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Houston is at 29.8 degrees north and the Sun's maximum declination is 23.5 degrees which means that the Sun gets within 6.3 degrees of overhead at midday on June 21. Note that during summer time that is 1 pm.
Houston's longitude is 95.4 degrees west which is 5.4 degrees west of the standard longitude for its time-zone, so the Sun's maximum altitude occurs a little later, at 1.22 pm on June 21.
But on June 21 the Equation of Time tells us that the Sun is 3 minutes 'fast' compared to its mean or average position, so the maximum altitude occurs at 1.19 pm.
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