adam_core.orbit_determination.herrick_gibbs module

adam_core.orbit_determination.herrick_gibbs.calcHerrickGibbs(r1, r2, r3, t1, t2, t3)[source]

Calculates the velocity vector at the location of the second position vector (r2) using the Herrick-Gibbs formula.

\[\]
ec{v}_2 =

-Delta t_{32} left (

rac{1}{ Delta t_{21} Delta t_{31}}

rac{mu}{12 r_1^3} ight ) ec{r}_2

  • ( Delta t_{32} - Delta t_{21}) left (

rac{1}{ Delta t_{21} Delta t_{32}}

rac{mu}{12 r_2^3} ight ) ec{r}_2

  • Delta t_{21} left (

rac{1}{ Delta t_{32} Delta t_{31}}

rac{mu}{12 r_3^3} ight ) ec{r}_3

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.

t1float

Time at r1. Units of MJD or JD work or any decimal time format (one day is 1.00) as long as all times are given in the same format.

t2float

Time at r2. Units of MJD or JD work or any decimal time format (one day is 1.00) as long as all times are given in the same format.

t3float

Time at r3. Units of MJD or JD work or any decimal time format (one day is 1.00) as long as all times are given in the same format.

v2~numpy.ndarray (3)

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