Lost at Sea - Longtitute
A traveler is lost with absolutely no idea what his location is. From a vantage point he has a clear unobstructed view both east and west to the distant horizon which are at similar altitudes to his location. He has a watch accurately set to North American Central time zone, GMT - 6 hr. The watch also indicates the correct date
On June 13 he notes the sunrise time at 9:49 am and the sunset time as 11:14 pm according to the time indicated on the watch.
What is the Longitude of his location ? Degrees west.
Assume his vantage point remains stationary for the two sightings.
The answer is 157.9.
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1 solution
The traveler was familiar with the general principles and use of the equation of time . He made his opbservations on June 13th for good reason. He knew that date would be, or very nearly be, one of the four dates each year when there is no adjustment required to convert solar time to mean time.
The first thing to calculate is what would be the time of midnight (or high noon) at his location according to his watch. High noon will occur close to half way between sun up and sun down on any given day.
11:14 pm = 23.233 hr. and 9:49 am = 9.817 hr
23.233-9:817 = 13.416 hrs day length.
Before high noon hrs. = 13.416 /2 = 6.708 hrs. high noon time ~= 9.817 +6.708 = 16.525 hrs. on the watch
16.526 cental time to GMT 16.525 +6 = 22.525 hr. GMT
High noon solar time on June 13 will always occur very nearly at 12.00 hr GMT at Greenwich, England where the longitude is 0 degrees.
Time difference between solar high noon at Greenwwich and the current location? 22.526 - 12.00 = 10.526 hrs.
Degree of angular rotation of the earth in 10.526 hrs? 10.526/24 *360 = 157.9
157.9 degees west will be well within one degree of correct longitude for this location.