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Difficulty: MediumThe Earth as a Planet and Earth Movements

A live international cultural event is broadcast from a venue at longitude 15∘E15^\circ\text{E} starting at 4:00 p.m. local time. What is the local solar time for a viewer watching the live broadcast at longitude 45∘W45^\circ\text{W}?

  1. A
    8:00 p.m.
  2. 12:00 p.m. (noon)Answer
  3. C
    2:00 p.m.
  4. D
    6:00 p.m.

Answer

12:00 p.m. (noon)
To find local solar time at 45∘W45^\circ\text{W} relative to 15∘E15^\circ\text{E}, calculate the total angular separation (15∘+45∘=60∘15^\circ + 45^\circ = 60^\circ). Dividing by 15∘15^\circ per hour yields a 4-hour difference. Because 45∘W45^\circ\text{W} lies to the west of 15∘E15^\circ\text{E}, subtract 4 hours from 4:00 p.m., resulting in 12:00 p.m. (noon).

Step-by-Step Solution

1
Calculate total longitudinal difference between the two locations.
Since 15∘E15^\circ\text{E} and 45∘W45^\circ\text{W} are in opposite hemispheres relative to the Greenwich Meridian, add the values: 15∘+45∘=60∘15^\circ + 45^\circ = 60^\circ.
Longitudes in opposite eastern and western hemispheres must be summed to find total angular distance.
2
Convert longitudinal difference into time difference using the rate of Earth rotation (15∘=1 hour15^\circ = 1\text{ hour}).
60∘15∘/hr=4 hours\frac{60^\circ}{15^\circ/\text{hr}} = 4\text{ hours}.
The Earth rotates 360∘360^\circ in 24 hours, which corresponds to 15∘15^\circ per hour.
3
Determine local time by applying the directional rule (East gain, West lose).
4:00 p.m.−4 hours=12:00 p.m. (noon)4:00\text{ p.m.} - 4\text{ hours} = 12:00\text{ p.m. (noon)}.
The target location (45∘W45^\circ\text{W}) is west of the broadcasting venue (15∘E15^\circ\text{E}), so the time difference must be subtracted.

Key Concept

Longitude, Earth Rotation, and Local Time Calculation
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Topics

The Earth as a Planet and Earth Movements

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