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Difficulty: HardLatitude, Longitude, and Time Calculations

An astronomical observatory located at longitude 64∘E64^\circ\text{E} records a cosmic ray pulse at 04:12 PM04:12\text{ PM} local solar time. Simultaneously, a ground monitoring station records the exact same event at 11:48 AM11:48\text{ AM} local solar time. What is the longitude of the ground monitoring station in degrees West (∘W^\circ\text{W})?

Answer: 2 ��W

Answer

The longitude of the ground monitoring station is 2∘W2^\circ\text{W}.
The time difference between 04:12 PM04:12\text{ PM} (16:1216:12) and 11:48 AM11:48\text{ AM} (11:4811:48) is 4 hours and 24 minutes4\text{ hours and } 24\text{ minutes}, which corresponds to an angular separation of 66∘66^\circ (4×15∘+24/4∘4 \times 15^\circ + 24/4^\circ). Because the time at the ground station is earlier, it lies to the west of 64∘E64^\circ\text{E}. Subtracting 66∘66^\circ from 64∘E64^\circ\text{E} crosses the 0∘0^\circ Prime Meridian to reach 2∘W2^\circ\text{W}.

Step-by-Step Solution

1
Calculate the difference in local solar time between the two stations.
Time difference = 16:12−11:48=4 hours and 24 minutes16:12 - 11:48 = 4\text{ hours and } 24\text{ minutes}.
Determining the time interval is the first step to finding angular separation.
2
Convert the total time difference into degrees of longitude.
(4×15∘)+(24÷4∘)=60∘+6∘=66∘(4 \times 15^\circ) + (24 \div 4^\circ) = 60^\circ + 6^\circ = 66^\circ.
The Earth rotates 15∘15^\circ per hour (1∘1^\circ every 4 minutes).
3
Determine the relative directional position of the ground station.
The ground station is 66∘66^\circ west of the observatory.
Earlier local solar time indicates a position further to the west.
4
Calculate the absolute longitude across the Prime Meridian.
66∘−64∘E=2∘W66^\circ - 64^\circ\text{E} = 2^\circ\text{W}.
Moving west from 64∘E64^\circ\text{E} uses 64∘64^\circ to reach 0∘0^\circ, leaving 2∘2^\circ in the Western Hemisphere.

Key Concept

Calculating longitude position across hemispheres using local solar time differences.
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Topics

Latitude, Longitude, and Time Calculations

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