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Difficulty: MediumLatitude, Longitude, and Time Calculations

A satellite communication signal is transmitted from a ground station located at longitude 40∘E40^\circ\text{E} at 04:30 PM local time. If the signal is received instantaneously at a tracking station located at longitude 20∘W20^\circ\text{W}, what is the local solar time at the tracking station at that exact moment?

  1. 12:30 PMAnswer
  2. B
    08:30 PM
  3. C
    03:10 PM
  4. D
    05:50 PM

Answer

12:30 PM
To find the local time at 20∘W20^\circ\text{W}, add the longitudes because they are in opposite hemispheres (40∘E+20∘W=60∘40^\circ\text{E} + 20^\circ\text{W} = 60^\circ). Convert the angular distance to time (60∘÷15∘=4 hours60^\circ \div 15^\circ = 4\text{ hours}). Because the receiving station is located to the west of the transmitting station, subtract 4 hours from 04:30 PM, obtaining 12:30 PM.

Step-by-Step Solution

1
Calculate total longitudinal distance between the two locations.
Longitudinal difference = 40∘E+20∘W=60∘40^\circ\text{E} + 20^\circ\text{W} = 60^\circ.
Locations in opposite hemispheres (East and West) require adding their longitudinal values to find total angular distance.
2
Convert the longitudinal difference into a time difference.
Time difference = 60∘15∘/hour=4 hours\frac{60^\circ}{15^\circ/\text{hour}} = 4\text{ hours}.
The Earth rotates 360∘360^\circ in 24 hours, which corresponds to 15∘15^\circ per hour.
3
Determine whether to add or subtract time based on direction.
Local time at 20∘W=04:30 PM−4 hours=12:30 PM20^\circ\text{W} = 04:30\text{ PM} - 4\text{ hours} = 12:30\text{ PM}.
Locations to the west are behind in local solar time compared to locations to the east.

Key Concept

Calculation of local solar time differences across meridians in opposite hemispheres
Estimated Time:1m 30s
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Topics

Latitude, Longitude, and Time Calculations

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