle at the end of the flyby. What I would like to know is the original angle, at start, of that spacecraft with respect to the planet velocity vector.

I thought using the HORIZONS Web-Interface and put the settings as following :

  • Ephemeris Type : VECTORS
  • Target Body : The spacecraft (e.g. Voyager 1)
  • Coordinate origin : The planet (e.g. Jupiter)
  • Time Span : Start of fly-by (e.g. 1979-Mar-4 / 1979-Mar-5 )

But then I'm completely lost in the generated tables ! Am I at the right place to find what I'm looking for ?

Thanks for your help

  • $\begingroup$ If the transfer orbit is coplanar with the planet's orbit and the planet orbit is circular, it'd be the flight path angle: en.wikipedia.org/wiki/Elliptic_orbit#Flight_path_angle . Another option might be to get the space craft vector and planet vector in a sun centered coordinate system. $\endgroup$
    – HopDavid
    Apr 11, 2017 at 12:28

1 Answer 1


Since I had nearly the same problem, here is what worked for me:

  1. Get two vector ephemerides from Horizons, one for Voyager and one for Jupiter. Choose the Sun as the Coordinate origin.

  2. Subtract the VX, VY and VZ values of Jupiter from the corresponding values of the spacecraft to get a velocity relative to Jupiter.

  3. Calculate the angle between that vector and the Jupiter velocity vector, good old $\cos \theta = \frac{\vec{u} \cdot \vec{v}}{||\vec{u}||||\vec{v}||}$

That should give you the angle between the Jupiter-centric spacecraft velocity, and the Jupiter orbital velocity vector. There might be other ways to get this directly, but this method only involves some minor coordinate math.


Your Answer

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

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