What is the relationship between Julian Days and other observable time periods?

[fizzy]

JD is a count of days since an arbitrary zero datum, in order to have a non variable timescale for astronomical calculations and ephemeris software.

Since these are real noon-to-noon days they must actually be variable in length due to variations in LOD over time. WonkyPedia tells us that it has changed around 70s in the last century.

So , how long is a JD? Does it vary with time? How do I compare or convert to some other observable time period like sidereal or tropical year?

Thanks.

 

[IsometricPion]

According to Wikipedia, a Julian Day (JD) is measured in Universal Time (UT). The article on UT references an article called Astronomical Time by McCarthy written in 1991 which says that

Currently, UT1 is determined from multiparameter solutions of very long baseline interferometry (VLBI), satellite laser ranging (SLR) and lunar laser ranging (LLR)

. Thus, a JD varies with time (presumably daily, assuming the solutions are obtained daily). The article suggests that

UT1 is often obtained by users through tabulations of the differences UT1-TAI or UT1-UTC

, so it seems like it would be easiest to convert to TAI (which ticks, as far as feasible, at a constant rate) and then look up the difference.

The wikipedia article on UT implies that some people use UTC rather than UT1 for determining the julian day fraction/length. UTC has days of 86400 seconds, except when leap seconds are added (or removed, in principle). UTC is defined to remain within 0.9 seconds of UT1.

For siderial time the conversion equation can be found on the associated Wikipeida page (or in the above linked article), and similarly for a tropical year. Note, however, that when calculations over long time periods are done, the ephemeris/SI second is often used, which essentially involves conversion to TAI. This is necessary since analytical calculations assume a uniform progression of time.

 

[fizzy]

Thanks for the reply. That paper starts by defining the local meridian as a plane defined by local vertical ( a vector ) , the centre of the Earth and the north pole. That it too much information to define a plane. A minimum of three points or a vector and one point defines a plane. Two points plus a vector many not even define a plane since they could disagree. This is high school geometry, not a reassuring start for a process of a definition of a standard.

Also the "centre of the Earth" is not an observable quantity, so seems pretty useless. Also, how can "local vertical be determined, it is not even defined.?

I then goes on to say Greenwich mean sidereal time does not account for nutation and periodic variations but accounts for the difference with a 3rd order polynomial; ie not a periodic function.A surprising lack of understanding for someone with the author's credentials.

I don't think this is a dependable document.

I look for an alternative academic source :
http://farside.ph.utexas.edu/Books/Syntaxis/Almagest/node15.html
This one starts talking about "compass points" ,implying magnetic north is involved. This gets messier the more I dig.

 

[IsometricPion]

That paper starts by defining the local meridian as a plane defined by local vertical ( a vector ) , the centre of the Earth and the north pole. That it too much information to define a plane. A minimum of three points or a vector and one point defines a plane. Two points plus a vector many not even define a plane since they could disagree. This is high school geometry, not a reassuring start for a process of a definition of a standard.

Also the "centre of the Earth" is not an observable quantity, so seems pretty useless. Also, how can "local vertical be determined, it is not even defined.?

The local meridian is the plane of constant longitude passing through ones location (see the Wikipedia article on Meridian (astronomy)). The description he gives is meant to be intuitive (like the picture on that Wikipedia page), not a prescription for measuring your local meridian. To find the local meridian, it is sufficient to look up the local longitude.

I then goes on to say Greenwich mean sidereal time does not account for nutation and periodic variations but accounts for the difference with a 3rd order polynomial; ie not a periodic function.

The point of Greenwich mean sidereal time is to have a time that is uniform across long time periods. In particular, nutation and precession are removed and/or averaged out (depending on the extent to which the source is modelable). I agree that approximating a periodic function (with period around 41000 years according to the Wikipedia article on Axial precession), by a third-order polynomial will not be accurate for times comparable to or larger than the period. However, astronomical equations such as this are typically updated every few years with more accurate values. For such short time scales, the polynomial approximation is sufficiently accurate (in fact, it is probably not wildly wrong for time scales comparable to the length of recorded history).

 

[fizzy]

His introductory waffle was not encouraging and does not inspire confidence in what may follow. A plane is not defined by a vector and two points. This either shows a lack of basic geometry to a lack of care in what he is writing. Should I then await a similar lack of care and accuracy in what follows ?

Thanks, I realize how the polynomials are used. I just re-read the paragraph before that and he appears to confuse nutation and precession !

This "invited paper" clearly is not a paper at all and did not get any peer review. It is very careless. Falling back on WonkyPedia is last resort since that is full or errors too. Look at the Y scale on the graph I posted . Did LOD change 70 seconds in the last century?

With at least three definitions of day and what appears to be 5 or so different time scales this is a nightmare to understand. Not having proper, reliable sources does not help at all. Very frustrating and time wasting.

 

[fizzy]

To add to the confusion, unlike all the other 'sidereal' terms, the sidereal day is relative to the vernal equinox, not fixed starts ( sidus ) !

ie a sidereal day is measured in the same frame as a tropical year, not a sidereal year.

Iso:
"UT1 is often obtained by users through tabulations of the differences UT1-TAI or UT1-UTC"

My problem is that I have a NASA figure for the mean orbital period of Jupiter given in MSD. I need to convert this to be compatible with other polynomials in JD evaluated at J2000. An instantaneous value from a table would not be suitable since it would include sub-annual variations such as tides and nutation. Jupiter's period varies quite a bit so the NASA value must be longer term average.

 

[IsometricPion]

My problem is that I have a NASA figure for the mean orbital period of Jupiter given in MSD. I need to convert this to be compatible with other polynomials in JD evaluated at J2000. An instantaneous value from a table would not be suitable since it would include sub-annual variations such as tides and nutation. Jupiter's period varies quite a bit so the NASA value must be longer term average.

The JD defined in terms of UT1 and that defined in terms of 86400 SI seconds only differ (on average) by a few milliseconds. The accumulated difference (which is what ΔT is) builds up, but only over long time periods (70s over the last 100 years as you note from the graph). I will respond in more detail on your thread Knowing What Day It Is.