Calculating the latitude and longitude from time of sunrise and sunset?

Question

Is it possible to calculate the latitude and longitude of a person if the only available information is the accurate time of sunrise and sunset at the place where the person is standing .

Answer 1

For all measurements I need a pole or column of precisely known height. Or erect a straight rod vertically(measure the verticality with a plumb line) the height of which is known. Plane of the floor around it shall be perfectly horizontal for measuring the shadow of column (rod). It would be better if the direction of 'true north' passing through the column (rod) is well marked. Precision leads to precision in the result.

Wait for noon time sun. Measure length of shadow cast by a vertical column or rod planted . At noon the shadow is the shortest, aligned to true north line. Dividing this by length of column (rod) gives, 'tangent' from which local latitude can be known from a calculator.

For longitude it is required to know the time of local noon. It is important to know this. I prefer noon time measurement to sunrise and sunset times.

Every time zone or country time is centered around a specific longitude. This is known for the local region. For IST (Indian Standard Time) it is 82 1/2 deg E. Mark the time of the shortest shadow along the true north line as per your wrist watch. Noon time news bulletin is normally broadcast on a radio channel, that is preceded by 'time pips'. Broadcaster follows the local standard time. Hear to the radio and mark the long pip for the noon as per your wrist watch. Measure the difference between the two times. Convert this difference into angle, at the rate of 1degree every 4 minutes (1minute of angle every 4 seconds & 15 seconds of angle every 1 second of time). If the noon time pip of news bulletin is earlier than local noon, subtract difference from standard time longitude corresponding to local standard time. If the former occurs after the local noon time, add it to standard time longitude. This is the way to arrive at local longitude. As an example positioned at my home in Hyderabad, I noted the time of local noon (on my watch) as 12:00:00, that occured earlier. Later I noticed the shortest shadow aligned to true north line at 12:15:44. As noon time broadcast pip occured earlier I compute the difference as -00:15:44. At the conversion rate I gave above (I used my calculator that has hexadecimal calculations for degree/'/" of angle and hour/' /" of time), the angle comes to -3deg 56'.So, local longitude

82deg 30' E - 3deg 56' = 78deg 34'

If there is no local news bulletin at noon time, tune to BBC's noon time world service, but keeping your local standard time for computations.

To know the longitude corresponding to the local standard time, know how many hours ahead(+GMT) or behind (-GMT). For every 1 hour ahead add  15deg E (+GMT) or 15deg W (-GMT). Indian Standard Time is 05:30:00 ahead of GMT; so

5 1/2 X 15 = 82 1/2 deg E

which is the longitude of IST.

Answer 2

If you know the time and date of sunrise, you could draw a line on a globe or map, of all the places that had the same date/time of sunrise.  Generally, this will be a great circle around 1/2 the world, at some angle to straight north/south.

If you also know where the sunrise is -- the angle from true north -- then you could  figure out where on the line you were.

Actually, sailors before radio navigation preferred to use the noon sun, instead of sunrise.  There is too much atmospheric distortion when the sun is low to the horizon; this makes an accurate measurement of the sun location difficult.  At night, you can also use a bright recognizable star.

P.S.  For the time, you need the Universal Time, not local time.  UT is the mean solar time on the prime meridian.  (UT = UTC + or - up to 0.9 seconds for irregularities in Earth rotation).

Of course, you also need an ephemeris, giving the sun, moon, and star locations for any UT time during the year.

[Side note:  if you don't have UT, as for example people in Jamaica didn't in 1660, you can still figure longitude by making several observations of the moon over a month.  But this is not practical for a moving ship at sea.]

Answer 3

There are several points to consider.

1) Sunrise and sunset must be at sea level

2) You must know the date.

3) This will only provide you with longitude as every place on a as everyplace on a given latitude will have the same sunrise and sunset. - given the same altitude landform etc.

So in a word the answer to your question is "NO".

Answer 4

No.  If you know one of these, you can get the other, but you can't get two pieces of data out of one datum.  You can draw a circle completely around the earth showing where sunrise is happening at a particular instant, and of course you could be anywhere on the circle.