The Quadrantids and the Edot

The Quadrantid meteor stream hits us in the night of Jan. 3/4. Here is the picture from Astronomical Calendar 2016 page 6, but more expansively and with an addition.

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Shannon Templeton, in Durham, North Carolina, wrote to me that she has “a love of astronomical motions [and] a passion for writing astronomy programs” but was puzzled over how to find the position in the sky of what she calls the “Earth’s Direction of Travel,” or EDOT: “the imaginary, ever changing point we are racing towards.” She had expected various trigonometric complications arising from our position on the spherical and spinning Earth, and the ellipticity of Earth’s orbit.

I think (someone may correct me) that there is no complication. The direction is simply that which is tangent to Earth’s orbit at the moment: in other words, it is in the ecliptic plane and at ecliptic longitude 90 degrees west of the Sun. For instance at 2016.0 the Sun is at longitude 280 degrees, so the EDOT is at longitude 190, latitude 0. No matter where you stand on Earth, you’re being carried toward this point.

Shannon replied, in effect, “Of course. It’s simpler than I thought.”

I hasten to add that Shannon is not just an enthusiastic but an advanced student of astronomy. She knows more than I do, and was once engaged in the study of binary-star motions and their apparent divergence from relativity.

It struck me that her “EDOT” is worth adding to sky illustrations (like the anti-Sun or “Earth’s shadow” point which I had already added and which is at a right angle to it), especially because of her further remark: “One reason the EDOT intrigues me is so I can visualize where the radiant of a meteor shower is compared to the EDOT, thus showing the angle of the comet debris orbit. This is of zero importance to anyone on the planet, but these are the kinds of things that keep me awake at night until I figure them out.”

Yes, it’s far from immediately obvious how the direction from which the Quadrantids, or other meteors, come toward us – in other words their radiant, which gives them their name – results from their curving orbit and its intersection with our curving orbit. In trying to visualize it better, this was the first diagram I plotted:

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– a sort of close-up of another Astronomical Calendar illustration, the one showing the orbits in space.

The dotted line represents the orbit of the meteors, though strictly – since the meteor stream in space is millions of miles wide – it is the path only of those few meteors that happen to arrive from the zenith.

And the Earth’s motion is shown by the thick arrow, a sort of rail along which Earth is riding in its journey around the Sun. (It’s like the flight-of-Earth arrow in the Astronomical Calendar pictures for solar eclipses, but longer.)

It is now fairly easy to see the relation between these two paths in space. But not easy to measure, since it is an angle in a solid picture.

But look back at the first picture, the sky scene. The distance between “the radiant of the Qudarantids” and “Earth’s direction of travel” is the angle between them.

I realized that I could make my plotting program spit out the position it had calculated for both of these points, and then calculate the angle between them. The radiant is 63 degrees from the EDOT. (And at a position angle of 71 degrees from it, as measured from the zenith. It could be given in other ways, as from the north celestial or north ecliptic poles.)

All that may not be particularly vivid to anyone other than me and Shannon. What surely twangs a note of excitement is that target-like symbol. We are all hurtling, at 67,000 miles an hour, toward that point.

Notice that the EDOT just about coincides with the position of the Moon on Jan. 2 when it was at Last Quarter. Naturally: for when the Moon is at that position, it is passing around in front of us, it’s “left” (west) side illuminated by the Sun.

As the remaining hours of the night go on, the point will move very slightly eastward down the ecliptic; and the horizon will move much faster downward; until, at the moment when the Sun is exposed, we will be on the “bow” of our Earth ship, our heads pointing up in the direction in which we are going.

– I had to hit “publish” to this post without giving it the usual preview, and go on a visit. Returning three hours later, I notice that the concave horizon in the sky scene makes it less easy for you to sense that we are on a spherical planet rolling forward as it hurtles toward that point in Virgo, that it will roll forward to reveal the Sun. Easy: I just change a number (the altitude of the viewpoint) from +25 to -5.

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It’s an arbitrary number. The horizon is a great circle: it’s concave if you think of it as surrounding the sky, it’s a straight line if you look at it, it’s convex if you think of it as part of the surface of our rolling and hurtling globe.

