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    Re: Mer-pass vs Upper Culmination
    From: Frank Reed
    Date: 2017 Oct 22, 20:08 -0700

    Sean, you wrote:
    "Culmination and meridian passage always occur at the same instant."

    It might seem that this is implied by that description you quoted, but it's not. Picture a bright star, like Altair, approaching the meridian this evening for us observers in mid-northern latitudes. It climbs from the east, eventually reaches the meridian due south and barely changes its altitude for several minutes, gliding almost horizontal across our sky before it starts to fall toward the west. Culmination and meridian passage match. Now suppose you're in a fast vehicle looking at Altair while you're driving south at 60 knots. That's a mile a minute. So during those several minutes when Altair should be nearly at constant altitude as it crosses the meridian, you would see it climb one minute of arc per minute, even when it's due south, right on the meridian. Eventually, sometime after it reaches the meridian, the star's normal falling altitude after meridian passage will catch up with and cancel out that mile a minute that comes from our motion. And at that time the star's altitude, as observed from our moving platform, will start to decrease. So that means that the maximum altitude for an observer moving south at 60 knots will occur well after meridian passage. 

    Now consider the Sun's motion across the sky, or better yet the Moon's motion. Even for a stationary observer, the Moon (or Sun) is moving north or south at some knots and that has just the same effect as observer motion. If the Moon or Sun is moving north at some knots, it's just the same as if we are travelling south at some knots. It means that culmination will occur after meridian passage. For the Moon this is fairly significant. For the Sun, the maximum north/south speed is just about one knot and occurs on the equinoxes. It's a good approximation for a month on either side of the equinoxes. But that's a snail's pace, so it's really not much of a worry for the Sun. For an observer at rest, the Sun's times of culmination and meridian passage are barely different. The difference doesn't amount to more than about 15 seconds for observers between 45°N and 45°S.

    Yes, yes, I know... if a snail was really doing one knot, it would be flying. Most impressive for a snail! One knot isn't literally a snail's pace. If a snail passed you at one knot, you might be tempted to think he was driving a snail car of some sort. And of course there would be a big 'S' painted on top of it... And then when it zoomed past you at one knot, you would say... [come on, you all know this one]. 

    Frank Reed

       
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