On Fri, 21 Apr 2006, Francois Ochsenbein wrote:
>
> Hi Ed,
>
> I don't understand your arithmetics -- double have 52 bits for the mantissa
> (53 if you include the hidden bit), that means a dynamics of 2^53 or 10^16.
> If the largest angle is 360degrees, to get an accuracy of 1 nano-arcsec
> you need only 51 bits only (360deg = 1.296E+15 nano-arcsec).
Hi,
The relevant 'limiting case' units are probably radians, since (especially if one is working out separations or precesing from B1950) most trig functions need radians.
1E-9 arcsec = 4.848E-15 radians
2pi contains exactly the same number of these as below, of course, but what you may be dealing with is something like sin(4.0 + 4.848E-15)
Is that still OK?
>From Ed:
> Another subtle point to keep in mind is that 4h 33min +/- 1.5 min
> is slightly different in meaning from its decimal representation. The
> difference is that 4h 33m is the measured value from a gaussian
> distribution with dispersion of 1.5m and then rounded to the nearest
> minute and IS different from 4h 33m 00.0s +/- 90.0s.
It is different to a human using a particular set of assumptions but not to software, as far as I know.
In general we need to be able to specify and preserve lack of precision as well as precision. That is an issue for some formatters, and another problem if we _emit_ as well as handling data in e.g. decimal degrees only.
189.1234567 +62.123456 is an awful lot more difficult for a human to look at - and even more so to derive an IAU name for - than 12 36 36.23456 +62 12 46.2345 (these are not exact equivalents, just done in my head!)
In other words we are stuck with conversions for presentation.
Regarding time, I am not sure if MJD are the best units to use rather than ISO time - both a precision issue (pulsar timing - nanoseconds?) and the fact taht ISO time has very good standards for relative time intervals etc. whilst the problem with MJD is that most astronomers don't even know what the M is.
cheers
a