Selected Questions-Answers From All Experts Astronomy Forum (Types Of Solar Time)

Question:  I am thoroughly confused about the different types of solar time including: how time zones work. Greenwich Mean Time. local mean time, apparent solar time. mean solar time etc. Can you explain these, especially the differences, using some examples? - Mystified in Maine


Answer:

A “time zone” is defined by taking the 360 degrees through which Earth rotates in one day, and dividing it by 24, since it requires approximately  24 hours (actually 23 h 56m) to make one revolution. Thus, one standard time zone would be generated via (360 deg/ 24 hr) = 15 deg/h or 15 degrees of longitude per hour - so be 15 degrees of longitude in expanse. Thus, time zones (calibrated per HOUR) were marked out by LONGITUDE differences.

Time zones don’t mean anything until referenced or calibrated to a fixed position-location, and that is the Greenwich Meridian, defined as 0 degrees longitude. All longitudes west of Greenwich mark time earlier – and all longitudes east of Greenwich mark times later. Thus, Berlin will always have a time later than London, and London will have a time later than New Orleans, just as Barbados will always have a time earlier than London and later than Miami.

The time difference is referenced to longitude difference for the central meridians. For example, if London is at approximately 0 degrees longitude, and New Orleans is at 90 degrees west longitude, then New Orleans is earlier than London by (90 deg/ 15 deg/h) = 6 hours. If the time in London is noon local mean time, then it is 6 a.m. in New Orleans.

In order to solve the problem of different local mean times, Greenwich Mean Time or GMT was developed, so people could compare the same clock times around the world. GMT is based on a 24 hour  clock defined at the Greenwich meridian. So, for example, if one is listening to the BBC from New Orleans and the time given is 13h 30 m GMT, then that means it’s 1.30 p.m. LMT in London. Since New Orleans is 6 hours earlier, that means it’s 7.30 a.m. local mean time in New Orleans.

 Thus, knowing GMT, one can always work out the local mean time at one’s location if one knows the longitude difference relative to Greenwich. (Note for the purposes here, I‘m taking London as having the same longitude as Greenwich. It's actually off by a few thousand feet but negligible in terms of computations.)

Apparent solar time, meanwhile, is erratic because it’s based literally on sundial time, and what’s called the equation of time (E.T.) (See Figure 1) :

The equation of time shows the Sun is an unreliable object by which to measure precise time, given the Sun can be "fast" by as much as 18 minutes on a given day (e.g. near Nov. 1st) and "slow" - e.g. lagging by as much as 15 minutes., e.g. in February.  This is why mean solar time was invented. Mean solar time is based on what we call the "mean Sun", a fictitious object which always moves at a uniform rate through the year, i.e. assumes the rate of the Earth's rotation is uniform through the year. (Thus, "Greenwich Mean Time" is based on the measurements of the "mean Sun" at the Greenwich meridian)

A more useful way to appreciate the meaning of apparent solar time is to construct a simple shadow stick such as shown in the diagram below (for March 21st, at Barbados), and using it to make apparent solar time measurements. 

We know that the height (H) of an object placed in  direct sunlight at local noon is related to its minimum shadow length (L_s) by:

tan (a) = H/ L_s

where (a) is the altitude of the Sun. So if H = 100 cm and L_s = 21 cm, then:

tan (a) = 100 cm / 21 cm = 4.76

And a = arc tan (4.76) = 78. ^o1

In fact, the actual value for Barbados for the given date should have been 77.0 ^o or the zenith distance of the Sun equal to the latitude  (e.g. 90.0 ^o  - 77.0 ^o =  13.0 ^o  N).  This is the precise measurement that would denote local noon apparent solar time.

 Exact local (solar) mean time for any given longitude is computed via a slight adjustment to standard time. For example, if Barbados actual longitude is 59 degrees 30’ minutes W then the local mean time requires a slight adjustment equal to the time difference corresponding to 30’ of angular difference, e.g. in longitude from the  60^o   meridian. Since the meridian referencing Atlantic Standard time (A.S.T.) is 60 deg W and (60 deg W - 59 deg  30’ W) = 30’. This is half of a degree, and we can see then that for every degree of rotation made by the Earth there elapses an equivalent 4 minutes of time. )

Since 15 deg = 60 minutes (1 hour), then 1 degree = 60 mins/15 = 4 minutes. Similarly 30’ corresponds to 2 minutes of time. So if A.S.T. (Atlantic Standard Time) at 60 deg W is 2 p.m. then the local mean time for Barbados’ specific longitude is: 2 p.m. – 2 mins. = 1: 58 p.m. L.M.T. .

Hopefully, these examples will shed light on the different types of solar time.

Where Did That Extra Second Come From?

As most readers are probably aware, yesterday (Saturday) featured 86, 401 seconds rather than the usual 86, 400. One leap second was added to compensate for a slowing Earth rotation (actually - if factored in from 1972, 24 full seconds slower than at that time). A cutesy explanation (on ABC News) last night was that "just as humans slow down when they age so has the Earth." Well, yes...and no.

The actual physical reason has less to do with aging per se and more to do with what we call "tidal friction" resulting from the Moon's cumulative gravitational effects (part of which causes our spring and neap tides as well as regular tides on Earth). Over time those gravitational effects add up....and a leap second must be added to correct it.

