The Sun on the equator

The equinox will strike, like a bell, on Friday September 22.  It heralds “fall” in America, “autumn” in Europe, but “spring” in the southern hemisphere, so the safe term for it is the September equinox.

It is the moment at which the Sun, traveling as ever on the ecliptic, crosses southward over that other sky-circling line, the celestial equator.  This moment is 20:02 Universal Time, which is four or more hours earlier by clocks in North America.

Our scene, for an hour after sunset on equinox day in mid-U.S.A., happens to be about three hours after the instant of the equinox.  You can see that the “anti-Sun,” as we can call the point 180 degrees from the Sun, appears to be just on the opposite crossroads of ecliptic and equator.  Actually it’s a little way past, the fraction of a degree that the Sun moves in three hours.  The anti-Sun is already a little way into the northern celestial hemisphere, as the Sun is a little way into the southern.

Earth is hurtling away from the point we mark as “antapex of Earth’s way,” 90° to the right of the anti-Sun.  As Earth curves on along its orbit, both of these points will shift to the left: the anti-Sun higher into the northern sky, the Sun deeper into the southern, our hemisphere of Earth deeper into autumn.

Each day, the Sun has been riding lower across our skies.  The park bench to which we used to take out breakfast no longer gets sunshine: the morning Sun now slinks behind the trees.  Each day the Sun has risen at points farther south along the horizon, and on equinox day it will rise exactly at the east point.  Or will it?

If we want to be exact, and mean by “Sun” the center of the half-degree-wide Sun, there is only one instant when it is on the celestial equator.  So it follows that there is only one spot on Earth’s equator which gets to have the Sun exactly overhead.  If the equinox had been at 12 UT, the Sun would have been overhead on the zero or Greenwich meridian, but, being 10h02m later, it’s overhead at longitude 150.46° (the hours multiplied by 15) east, which is in the Pacific Ocean, north of the islands that are north of eastern New Guinea.

Only at this instant, and at a point 90 degrees west from there on the equator, does the Sun’s center rise exactly in the east.  But not only on the equator: also at the other points on Earth along a circle that you could draw with center at this Pacific point and radius 90°.  On the western half of this circle the Sun is at this moment rising due east and for the other half it is setting due west.  At the top of this circle, which is our north pole, the Sun’s geometrical center comes up and touches the horizon (at longitude 150.46° east) for an instant, and goes down.  At least I think so.  Didn’t really mean to get into so much geometry.

Though it’s all most conveniently described by saying that the Sun circles around our sky,

we’ve been convinced by Copernicus that, really, it’s the Earth that does the circling, around the Sun.  The two models are geometrically equivalent, but, as we now know and even Copernicus didn’t, the Sun is 109 times wider than Earth and 333,000 times more massive.  You could say, of a fly and a horse, that the fly buzzes around the horse or the horse buzzes around the fly.


9 thoughts on “The Sun on the equator”

  1. I’m puzzled when you say the sun at the north pole “comes up and touches the horizon (at longitude 150.46° east) for an instant, and goes down.” I thought at the north pole the sun’s center would always be going down at this time of year, touching the horizon at the moment of the equinox.

    1. Yes. that was badly expressed. At the north pole, on days before the September equinox, the sun travels all around just above the horizon. At the equinox, its center is (geometrically) exactly on the horizon. After the equinox, it travels all around just below the horizon.

  2. By an interesting coincidence, here at 122 degrees 25 arcminutes west longitude the equinox coincided with local true noon to the minute, 1302 PDT. I measured the height of the Sun by sextant as 52 degrees 6 arcminutes, and took advantage of the momentarily simplified math to easily calculate my latitude as 37 degrees 56 arcminutes north — only 9 arcminutes or 9 nautical miles north of the GPS latitude. Not great, but not bad.

    Measuring longitude is harder, but I’m working on it.

  3. On looking it up, the comment on spring is during the introduction preceding the actual song (A Song of the Weather)

  4. I recall a line from Flanders and Swann (about the fine weather in GB) where he misses spring – he was “in the bathroom”. Perhaps spring had occurred only at some antipodal longitude.
    And, from a barycentrephile; absent ground to stand on, the horse and fly buzz mutually ’round one another … of course.

  5. Here in our sublunar mundane world, everything is more or less approximate. From my back steps I have a clear view of the ridgeline of Potrero Hill to the east. Around the equinoxes I enjoy taking bearings to the rising Sun, watching the Sun move north in Spring and south in Autumn. The Sun rose due east, 90 degrees true azimuth, on September 15, a week before the equinox (and 17 minutes later than the “official” sunrise time for my latitude and longitude). The ridgeline is higher than my back steps, so by the time I see a speck of sunrise the Sun had already moved that much farther south since the idealized sunrise 17 minutes earlier. Also, there’s a notch in the buildings along the ridgeline right at 90 degrees true, so I see the first glint of sunlight through that notch for a few days in a row.

    I’ll leave it to the Copernicans, Keplerians, Newtonians, and Einsteinians to mentally translate these geocentrically perceived movements into successively more precise terms of the Earth’s rotation and orbit around the Sun.

    1. Whoops, I mangled a verb tense. “so by the time I see a speck of sunrise” should read “saw a speck”.

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