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    Re: JPL ephemeresis and Nautical Almanac - speed of light question
    From: Paul Hirose
    Date: 2018 Apr 4, 21:56 -0700

    On 2018-04-03 12:30, John D. Howard wrote:
    > If the speed of light was important for navigation almanacs how would you 
    figure the position of a star that is 2000 light-years away?
    
    It doesn't require any allowance for light time because the coordinates
    in a star catalog are the place where the star was, when it emitted the
    light that reached the solar system barycenter (center of gravity) at
    some standard epoch (usually 2000 Jan 1). I.e., light time is already
    included.
    
    To be strictly correct, Earth is 8 light minutes from the barycenter, so
    there is a small error due to the difference in light time. This is
    called the "Roemer effect." The worst geometry occurs when the
    barycenter, Earth, and star are in syzygy. In that case the error equals
    the proper motion of the star in 8 minutes. It's a fraction of a
    millisecond of arc even for the stars with the highest proper motions,
    so normally we ignore light time.
    
    That won't do for solar system objects. Compared to the stars their
    angular rates are extremely high, so the light time correction is
    sensitive to the observer's location. Light time is not included in the
    JPL ephemerides. They give the barycentric geometric place of the body:
    where it actually is, with respect to the barycenter. The user must
    compute the astrometric place: where it was, when it emitted the light
    that reaches the observer at the time of interest.
    
    Suppose you want the geocentric astrometric place of Jupiter at time t.
    Initialize tau (light time) to zero. From the ephemeris get the
    barycentric geometric place of Earth at t and Jupiter at t-tau. Call
    these quantities Eb(t) and Jb(t-tau).
    
    Compute the first approximation of the astrometric place: J1(t) =
    Jb(t-tau) - Eb(t). (This is identical to the geocentric geometric place.)
    
    Now the iteration begins. Compute a more accurate light time: tau =
    |J1(t)| / c, where c is the speed of light. With the new tau, compute a
    more accurate astrometric place: J2(t) = Jb(t-tau) - Eb(t). Compare the
    old and new astrometric places: J1(t) vs. J2(t). If they are equal, plus
    or minus the desired accuracy, J2(t) is the astrometric place.
    Otherwise, J1(t) = J2(t) and repeat the paragraph.
    
    The more rigorous procedure in section B of the Astronomical Almanac
    includes a light time correction due to the Sun's gravitation. This is
    separate from the deflection of light, which is one of the corrections
    in the transformation from astrometric place to apparent place.
    Retardation and deflection are relativistic effects and insignificant at
    Nautical Almanac precision.
    

       
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