An Ascent into the Maelstrom

Have you ever tried to image an object near the zenith? Usually, your smart scope will tell you it can’t go there if you’re too close even before you begin, but you can get unlucky like I have and do a long set of frame stacking when your object drifts too close to straight up and it stops. This problem reminds me of Edgar Allen Poe’s short story, “A Descent into the Maelstrom,” in which the narrator tells a tale about when he mistakenly set sail too late, because of his unwound watch, with his siblings and they found themselves sucked into a deadly — though predictable — whirlpool. Only the narrator survived. Curiously, the story is a precursor to Andy Wier’s “The Martian,” in the sense that the narrator used his scientific observations of the buoyancy of different debris to hitch his ride to a barrel which would not find itself in the abyss. In the instance of smart telescopes, there is an abyss we need to avoid. So, as with Poe’s and Wier’s characters, we need to “science the s__t out of it.”

So, what’s going on? With all of a smart telescope’s amazing technology it seems crazy that we can’t image something straight up. After all, there’s nothing there to get in the way! (As opposed to my observing space where I have trees, utility poles, overhead wires, and street lights.) The problem at the top of the sky is the apparent rotation of the image on our sensors due to the type of mountings we use. The effect is called Field Rotation and it’s an effect that panoramic night sky photographers have known about for years and any astronomer who uses a telescope with an Alt-Az mount.

It’s important to realize that as the earth rotates, the sky appears to drift from east to west. But this isn’t the rotation I’m talking about. For if you mount your telescope on a polar mounting it tracks along with the earth’s motion just fine and the Field Rotation problem doesn’t exist. That’s why really top notch astro photography rigs are all on polar mounts. The latter rigs can take rather long time exposures which can be further stacked off line and used to generate the astonishing picture we see in astronomy magazines. The DWARF II can apparently be polar aligned to counter this effect too, but the other smart telescopes, as far as I know, are restricted to being operated with their Alt-Az mounts.

I won’t go into why not, but I’m assuming its just far more convenient and compact to engineer a scope like these with Alt-Az mounts. They would also have to have much more robust mounts and motors too. Note that large observatory instruments and Stellina by Vaonis does have a field de-rotator to keep the overall frame in the same position. I believe Stellina rotates between exposures but it is steady during image recording and still has to abide by the Field Rotation limits with relatively short exposures. But most of what I will be talking about are smart scopes that de-rotate for stacking with only their software.

Why is Field Rotation even a problem? It is if you’re trying to take a time exposure. Because, if you could do a very long time exposure you would see the stars trail in circles about the center of the field you’re tracking with those farthest from the center trailing the fastest. Maybe you have seen an image like this when something has gone amiss. Our fields are always rotating, but the typical short exposure times: 4 to 15 seconds* are not long enough to cause the field to drift across enough pixels to be apparent. The scopes' software of course understands all this and it incrementally rotates each image before stacking.

Without a polar mount, the problem is unavoidable because it’s embedded in the math of the Field Rotation. I’m going to try and stay away from too much math in these blog posts, but for those who want to delve into it, there is an excellent description on this page: www.californiaskys.com/field-rotation.html.

In our case all we need to realize is that the rate of Field Rotation is singular at the Zenith. A mathematical singularity means one is trying to divide by zero. Well, the Field Rotation rate has a term with the cosine of the altitude in the denominator. Maybe you don’t want to remember your high school trigonometry, but trust me, the cosine of 90 degrees is always zero. Anything divided by zero is infinity. And that’s where the problem hits the overhead celestial fan and threatens to spin out of control.

So, this is a difficulty we have to live with. What does that mean? It means, first of all, there are exposure time limits. See the article above, which delves into how one calculates those times. Our smart scope engineers have already done the math and the lengths of our exposures all deal with this.

And then, of course, don’t get too close to the abyss at the zenith. My rule of thumb is that I like to observe objects when they are relatively at a high altitude, say above 60 degrees, but not too high. For me too high is typically 80 degrees. Usually the scopes will tell me, but I also try to carefully plan my observing ahead of time. I’ll do a blog post on that sometime in the future.

Enough of this technical limits talk, however. My plan is to alternate tech talk posts with important smart telescope astronomy. The science is what makes all this the most meaningful for me.

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*Stellina, I believe can go to 30 seconds in expert mode, but I think usually stays with 10 seconds per exposure.

(The illustration included here was by Harry Clarke for a 1919 edition of Poe's story.)