Date line, standard time and local mean time at 170°E
A flight departs Tokyo Narita, which keeps UTC+9, at 23:40 local time on 12 March. The planned flight time to Honolulu, which keeps UTC−10, is 9 hours 20 minutes. The aircraft crosses the date line eastbound and the captain asks for an arrival time in both UTC and Honolulu local time. A diversion airfield at 170°E is also being considered; its standard time is UTC+12, but the captain wants local mean time for a daylight assessment. You must also consider a 40-minute departure delay caused by a slot. The crew duty limit is expressed in local time at the destination, so the date and hour of arrival matter as much as the elapsed time.
1. Calculate the arrival time in UTC and in Honolulu local time for the original schedule.
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Convert departure to UTC: Tokyo local 23:40 on 12 March at UTC+9 is 23:40 − 9 = 14:40 UTC on 12 March. Add the flight time of 9 h 20 min: 14:40 + 9:20 = 24:00 UTC, which is 00:00 UTC on 13 March. Honolulu is UTC−10, so local time = 00:00 − 10 h = 14:00 on 12 March. The local calendar date at arrival is therefore 12 March, one day earlier than the UTC date and the same local date as departure, because the eastbound date-line crossing subtracts a day. Arrival is 14:00 HST on 12 March, or 00:00 UTC on 13 March.
2. Calculate the local mean time at 170°E at the moment of arrival.
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Local mean time depends on longitude, not on the political time zone. At 170°E, LMT = UTC + (170/15) hours = UTC + 11 h 20 min. Arrival is 00:00 UTC on 13 March, so LMT = 11:20 on 13 March. The standard time at 170°E is UTC+12, giving 12:00 on 13 March. The 40-minute difference arises because the zone is centred on 180° but the longitude is 10° west of that meridian; 10° of longitude corresponds to 40 minutes of mean solar time. For a daylight assessment, use 11:20 LMT, not 12:00 zone time. Confusing the two can put sunrise or sunset calculations out by nearly three-quarters of an hour.
3. If departure is delayed by 40 minutes, what are the new UTC, Honolulu local and 170°E LMT arrival times?
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A 40-minute delay moves departure to 15:20 UTC on 12 March. Adding 9 h 20 min gives 24:40 UTC, i.e. 00:40 UTC on 13 March. Honolulu local = 00:40 − 10 h = 14:40 on 12 March. At 170°E, LMT = 00:40 + 11 h 20 min = 12:00 on 13 March, and standard time there would be 12:40 on 13 March. The date-line logic is unchanged: the eastbound crossing still produces a local date one day behind UTC. The delay also shifts the Honolulu arrival from 14:00 to 14:40 on the same local date, which matters for the duty limit and for the airport's closing time if it is expressed in local time.