I am designing an Earth-Mars transfer. The launch window is 03-Jul-2026 (departure from Earth) & 22-Jun-2028 (Mars arrival).

The declination and right ascension for the departure asymptote from earth were given in NASA reports but I am not aware of any method to calculate these for arrival into Mars.

Any help would be appreciated.


2 Answers 2


To compute the arrival asymptotes, convert the heliocentric position and velocity into the planetocentric frame (the Mars J2000 frame in your case). Then, compute the B-Plane parameters as derived here , and a decent visualization is here.

Once you are in that frame, you may compute the declination $\delta$ and right ascension $\alpha$ at arrival as follows:

$$ \delta = \sin^{-1} \frac {z} {||\mathbb{r}||}$$

$$ \alpha = \tan^{-1} \frac y x $$


If you have the arrival hyperbolic excess velocity vector $\vec{v_{\infty}}$ and its magnitude $\big|\vec{v_{\infty}}\big|$, then you can calculate the unit vector $\hat{s}$ parallel to it by doing the following:

$$\hat{s} = \frac{\vec{v_{\infty}}}{\big|\vec{v_{\infty}}\big|}$$

You can then use the algorithm to calculate the right-ascension and the declination of a certain point on the geocentric equatorial frame. An explanation of the algorithm (ALGORITHM 4.1) can be found here: https://www.sciencedirect.com/topics/engineering/geocentric-equatorial-frame

The same method is also applicable for outbound velocity vectors.


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