If the following local hour angles are expressed in terms of hours, minutes, and seconds, which formula correctly represents local mean time?

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Multiple Choice

If the following local hour angles are expressed in terms of hours, minutes, and seconds, which formula correctly represents local mean time?

Explanation:
Local mean time is tied to the mean Sun’s position in the sky. The local hour angle of the mean Sun is defined so that it is zero when the mean Sun is on the local meridian (solar noon). Since solar noon corresponds to 12:00 local mean time, you convert the current hour angle into a time by adding 12 hours. Therefore, local mean time equals the mean Sun’s hour angle plus 12 hours. If the hour angle is positive (west of the meridian), LMT is in the afternoon; if negative (east), it’s before noon. Adding 12 hours aligns the zero-hour angle with 12:00, which is why the correct relation is LMT = LHA(mean sun) + 12 hours.

Local mean time is tied to the mean Sun’s position in the sky. The local hour angle of the mean Sun is defined so that it is zero when the mean Sun is on the local meridian (solar noon). Since solar noon corresponds to 12:00 local mean time, you convert the current hour angle into a time by adding 12 hours. Therefore, local mean time equals the mean Sun’s hour angle plus 12 hours. If the hour angle is positive (west of the meridian), LMT is in the afternoon; if negative (east), it’s before noon. Adding 12 hours aligns the zero-hour angle with 12:00, which is why the correct relation is LMT = LHA(mean sun) + 12 hours.

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