[vsnet-chat 1091] Re: eclipse timing

[Taichi Kato <tkato>]

Re: eclipse timing

Gianluca Masi wrote:

> theta=sun longitude
> alpha, delta= equatorial coordinates of the star
> obl=mean obliquity of the ecliptic
> 
> ALL THESE DATA HAVE TO BE REFERRED TO THE DATE OF INTEREST.

   For reader's convenience, I may comment that one should use the same
equinox (J2000.0, or the observed epoch) consistently to all the variables
stated above.  It would be convenient to use J2000.0 sysmtatically.

Fraser Farrell wrote:

> I think the precision of the formula is limited only by the precision of
> "R" and "theta".

   Yes, it's true.  However, I have seen in several cases users have used
"R" and "theta" from some sort of Almanac, which used to express these
values using the "instant" equinox, rather than J2000.0.  Another concern
is the value of "obl"; I have seen, in some cases, users adopt obl(T)
rather than obl(J2000.0).  These all are potential major causes of
inconsistency.

> This would yield a worst-case HC error of about 0.001 seconds;

   In terms of HC, one will be able to obtain this degree of accuracy without
too much calculation.  As Dr. Thorstensen stated, when chasing the uniformity
of time better than seconds, one must at least take the following terms
into consideration.

  1) the difference between the heliocenter and barycenter (up to 4-5 sec,
     as Masi stated)

  2) the difference between UTC and TD (depending on "leap seconds", the
     accumulation of which may be quite large)

  3) topocentric correction (up to ~20 msec)

  4) correction from TDT to TDB (the base of modern ephemerides), which
     arises from the relativistic effect of the motion of the earth and
     the changing gravitational field (up to +/- 1.66 msec)

  5) Shapiro delay, through the gravitaional field of the Sun (~ msec?)

   Are there any more major terms when considering the 0.001-second accuracy?

Regards,
Taichi Kato

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