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eraLdn

sn = ERFA.ldn(n, b, ob, sc)

For a star, apply light deflection by multiple solar-system bodies, as part of transforming coordinate direction into natural direction.

Given:

   n    int           number of bodies (note 1)
   b    LDBODY[n]  data for each of the n bodies (Notes 1,2):
    bm   double         mass of the body (solar masses, Note 3)
    dl   double         deflection limiter (Note 4)
    pv   [2][3]         barycentric PV of the body (au, au/day)
   ob   double[3]     barycentric position of the observer (au)
   sc   double[3]     observer to star coord direction (unit vector)

Returned:

   sn    double[3]      observer to deflected star (unit vector)

  1. The array b contains n entries, one for each body to be considered. If n = 0, no gravitational light deflection will be applied, not even for the Sun.

  2. The array b should include an entry for the Sun as well as for any planet or other body to be taken into account. The entries should be in the order in which the light passes the body.

  3. In the entry in the b array for body i, the mass parameter b[i].bm can, as required, be adjusted in order to allow for such effects as quadrupole field.

  4. The deflection limiter parameter b[i].dl is phi^2/2, where phi is the angular separation (in radians) between star and body at which limiting is applied. As phi shrinks below the chosen threshold, the deflection is artificially reduced, reaching zero for phi = 0. Example values suitable for a terrestrial observer, together with masses, are as follows:

      body i     b[i].bm        b[i].dl

      Sun        1.0            6e-6
      Jupiter    0.00095435     3e-9
      Saturn     0.00028574     3e-10

  1. For cases where the starlight passes the body before reaching the observer, the body is placed back along its barycentric track by the light time from that point to the observer. For cases where the body is "behind" the observer no such shift is applied. If a different treatment is preferred, the user has the option of instead using the eraLd function. Similarly, eraLd can be used for cases where the source is nearby, not a star.

  2. The returned vector sn is not normalized, but the consequential departure from unit magnitude is always negligible.

  3. The arguments sc and sn can be the same array.

  4. For efficiency, validation is omitted. The supplied masses must be greater than zero, the position and velocity vectors must be right, and the deflection limiter greater than zero.

Reference:

Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to the Astronomical Almanac, 3rd ed., University Science Books (2013), Section 7.2.4.

Called:

   eraCp        copy p-vector
   eraPdp       scalar product of two p-vectors
   eraPmp       p-vector minus p-vector
   eraPpsp      p-vector plus scaled p-vector
   eraPn        decompose p-vector into modulus and direction
   eraLd        light deflection by a solar-system body

This revision: 2021 February 24

Copyright (C) 2013-2021, NumFOCUS Foundation. Derived, with permission, from the SOFA library.