1.4j interpret simple shadow stick data to determine local noon and observer s longitude
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1 1.4j interpret simple shadow stick data to determine local noon and observer s longitude There are many opportunities for making observations of shadows cast with a vertical stick and the Sun. Observations during a day, or comparing observations through the seasons, help explain many astronomical events. The schematic diagram below shows the significance of shadow stick observations:- SUMMER WINTER SUMMER and WINTER Shadows
2 Features explained using shadow stick observations Knowing that the Sun moves because of the Earth spinning on its axis, the observations show:- Daily variations In Britain, shadows point north of the Sun the Sun is to our south Shadows are longest in the early morning and late afternoon, when the Sun is lower in the sky Shadows are shortest at noon, when the Sun is highest in the sky (The time of the shortest shadow gives us the time of local noon) Shadows move clockwise, indicating that the Earth is rotating in an anti-clockwise direction Seasonal variations Shadows are longer in the winter and shorter in the summer, showing that the angular height of the Sun varies during a year (the angle can be found to give a difference of 47 ) The shortest shadow is at noon on the summer solstice The longest noon shadow is at the winter solstice Local noon is found when the Sun casts its shortest shadow of the day On the following days of the year, the apparent solar time = mean solar time 16 th April 14 th June 2 nd September 25 th December If a sundial is at longitude, this means that the shortest shadow that the Sun produces is exactly at noon.
3 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 = shortest shadow at 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.
4 Stowmarket, Suffolk = shortest shadow at 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 mentioned where the apparent solar time = mean solar time On other days of the year, these two times are not the same. The differences are shown on the chart below and need to be taken into account for the time at which the Sun produces its shortest shadow. 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 VARIATION DATE TIME VARIATION 1 ST JANUARY - 3m 12s 9 TH JULY - 4m 58s 22 ND JANUARY - 11m 25s 30 TH JULY - 6m 21s 12 TH FEBRUARY - 14m 20s 20 TH AUGUST - 3m 30s 5 TH MARCH - 11m 45s 10 TH SEPTEMBER + 2m 47s 26 TH MARCH - 5m 58s 1 ST OCTOBER + 10m 5s 16 TH APRIL + 1s 22 ND OCTOBER + 15m 22s 7 TH MAY + 3m 27s 12 TH NOVEMBER + 15m 53s 28 TH MAY + 2m 56s 3 RD DECEMBER + 10m 26s 18 TH JUNE - 49s 24 TH DECEMBER + 43s
5 Okehampton, Devon = shortest shadow at W No difference No difference EOT = 0 EOT = 0 12 th November 12 th November EOT = EOT = -15min 53s min 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.
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