## Thursday, May 3, 2018

### 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

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 (Ls) by:

tan (a) = H/ Ls

where (a) is the altitude of the Sun. So if H = 100 cm and Ls = 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 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  60o   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.