Time, Longitude, Latitude and Solar/Local Time
The relationships
The Earth turns 360 degrees in 24 hours: 15 degrees per hour, 1 degree per 4 minutes, 1 minute of arc per 4 seconds of time. Longitude east is later, west is earlier. Local mean time = UTC plus longitude/15 for east, minus for west. Standard time zones approximate this, and New Zealand uses NZST (UTC plus 12) and NZDT (UTC plus 13), with the Chatham Islands offset by 45 minutes further east.
Latitude arithmetic
One minute of latitude is one nautical mile. Along a parallel, departure (nm) = change of longitude in minutes x cos(latitude). This is the basis of questions about distance flown east or west, and about how far apart two points are at a given latitude.
Worked example
UTC is 0300. What is the local mean time at 075 degrees west? 75/15 = 5 hours, west means earlier, so LMT = 2200 on the previous day. In New Zealand at the same moment the time is 1500 NZST (0300 plus 12) and 1600 NZDT. Suppose also an aircraft at 30 degrees south flies 300 nm due east: change of longitude = 300 / (60 x cos 30) = 300 / 51.96 = 5.77 degrees, about 5 degrees 46 minutes of longitude.
Related points
Sunrise and sunset occur earlier in the east; the equation of time makes apparent solar time differ from mean time by up to about 16 minutes, which matters for twilight and ETA planning. Crossing the date line changes the date but not the elapsed time.
Traps
Reversing east and west; forgetting the date change when crossing the date line; using 1 degree = 4 seconds instead of 4 minutes; ignoring the Chatham offset and daylight saving; and using cos(latitude) where it does not apply, such as on a meridian.