Venus is at its brightest in the morning sky. It’s been appearing in the sky-scenes I’ve been showing, in which I included “past-and-future Earths” as a trick for visualizing Earth’s orbit as seen from Earth. I said I would give the past-and-future Earths a rest, but they won’t let me rest; they keep waking me in the middle of the night, and I must show a yet-improved version of them – before announcing something more important.
Here is the scene in the west this evening.
The nearest past-Earth is only one hour back along our orbit! And it is shown at its real size.
The others are successively 10, 20, 30, 40… days back. And they are shown 100 times exaggerated in size!
Much trial and error led to finding that only thus could I make clear the swooping of the past-Earths around our orbit toward us, as on a circular railway around the Sun, without making the more distant Earths too small and without making the nearest one so gigantic that it covers many of the others.
You can see that the Earth of an hour ago is just about exactly at the “antapex of Earth’s way,” the direction straight backward along our orbit from our present point in it. And almost at that direction happen to be Mars and Neptune – which indeed are at their moments of “east quadrature,” 90° from the Sun, on Dec. 3 at 1 Universal Time and Dec. 5 at 22 UT.
And almost as close to the same direction is the fundamental geometric point called the vernal equinox direction or (for historical reasons) the “First Point of Aries”: the point where the ecliptic ascends through the celestial equator. It’s the point where the Sun appears from Earth at the March 20 equinox, or, oppositely, where Earth appears from the Sun at the September equinox.
If we were to draw this scene for some days later, Dec. 21, the date of the solstice, the antapex and past-Earth would be exactly at that crossroads. It makes sense. We’re looking along the tangent to our orbit. If you mentally stretch a wire from the Sun, down at the right, to the December solstice point far up off the picture to the left, our line of sight is perpendicularly across this wire.
I’ve also managed to disentangle the geometry better. You can see that each Earth’s sunlit side faces along the ecliptic toward the Sun, and that the equator drawn on it is parallel to the celestial equator, that is, it is in that plane.
And this shows that, in this December part of the orbit, the Earths’ north poles are tilted away from the Sun – sunlight is overhead in the southern hemispheres.
And here is tomorrow morning’s pre-sunrise scene.
The nearest future-Earth is only one hour ahead, and is at actual scale. The others are successively 10, 20, 30… days into the future, and are exaggerated 100 times in size.
Compare them with the Moon and Venus, which are shown at respectively 2 and 150 times their size. The Moon passes closest (3.4°) to Venus later in the day, Dec. 3 at 22 UT.
The Earth only an hour ahead is almost exactly at the Apex of Earth’s Way, called more straightforwardly (by Shannon Morgan) the EDOT or Earth’s direction of travel.
If you contemplate first the evening picture, with the past Earths curling around toward us, and then the morning picture, with the future Earths curving away into the distance, they together form a horseshoe shape in space. We can stand back and look at this as a whole.
We’ve zoomed out to a viewpoint 6 astronomical units (Sun-Earth distances) from the Sun and 15° north of the ecliptic plane. Shown is the “horseshoe” of Earth’s course along its orbit in the half-year centered about now (September to February). And other planets’ courses in December, and the sight-line from Earth to Venus at December 3.
Venus passed between us and the Sun on October 26, and will not appear at its farthest out (46.9°) into the morning sky (greatest westward elongation) until January 6. The elongation maximum is the climax of the planet’s performance in that it can appear about at its highest above the dawn horizon, but actually it is slightly brighter now than it will be then. The peak of brightness (at magnitude -4.7) was on November 30; and another kind of climax, the moment of greatest illuminated extent (when the sunlit part showed an area of 54 square seconds), was on December 1.
Oh, and that important announcement? It will be about our Zodiac Wavy Chart. Hold your breath.
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DIAGRAMS in this post were made with precision but had to be inserted in another format. You may be able to enlarge them on your monitor. One way: right-click, and from the drop-down list choose “View image” Or from that list choose “Copy image”, then put it on your desktop, then open it. I would welcome learning of any other methods.
This weblog asserts its right to be about astronomy or anything under the sun.
Cato ended every speech to the Roman Senate with: “Carthage must be destroyed.” I want to end every message with: “If you’re not doing something to slow carbon emission, you’re speeding the end of civilization.”
Hi Guy, Before too long, Roland will be reading your blog posts to Madeline. The other night when Madeline was in her crib and not sleeping, Roland had a conversation with her about astronomy. He explained that the earth does one rotation around the sun every year, so that her birthday comes just once a year (in response to her request for another birthday). Then she asked him about the moon, and he explained that to her, too.
My goodness, thanks for doing this work!
Instructions to “right click” and choose “View Image” or “Copy Image” from a drop-down menu don’t seem to work on my my Mac with OS10-Sierra. Probably they work on a Windows PC. The diagrams are marvelous, as they have always been. If anyone has any ideas how to view them adequately on a Mac, I’d like to hear them.