 

5 thoughts on “The Quadrantids and the Edot”

  1. Sadly, the Quadrantids here in NE England passed behind solid overcast and rain (now into day three without a break), the current part of the storm hereabouts that began on November 8th (well, it’s barely stopped blowing a gale or raining since then, so that’s how it seems!). Early reports from elsewhere in the world suggest only a few people saw anything much of the meteor shower, with just the radio observers enjoying a particularly good “view”, as you might expect.

    Interesting discussion of the EDOT phenomenon, what we in meteor astronomy have long called “The Apex of the Earth’s Way”. It’s an area of interest meteorically because it has quite an influence on the observed rates of non-shower, so sporadic, meteors throughout the year. When the Apex/EDOT is highest in the sky, the Earth “sweeps up” greater numbers of sporadic meteors. As the Apex lags the Sun’s position on the ecliptic by 90°, that equates to the later stages of each night, and towards the autumnal equinox time of year. So for Northern Hemisphere observers, sporadic rates are highest each year after midnight in September-October, with daily sporadic activity highest towards dawn (actually about 06h local solar time, but it’s rare to be able to continue meteor observing for most people visually around this time to confirm it).

    However, observations from both Northern and Southern Hemispheres have also suggested there’s a real difference in the relative density of sporadic meteoroids in space during the year too, so it’s not the only factor involved. Logically, we might anticipate that difference, because for unclear reasons, there are scarcely any strong, annual meteor showers with radiants in the southern half of the sky. There’s random and then there’s “sporadic”, it seems!

    1. Yes, when Shannon first corresponded with me about her EDOT and asked whether there is a name for it, I said “the point you want might be called the apex of the earth’s way, on the analogy of the apex of the sun’s way. That is the term used for the direction in which the sun is traveling relative to the surrounding stars.” I didn’t realize that “apex of the earth’s way” is in fact used, and that, as Alastair explains, it has an actual annual effect on observed meteor rates.

      Despite Shannon’s comment of today, she has pointed out to me (aside, as it were) that I am wrong: the ellipticity of the orbit DOES alter the direction of the Apex/Edot; it is NOT (except at perihelion and aphelion) exactly 90 degrees from the Sun, and this would be obvious in a more highly eccentric orbit. I am in process of thinking more about this!

  2. Thank you for such a lovely write up in your blog, I am glad you enjoy thinking about the edot as much as I do.

    The first image in your blog, the one from the calendar but with the addition of the edot, is exactly what I have been trying to picture in my head and it was wonderful to see such a gorgeous illustration showing the radiant in comparison to the edot. It is perfect!

  3. I love thinking that at the quarter moons we are traveling towards or away from it and will be or were where it was in about 3hr and 50 min. I do have a question though. Does the sun’s motion through the Milky Way affect this at all? I guess what I’m asking is what percentage of the near-by stars are following the sun’s path around the galactic center.

    1. Hi, Jack. I have a bit about this in the Astronomical Companion, page 58. The stars in our neighborhood are, in their collective orbit around the center, moving toward a point near the star Deneb. (Each has its slightly differing individual orbit, and the Sun’s is carrying it – in relation to the local swarm – toward a point near Vega; but I don’t think that affects what you are thinking about.)
      “Does the sun’s motion through the Milky Way affect [such facts as that the moon at last quarter is where the earth will be 3 hours later]?” I don’t see how it could, though conceivably gravitation of nearby stars could have effects – vanishingly small unless a star were to pass very close – on any of the orbits within the solar system.
      “What percentage of the near-by stars are following the sun’s path around the galactic center?” I think you refer to the difference between stars that belong to the disk population and those that belong to the halo. The halo stars travel up and down through the disk at random angles, Arcturus being an example. I haven’t found a figure for the number of halo stars. Say it’s something like 10 percent of the total if the globular clusters are excluded; so the percentage of those that are “near the sun”, i.e. happening to be traveling through the disk, would be something smaller, but it would depend on what you meant by being “in the disk” or “near the sun”.

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