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Plate solve, #40 on Fundamentals Path — posted 24/1/2024
Jupiter calculation
I tried to send this as an email, but it was rejected because of non-standard characters, so I am posting it here.
I have been greatly enjoying PixInsight Fundamentals, learning a lot. I worked my way through Stretch Academy and Fast Track, and am now going through Fundamentals Path. Coincidentally, the next thing for me to look at was the new #40, plate scales. Having read it, I think there are a couple of problems with the analysis; I’ve written an alternative analysis below, and am interested in hearing what people think.
The first problem is that when you divide 36,000 by 1,296,000, you are getting seconds/arc second, so the number 0.027…=1/36 is how long it takes Jupiter to rotate one arc second. Alternatively, it can be interpreted as a rotation of 36 arc seconds per second, which is not how it’s described in the video.
The second problem is that an arc second of rotation by Jupiter wouldn’t look like an arc second of movement by us on Earth.
Here is my explanation. I’ve kept the numbers smaller by quickly going to a rotation of 1º.
Jupiter rotates 360º in 10 hours = 36000 seconds so it rotates 1º in 100 seconds so 1 arc second in 100/3600=1/36=0.027.. seconds. Thus it’s rotating at 36 arc seconds per second.
However, this doesn’t mean that since a pixel on the sensor subtends about 0.33 arc seconds that we see a rotation of about 36/.33 = 110 pixels per second. That’s because an arc second of rotation on Jupiter doesn’t subtend an arc second from our point of view.
If we don’t worry about the curvature of Jupiter, we can roughly say that we are looking at 180º of Jupiter at its equator, and that subtends something like 48 arc seconds from our point of view, so one arc second from our point of view is about 180/48 = 1.8º on Jupiter’s surface. Thus one pixel from our point of view is about 0.6º on Jupiter. That’s about 2160 arc seconds on Jupiter. If Jupiter is rotating at about 36 arc seconds per second, that takes about 60 seconds. So it looks like on the setup described it’s about a minute per pixel, and 3 minutes for 3 pixels, accounting for seeing. Since the 0.33 arc seconds is pretty standard for planetary work, that’s seems consistent with the general advice not to go longer than 3 minutes on a video of Jupiter if you’re not going to de-rotate it.
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