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I'm trying to learn celestial navigation using the Sun to determine longitude. I'm starting to understand some of these concepts, but I can't figure out how to calculate longitude accurately. Hoping someone can point out the error(s) in my math.

Starting Information:

  • I sighted solar noon in New York at 12:02PM EST.
  • The Earth rotates at 15°/hour.

Calculation:

Since I'm in the Eastern Timezone (UTC-5) I know the elapsed time from GMT is 5 hours plus 2 minutes or 5.0333 hours. I multiply the elapsed time by the Earth's rate of rotation to determine my longitude.

5.0333 hours * 15°/hour = 75.4995°W

My answer is incorrect. The longitude of New York is to ~74.01°W. My answer would put me 100 miles away! However to get the correct answer I would have needed to observe solar noon earlier at 11:56AM EST or 4.934 hours elapsed.

4.934 hours * 15°/hour = 74.01°W

I used the NOAA Solar Calculator to confirm Solar Noon did occur at 12:02PM not 11:56AM. So what gives? Where is the error coming from and how do I compensate? Thank you!

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  • $\begingroup$ Ate you assuming that solar noon at 0 longitude occurs at 12:00 UT? That would be your error. The time of solar noon depends on the date. $\endgroup$
    – JohnHoltz
    Jul 25, 2023 at 21:59
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    $\begingroup$ You need the Greenwich Hour Angle of the Sun. This is tabulated in the Nautical Almanac for every hour of the year. The method described in Mike G's answer also works, but is an approximate method. $\endgroup$ Jul 25, 2023 at 23:51
  • $\begingroup$ FWIW, I have some graphs & Python code related to the Equation of Time here: astronomy.stackexchange.com/a/49546/16685 $\endgroup$
    – PM 2Ring
    Jul 26, 2023 at 6:07

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You observed the apparent solar time, but in order to compute longitude you need the mean solar time. The difference between the two is the equation of time, a combined effect of (1) the obliquity between Earth's equator and ecliptic and (2) the eccentricity of its orbit. Almanacs commonly tabulate this quantity.

The NOAA calculator shows -6.55 minutes for the equation of time at midday in NYC on 2023-07-25. If you observed apparent solar noon at 17:02:00 UT, then mean solar noon was at 16:55:27 UT, indicating a longitude only 0.15° off the expected value. Not bad!

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  • $\begingroup$ This is the answer I was looking for! I was missing the distinction between solar noon and mean solar time. $\endgroup$ Jul 26, 2023 at 0:22

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