# Is there a way to get the angle of approach of a spacecraft with respect to a planet velocity vector?

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

• 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. Apr 11, 2017 at 12:28

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 $$\cos \theta = \frac{\vec{u} \cdot \vec{v}}{||\vec{u}||||\vec{v}||}$$