Understanding Astronomical Days & Measuring a Year's Length

[fizzy]

I found an excellent article on the different meanings there are for the word day in astronomy. Very will written:

https://www.physicsforums.com/insights/measuring-how-many-days-are-in-a-year/

Now often astronomers work in Julian days to have a consistent time scale without skips and bound.s. Various parameters are often presented as polynomials using JD , J year of even J millennia.

The days are human noon to noon days, so presumably these equate to mean solar days of 86400 s ( by definition ) but there again there may be qualifications due to tidal drag etc.

http://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html

                                    J            E           ratio

Sidereal orbit period (days)      4,332.589     365.256      11.862

Tropical orbit period (days)    4,330.595     365.242      11.857

(E=365.256 thus must be msd.)
pJ=4332.589 msd.

What I would like to know is how to compare orbital period of Jupiter , polynomial functions of say lunar precession period in JD and eclipse series Saros periods.

Supplementary question: what is the best average value for Saros centred on J2000 ? I need a value compatible with the previous, not a derivative approximation in year,months,days and hours, or N synodic months etc.

I looked at data from NASA and averaged over series of similar eclipses but always came up with results a little shorter than values found stated elsewhere for Saros.
https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros135.htmlthanks to anyone who can clarify this infernal mix of different "days".

 

[IsometricPion]

The days are human noon to noon days, so presumably these equate to mean solar days of 86400 s ( by definition ) but there again there may be qualifications due to tidal drag etc.

I think that astronomers in modern times use JD as defined by UT1 (or UTC) (which are, by definition solar days (for UT1 it is not a mean)). However, when doing calculations, a constant day of 86400 SI seconds (in Geocentric Coordinate Time TGC) is more typical (since a uniform timescale is assumed in analytical and numerical calculations). For short time periods and purposes that do not require great precision there is no significant difference between the two (currently the difference accumulates to 0.9s every few years see UT1-UTC on the International Earth Rotation Service website).

What I would like to know is how to compare orbital period of Jupiter , polynomial functions of say lunar precession period in JD and eclipse series Saros periods.

I think the best way is to convert everything into JD (or possibly Julian centuries) and then compare (here, since long time periods are involved, a JD should be taken to be 86400 SI seconds). Then convert back to local time at the end of your calculation (if necessary). (I hope this answered the question you were asking here, it was not entirely clear to me what the question was precisely.)

Supplementary question: what is the best average value for Saros centred on J2000 ? I need a value compatible with the previous, not a derivative approximation in year,months,days and hours, or N synodic months etc.

I looked at data from NASA and averaged over series of similar eclipses but always came up with results a little shorter than values found stated elsewhere for Saros.

For Saros cycles, I found a paper Five Millennium Catalog of Solar Eclipses, which describes the methodology and statistics of the Saros data that you linked to. Table 5-12 (pg. 61 of the paper, pg. 69 of the pdf) gives the length of a Saros cycle as a function of time in units of draconic and anomalistic months (a Saros cycle is defined to be 223 synodic months exactly). This information pertains to length of time that a Saros series lasts. If, instead, you just want the length of a Saros cycle in days, that is given at the beginning of section 5.3 (pg. 48/56) as approximately 6585.3223 days (in the year 2000).

Note that in the paper Terrestrial Dynamical Time (TDT or TD in the paper, or TT in most other places) is used (see section 1.2.4 pg. 2/10 for first mention, section 2.3 pg. 9/17 for a description).

 

[fizzy]

Thanks very much Iso. That is a great help. I will have more questions once I've gone through that in more detail, but just wanted to drop you a courtesy thank you.