radialvel

stistools.radialvel.earthVel(mjd)

Compute and return the velocity of the Earth at the specified time.

This function computes the Earth’s orbital velocity around the Sun in celestial rectangular coordinates. The expressions are from the Astronomical Almanac, p C24, which gives low precision formulas for the Sun’s coordinates. We’ll apply these formulas directly to get the velocity of the Sun relative to the Earth, then we’ll convert to km per sec and change the sign to get the velocity of the Earth.

Parameters:
mjd : float

time, Modified Julian Date

Returns:
vel : ndarray

the velocity vector of the Earth around the Sun, in celestial coordinates (shape=(3,),ndtype=float64)

Notes

We get the velocity of the Sun relative to the Earth as follows:

The velocity in the ecliptic plane with the X-axis aligned with the radius vector is:

  • Vx = radius_dot,
  • Vy = radius * elong_dot,
  • Vz = 0

where:

  • radius is the radial distance from Earth to Sun
  • elong is the ecliptic longitude of the Sun
  • eps is the obliquity of the ecliptic
  • _dot means the time derivative

Rotate in the XY-plane by elong to get the velocity in ecliptic coordinates:

radius_dot * cos (elong) - radius * elong_dot * sin (elong)
radius_dot * sin (elong) + radius * elong_dot * cos (elong)
0

Rotate in the YZ-plane by eps to get the velocity in equatorial coordinates:

radius_dot * cos (elong) - radius * elong_dot * sin (elong)
(radius_dot * sin (elong) + radius * elong_dot * cos (elong)) * cos (eps)
(radius_dot * sin (elong) + radius * elong_dot * cos (elong)) * sin (eps)
stistools.radialvel.precess(mjd, target)

Precess target coordinates from J2000 to the date mjd.

Parameters:
mjd : float

time, Modified Julian Date

target : array_like object

unit vector pointing toward the target, J2000 coordinates

Returns:
vector : ndarray

the target vector (or matrix) precessed to mjd as an array object of type float64 and the same shape as target, i.e. either (3,) or (n,3)

Notes

target can be a single vector, e.g. [x0, y0, z0], or it can be a 2-D array; in the latter case, the shape should be (n,3):

target = [[x0, x1, x2, x3, x4],
          [y0, y1, y2, y3, y4],
          [z0, z1, z2, z3, z4]]

The algorithm used in this function was based on [1] and [2].

References

[1](1, 2) Lieske, et al. 1976, Astron & Astrophys vol 58, p 1.
[2](1, 2) J.H. Lieske, 1979, Astron & Astrophys vol 73, 282-284.
stistools.radialvel.radialVel(ra_targ, dec_targ, mjd)

Compute the heliocentric velocity of the Earth.

This function computes the radial velocity of a target based on the Earth’s orbital velocity around the Sun. The space motion of the target is not taken into account. That is, the radial velocity is just the negative of the component of the Earth’s orbital velocity in the direction toward the target.

Parameters:
ra_targ : float

right ascension of the target (degrees)

dec_targ : float

declination of the target (degrees)

mjd : float

Modified Julian Date at the time of observation

Returns:
radial_vel : float

the radial velocity in km/s