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Wikipedia defines solar noon as

the moment when the Sun contacts the observer's meridian (culmination or meridian transit), reaching its highest position above the horizon on that day and casting the shortest shadow.

But it seems to me that "the moment when the Sun [crosses] the observer's meridian" and the moment when the Sun "reach[es] its highest position above the horizon on that day and cast[s] the shortest shadow" are actually two different times.

My intuition is that the latter moment, when the Sun is highest in the sky, is when the path of the subsolar point comes closest to the observer's position.

The Earth's period of revolution is much longer than its period of rotation, so the path of the subsolar point is almost directly westward, so these two moments are very close to each other. But the path still has a slight northward or southward component, reflecting the slight revolution about the Sun that occurs over the course of the day. So it will lie at a different meridian than the observer's at the point of closest approach.

Consider a hypothetical orbit where the periods of rotation and revolution were comparable (e.g. if the satellite were nearly tidally locked). Then the path of the subsolar point would generically not be close to westward; it would have a significant component parallel to the local meridian. So it would not come closest to the observation point at the same moment that it crosses the observation point's meridian.

Am I correct that the two moments defined in the Wikipedia article are different? If so, which one is the standard definition of solar noon?

(I'll ignore any complications related to either atmospheric effects, the eccentricity of the Earth's orbit, the Earth's axial procession, the fact that the Earth is not perfectly spherical, or the angular spread of sunlight. I believe that the discrepancy still exists even if we treat the Earth as a perfect sphere with no atmosphere, a constant rotation axis, orbiting the Sun in a perfectly circular orbit with a large enough radius that we can treat the Sun's incoming rays as perfectly parallel.)

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Yes, you are correct.

From an initial inspection of the equation for the solar altitude (elevation) from hour angle, latitude, and declination (from Wikipedia), it appears that maximum elevation should occur when the hour angle equals zero, which is when the Sun crosses the local meridian, if we assume that the solar declination is constant. But the declination isn't constant, and that affects the exact time of maximum solar elevation. (The latitude of the subsolar point equals the solar declination).

However, the discrepancy is quite small, under half a minute, even near the equinoxes, when the rate of change of the solar declination is the largest.

Here's some data from JPL Horizons to illustrate. The observation site is Greenwich Observatory.

 Date__(UT)__HR:MN:SC.fff     Azi____(a-app)___Elev  L_Ap_Hour_Ang
******************************************************************
$$SOE
 2026-Apr-01 12:03:30.000 *   179.886340  43.175347   -0.005544122
 2026-Apr-01 12:03:35.000 *   179.914820  43.175392   -0.004154909
 2026-Apr-01 12:03:40.000 *   179.943301  43.175430   -0.002765695
 2026-Apr-01 12:03:45.000 *   179.971781  43.175462   -0.001376482
 2026-Apr-01 12:03:50.000 *t  180.000261  43.175487    0.000012731
 2026-Apr-01 12:03:55.000 *   180.028741  43.175506    0.001401944
 2026-Apr-01 12:04:00.000 *   180.057221  43.175519    0.002791157
 2026-Apr-01 12:04:05.000 *   180.085702  43.175525    0.004180371
 2026-Apr-01 12:04:10.000 *e  180.114182  43.175525    0.005569584
 2026-Apr-01 12:04:15.000 *   180.142662  43.175518    0.006958797
 2026-Apr-01 12:04:20.000 *   180.171142  43.175505    0.008348010
 2026-Apr-01 12:04:25.000 *   180.199623  43.175485    0.009737224
 2026-Apr-01 12:04:30.000 *   180.228103  43.175459    0.011126437
$$EOE

The 't' marker indicates that transit has occurred, the 'e' marker indicates that maximum elevation has occurred. So the maximum elevation occurs ~20 seconds after the Sun transits the meridian.

That's just an excerpt of the data returned by Horizons. You can see the full output using this query

The standard definition of solar noon is the instant of meridian transit, when the solar hour angle is zero. Practically, it's quite hard to determine the instant of maximum elevation by observation, since the rate of change of elevation angle approaches zero as the angle approaches its maximum.

Back when astronomical observation was the basis of timekeeping, before we switched to atomic clocks, the observations were made using special transit instruments. However, the main precision timekeeping observations were made using the stars, and the Moon. It's difficult to make precision observations of the Sun, due to its brightness, and of course it's not safe to look at the Sun through a telescope!

The Moon is useful for timekeeping because it moves so quickly relative to the celestial sphere. However, to use lunar motion for timekeeping, you need to be able to predict those motions precisely, and that requires heavy number-crunching. Lunar theory is hard!

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  • $\begingroup$ Do you know which of the two inequivalent definitions of "noon" is more standard? $\endgroup$ Commented 2 days ago
  • $\begingroup$ If I'm understanding the geometry of the solar hour angle correctly, then that's the first definition ("the moment when the Sun [crosses] the observer's meridian") rather than the second definition, correct? $\endgroup$ Commented 2 days ago
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    $\begingroup$ Yes, that's correct. FWIW, here's a graph I made a few years ago using Horizons, showing how much the solar day length differs from 24 hours over the year, measured from solar noon to solar noon at Greenwich. i.sstatic.net/wmiBJ.png $\endgroup$ Commented 2 days ago
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20 seconds. Time for the subsolar point to move is 5 minutes of arc, or approximately 5 nautical miles.

In the days of the sextant mariners would notice that, so must have known about this and tables would have been clear whether they were calibrated for local meridian or highest point.

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