Calculations Equation of Time APPARENT SOLAR TIME is the time that is shown on sundials. A MEAN SOLAR DAY is a constant 24 hours every day of the year. Apparent solar days are measured from noon one day to noon the next day (noon being the point at which the Sun is at its highest in the sky). An apparent solar day may differ from a mean solar day (of 86,400s) by as much as nearly 22s shorter to nearly 29s longer. As many of these short or long days occur in succession, the difference builds up to as much as nearly 17 minutes ahead or a little over 14 minutes late. The difference between apparent solar time and mean solar time is called the EQUATION OF TIME (EOT) EQUATION OF TIME = apparent solar time - mean solar time A table showing the Equation of Time through a year (the difference between the time on a sundial and the time on a clock) DATE TIME TIME DATE VARIATION VARIATION 1 ST JAN - 3m 12s 9 TH JUL - 4m 58s 22 ND JAN - 11m 25s 30 TH JUL - 6m 21s 12 TH FEB - 14m 20s 20 TH AUG - 3m 30s 5 TH MAR - 11m 45s 10 TH SEP + 2m 47s 26 TH MAR - 5m 58s 1 ST OCT + 10m 5s 16 TH APR + 1s 22 ND OCT + 15m 22s 7 TH MAY + 3m 27s 12 TH NOV + 15m 53s 28 TH MAY + 2m 56s 3 RD DEC + 10m 26s 18 TH JUN - 49s 24 TH DEC + 43s Shown on a graph, the readings appear as below:- EQUATION OF TIME November 3 rd Furthest ahead of Mean Solar Time + 16m 23s J F M A M J J A S O N D J MONTH February 12 th Furthest behind Mean Solar Time - 14m 20s tch shows
EQUATION OF TIME = apparent solar time - mean solar time If the Sun is observed due south at 11.50 GMT, this is the mean solar time. With the Sun due South, this is local noon as seen on a sundial apparent solar time = 12.00 EQUATION OF TIME = apparent solar time - mean solar time = 12.00-11.50 = + 10 minutes On March 7 th, the EOT is -11 minutes A person looks at their watch and notes the time at 11.09 GMT The time on a sundial (apparent solar time) = EOT + mean solar time = -11 + 11.09 = 10.58 If a sundial shows a time of 13.30 on a day when the EOT is +6 minutes, mean solar time = apparent solar time - EQUATION OF TIME = 13.30-6 = 13.24 All the clocks in the UK are set to time on the Greenwich meridian at longitude. However, if you do not live on the longitude meridian line, the Sun will arrive at your longitude line at a slightly different time to Greenwich. We know that the sidereal day is 23 hours 56 minutes, which means that the Earth spins 1 every 4 minutes. West of Greenwich Sun produces shortest shadow after noon East of Greenwich Sun produces shortest shadow before noon
Okehampton, Devon 12.16 4 W The shortest shadow is at noon in Greenwich, but 16 minutes later at Okehampton. A delay of 16 minutes is equivalent to a 4 difference in longitude. As the difference is after the expected time, the longitude will be west of Greenwich and so the longitude of Okehampton, Devon is 4 W. Stowmarket, Suffolk 11.56 1 E The shortest shadow is at noon in Greenwich, but 4 minutes earlier at Stowmarket. A difference of 4 minutes is equivalent to a 1 difference in longitude. As the difference is before the expected time, the longitude will be east of Greenwich and so the longitude of Stowmarket, Suffolk is 1 E. This is quite straightforward for the 4 days of the year where the apparent solar time = mean solar time (16 th April 14 th June 2 nd September 25 th December) On other days of the year, these two times are not the same. The differences are shown on the Equation of Time table above and need to be taken into account for the time at which the Sun produces its shortest shadow.
Okehampton, Devon 12.00.07 4 W No difference 12.16 12.00 No difference 12 th November 12 th November -15min 53s 12.00.07 11.44.07-15min 53s Time of shortest shadow at Okehampton Time of shortest shadow at Greenwich The difference in time of the shortest shadow between Greenwich and Okehampton is still 16 minutes, representing a 4 difference in longitude. The change for 12 th November is that the Sun culminates (reaches its highest point in the sky) 15 minutes 53 seconds earlier, bringing forward the times of the shortest shadow at each location. 1 On Christmas Day, a sundial shows the time is ready for the Queen s speech at 15.00. What is the mean solar time used by the BBC for their broadcast? 2 a The Sun is observed due south at Greenwich at 12.14 GMT. What is the value of the Equation of Time? b What month of the year would this be in? 3 Someone observes the culmination of the Sun (where the Sun reaches its highest point) at 11.54 at Greenwich. On the same day, a person in Truro, Cornwall at longitude 5 W, notes the time the Sun culminates. What will the time be in Truro for this event? 4 a The shortest shadow for a shadow stick placed on the Greenwich meridian occurs on a day when the EOT is +6 minutes. What is GMT at this moment of time? b A person carrying out an experiment on the same day notices that the shortest shadow occurs 6 minutes before the shortest shadow of their friend on the Greenwich meridian. What would the longitude be of this observer?
5 What is the Equation of Time when a clock at Greenwich reads 11.58 GMT and a sundial shows 11.52? 6 On 20 th August, a sundial at Blackpool (longitude 3 W) shows the time as 10.43. a What is GMT in Blackpool at the time shown on the sundial? b What will GMT be for the shortest shadow in Blackpool on that day? 7 My watch shows the time as 16.15. The Equation of Time for the day is +10 minutes. What is the apparent solar time? 8 On 28 th May, a sundial reads 13.21. What is the mean solar time? 9 What is the apparent solar time on 1 st October when my clock reads 15.14? 10 Apparent solar time at Greenwich on 26 th March is 10.24. What is the mean solar time?