adam_core.orbit_determination.gibbs module

adam_core.orbit_determination.gibbs.calcGibbs(r1, r2, r3)

Calculates the velocity vector at the location of the second position vector (r2) using the Gibbs method.

\[\]

ec{D} = ec{r}_1 imes ec{r}_2 + ec{r}_2 imes ec{r}_3 + ec{r}_3 imes ec{r}_1

ec{N} = r_1 ( ec{r}_2 imes ec{r}_3) + r_2 ( ec{r}_3 imes ec{r}_1) + r_3 ( ec{r}_1 imes ec{r}_2)

ec{B} equiv ec{D} imes ec{r}_2

L_g equiv sqrt{

rac{mu}{ND}}

ec{v}_2 = rac{L_g}{r_2} ec{B} + L_g ec{S}

For more details on theory see Chapter 4 in David A. Vallado’s “Fundamentals of Astrodynamics and Applications”.

r1~numpy.ndarray (3)

Heliocentric position vector at time 1 in cartesian coordinates in units of AU.

r2~numpy.ndarray (3)

Heliocentric position vector at time 2 in cartesian coordinates in units of AU.

r3~numpy.ndarray (3)

Heliocentric position vector at time 3 in cartesian coordinates in units of AU.

v2~numpy.ndarray (3)

Velocity of object at position r2 at time t2 in units of AU per day.