Longitude and time: local time

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Detail

Longitude is the angular distance of a place east or west of the Prime Meridian. The Prime Meridian is the 0° line through Greenwich, England. The antimeridian is on the opposite side of the earth, at 180° [2].
Earth's rotation gives us the rule, step by step:
The earth turns from west to east. It turns through 360° in 24 hours.
360° ÷ 24 h = 15° of longitude per hour [3].
60 minutes ÷ 15° = 1° every 4 minutes.
So the sun seems to move across the sky from east to west. It crosses one meridian after another.
Arc-to-time conversion (useful for exam sums):

Each hour of difference between local noon and the time at Greenwich equals 15° of longitude [2]. This is how sailors found their longitude: they compared local noon with a clock kept on Greenwich time.

Places to the east turn towards the sun first. So they see sunrise, noon and sunset earlier.
So time increases eastward and decreases westward.
Example: when it is noon at your place, a place 15° east has 1 p.m. That meridian faced the sun an hour ago. A place 15° west has 11 a.m. [3].

Local time: the time of a place set by the sun over that place's own meridian.
Local noon: the moment the sun is highest in the sky over that meridian. In the northern hemisphere the sun is then due south and at its greatest height above the horizon [3].
Same meridian = same local time. Latitude does not matter. Local noon happens at the same moment for every place on one meridian [3].
Delhi (north India) and Bengaluru (Karnataka, south India) both lie near 77°E. So their local time difference is zero, even though they are far apart from north to south.
Different meridians = different local times. Every meridian has its own local time. So a country that stretches far from east to west has many local times. India uses one standard time instead: Indian Standard Time (IST). IST is the local time of the 82°30'E meridian (NCERT).

Step 1: Find the difference in longitude between the two places.
If both places are on the same side of Greenwich (both E or both W), subtract the smaller longitude from the larger one.
If they are on opposite sides (one E, one W), add the two longitudes.
Step 2: Multiply the difference by 4 minutes. Change the answer into hours and minutes.
Step 3: If the place you want is to the east, add this time. If it is to the west, subtract it.

Place	Longitude	Working	Local time
Thimphu (Bhutan)	90°E	90 × 4 = 360 min = 6 h; east, so add: 12 + 6	6 p.m.
New Orleans (USA)	90°W	90 × 4 = 360 min = 6 h; west, so subtract: 12 − 6	6 a.m.

Check with the opposite-sides rule. Thimphu and New Orleans are on opposite sides of Greenwich.
Add the longitudes: 90° + 90° = 180°.
180 × 4 = 720 min = 12 hours.
6 a.m. to 6 p.m. is 12 hours, so the answer checks out.

Porbandar is on the west coast of Gujarat. Tinsukia is in eastern Assam, in the north-east.
Take the longitude difference as 30°.
30 × 4 = 120 minutes, which is about 2 hours.
Tinsukia is to the east, so its local time is about 2 hours ahead of Porbandar.
What you see on the ground: the sun has already set in Assam while Gujarat still has daylight.
Same problem in national debate: a question in Parliament noted that the sun rises nearly two hours earlier in the east (Arunachal Pradesh) than at the western tip (Gujarat). It also mentioned proposals for two time zones:
an Eastern Indian Time (Arunachal Pradesh to Bihar), one hour ahead
a Western Indian Time (Uttar Pradesh to Gujarat) [4]

360° in 24 h → 15° = 1 hour, 1° = 4 minutes, 15' of arc = 1 minute, 1' of arc = 4 seconds.
Time is ahead in the east and behind in the west, because the earth rotates west to east.
Local noon = the sun at its highest over a place's meridian. All places on one meridian have local noon at the same moment, whatever their latitude.
Delhi and Bengaluru (both near 77°E): local time difference = zero. Trap: their big north–south distance does not change the time.
Noon at Greenwich → Thimphu (90°E) = 6 p.m.; New Orleans (90°W) = 6 a.m.
Places on opposite sides of Greenwich: add the longitudes. 90°E and 90°W → 180° → 12 hours.
Porbandar (Gujarat) – Tinsukia (Assam): 30° → about 2 hours. Tinsukia is ahead.
Prime Meridian = 0° through Greenwich. Antimeridian = 180° [2].
IST = local time of 82°30'E (NCERT).

Local time comes from rotation and longitude, not latitude.
The earth turns 15° every hour, so each meridian reaches noon at a different moment.
This is why countries with a wide east–west spread need standard time and time zones.
India's wide east–west spread (about 30°, roughly 2 hours) causes real problems with a single IST.
The sun rises and sets early in the north-east, but offices open by IST.
So daylight hours are lost, and energy use and work routines suffer.
This is the basis of the demand for a separate time zone in the north-east [4].
Longitude–time link in navigation and mapping.
Comparing local noon with Greenwich time gives a place's longitude. 1 hour of difference = 15° [2][3].
This method is the basis of the global system of meridians and time zones.