Thus did the concept of Ephemeris time (ET) enter the picture and ET thereby became part of the lexicon of astronomers, and integrated within the specialized sub-discipline of astrometry. The job of astrometry is to keep careful quantitative track of any changes that would lead to time corrections, specially related to ET. This isn't so stirring an idea now, but a couple of centuries ago it was almost a given that the Earth's period of rotation about its axis was constant. (Apart from a slow secular increase due to tidal friction). 

Note that "secular changes" are essentially non-reversible, and hence proportional to time passed.

Meanwhile, the value of ET at a given instant is reckoned by extremely accurate observations of sudden variations in the longtiudes of Sun, Moon and planets which of course emanate from variations in Earth's rate of rotation. Hence, if I detect a rather sudden "jump" in the Sun's (heliographic) longitude - say during lengthy observations of a sunspot group, I can tie that in to variation in Earth's rotation. (Generally, however, such changes wouldn't occur that fast.)

To get into the nitty gritty, Simon Newcomb (1895) originally provided us with the detailed expression for the longitude of the Sun (cf. 'Spherical and Practical Astronomy Applied to Geodesy', p. 168):

L= 279 deg 41'48."04 + 129, 602, 768."13 t_e  + 1."089 t_e^2

where t_e is the length of the tropical century from the standard epoch. (Recall the 'tropical year' is the time taken by the fictitious Sun to make one passage between the mean Vernal equinox. Hence, a tropical century refers to 100 such passages.)

Now, differentiating the preceding with respect to time t_e,  the instantaneous rate of change of L per second of ET is obtained, viz.

dL/ dt_e  = 0."0410686389744 + 6."9017 x 10^-10t_e

The last factor featuring the 10 raised to the negative 10 power is an important marker. It allows us to estimate the frequency at which time corrections, say to Earth's rotation, need to be made. Thus, the equation shows us that to define Ephemeris time correctly to 1 part in 10^10 (or one part in ten billion) observations of the Moon are required over at least 5 years.

Another quantity that makes its way into such computations is the Right Ascension of the fictitious mean Sun;

RA = 18 h 38 m 45.s 836  = 8, 640, 184.s 542 t_e  =0.s 0929 t_e^2

What exactly is the fictitious mean Sun? What, for that matter, is the fictitious Sun (referenced earlier in connection with the tropical year, and century)? Basically, the former is that fictitious entity which is presumed to travel always at a uniform rate every hour and every day. This fictional creation enables us to fabricate "time zones" based on the fiction that the Earth turns uniformly through 360 degrees every 24 hours, hence through 15 degrees every hour. Hence, we set out longitude markers to reference the mean time for all locations, say within 15 degrees of longitude.

Hence, in regular standard time (not 'daylight saving') one has the time zone for the Greenwich meridian registering say 12 noon, then at a longitude of 15 deg W. the time is one hour earlier, and at 30 W two hours earlier, and so forth. All locations within the time zone agree (with few exceptions) to keep the same time.

By contrast, the fictititous Sun is not so regularized so its motion is erratic. This is also referenced to what we call "apparent solar time" or "sundial time".  Based on comparisons of the two, one can then compute what is called the "equation of time", see e.g.

http://brane-space.blogspot.com/2011/07/tackling-simple-astronmoyh-problems.html

Now, if we reckon Ephemeris time into the context of the "fictitious Suns" we will be using two key hour angles: h (the hour angle of the fictitious mean Sun) and h' (the ephemeris hour angle of the fictitious mean Sun. Based on this, Ephemeris time (ET) would be expressed:

ET = h + 12h

While the equation of time (EQN T) is:

EQN T =   h"   -  h'

where h" is the hour angle of the fictititous Sun.(Those who'd like to review hour angles and how to work them out can consult two earlier blogs:

http://brane-space.blogspot.com/2011/03/more-spherical-astronomy.html

and

http://brane-space.blogspot.com/2011/03/solutions-to-spherical-astronomy.html

I will also give here, without derivation (though I welcome energized readers attempting it using material from prior blogs) the relation between the corrected time delta T, Ephemeris time and Universal Time (UT):

delta T = ET - UT

Generally, delta T is computed - or at least used to be before the era of atomic clocks - through inverse interpolation in the ephemeris of the Sun, Moon & planets...and deducting the recorded UT time of observation. (Note: An 'Ephemeris' is a manual giving all the changing positions correlated with times, dates for celestial objects).

In the modern atomic clock -time epoch, things are (fortunately!) much more streamlined and we have powerful Cray and other supercomputers to boot. Basically, one associates the atomic time (AT) and Ephemeris time (ET) via the generic expression:

AT - ET = a + bt  + ct^2

where t denotes the time from the epoch when AT = ET + a

Hence, the coefficient 'a' determines the epoch of atomic time in relation to Ephemeris time. The coefficient 'b' is the division ratio adopted for the atomic resonator (as we know, different atomic clocks, e.g. cesium , quartz etc. have different frequencies, hence differing resonator rates). Finally, coefficient c is a cosmic constant which value may be 0 or more likely on the order of 0.s001 per year.

As we can see from the above considerations, for the most recent leap second correction:

ET - UT = 1 s  =  AT  - ET

Just be glad you only have to savor that extra second of time, not figure out when exactly you have to add it!