19 Friday Jun 2026
Posted in astronomy, astrophysics, Hopewell Observatorry, Math, Optics, science
Tags
astronomy, exoplanet, Hopewell Observatory, Math, Seestar, Seestar s50, Telescope, transit, variable stars
Do you see a transit in this data? I would say, “Maybe”.
Since the Seestar has quite a bit of error, caused in part by its Bayer array of green, red, and blue pixels, I grouped my original measurements (processed in AstroImageJ) in groups of 5, using Excel to do so.
27 Wednesday May 2026
Posted in astronomy, astrophysics, Hopewell Observatorry, Math, monochromatic, science
Latest results on a known variable star, W Ursae Majoris with my Seestar S50 during a very nice night: complete garbage. The graph below shows the flux of my star, WUMa, compared to the median of 9 comparison stars in the same frame, chosen by AstroImageJ.
As you can see, there is no real pattern.
If this data were real, then this star would be changing its brightness by a factor of three or for in less than a minute, with no discernable pattern. While a candle flame will flicker like that, it is simply not possible for something as large as a star to vary as quickly as that. In fact, this star is actually a contact-binary (double star) with a rotational period of about 8 hours. Even with the noise, I see no sign of a trend over these two hours.
The weather was very good, there was very little light pollution, and this star was quite high up in the sky the entire time, and none of the stars were saturated. But this data is just so, so noisy.
(I used ASTAP and AstroImageJ to do the plate solving and comparison of brightnesses. AIJ is an absolutely amazing program that automates so much of the tedium of this sort of process. For this graph, I had AIJ extract the green channel from the GRGB Bayer pattern, hoping that eliminating the blue channel would reduce atmospheric problems, but no luck so far. Combining all channels was no better.)
Other people claim success, but so far I’m zero for 12 in detecting exoplanet transits, and only 1 out of a dozen or so variable star measurements. Not sure what I am doing wrong or how I can reduce the errors. Yes, it’s true that this is only 2 hours out of an 8-hour period, but this data does not make any sense!
18 Monday May 2026
Posted in astronomy, astrophysics, education, Hopewell Observatorry, Math, science
Tags
AP1600, ASTAP, Astro-Physics, AstroImageJ, Canon 6D, CMOS, DSLR, exoplanet, Hopewell, NINA, Telescope, transit
As you probably have guessed, detecting exoplanets is not easy.
So far I am about zero detections for 12 attempts.
My equipment has been a Seestar S50, and either a ZWO CMOS camera on an Explore Scientific 5″ f/7 triplet refractor, and a Canon 6D DSLR affixed to a venerable C-14 mounted on an Astrophysics 1600 GTO mount.
The Seestar is able to detect brightness changes in other variable stars like RRLyrae, but so far the small changes in flux from exoplanet transits gets drowned in the noise. The DSLR on the C-14 has much less noise, but I still haven’t seen any clear and obvious signs of a transit.
Here are graphs from my latest attempt at detecting WASP-135-b. In the first one, I plotted the fluxes of that star against four of the comparison stars. I added a fixed number to the fluxes of the other stars so you could see trends more clearly. Shortly after 3:30 AM, measurements became very strange for every single star. I was asleep at that time. I’m guessing that there were clouds. Do you see any noticeable dip in brightness of the target star at 3:07? I sure don’t.
In the second graph, I asked Excel to take the average of the fluxes of several of the comparison stars, and then divide the flux from WASP-135 by that average. Again, I see no dip at the appropriate time (Julian Day).
I used NINA to program my cameras and the Hopewell Observatory’s AP mount to take these images. I used ASTAP and AstroimageJ to load all of the images from my various cameras, figure out exactly where the cameras were pointing (aka plate solving), find a bunch of comparison stars, and then measure the fluxes of each of those stars, on each and every single 30-second frame. That set of software — all free!!!– has made all of this work much easier. Thank you to all the incredibly smart and generous people who wrote, and then made freely available, all those complicated computer programs!
I will try TOI-1811 tonight, with some different settings.
02 Tuesday Dec 2025
Most (but not all) of the variable stars I tried over the past month or so were simply too bright for this sensor. The target stars were saturated (ie some of the pixels’ electron wells simply overflowed) despite using the shortest available exposure, adding the light pollution filter and refocusing. Seestar won’t let your change the ISO nor open the shutter for less than 10 seconds.
I did get some believable light curves on BE Lyncis (aka HD67390)and U Cephii (aka HD 5679). I attack some graphs I made.
I used some black plastic I had,and my set of Forster bits, to make holes of sizes 1”, 1-1/8”, 1-1/4”, and 1-1/2”, in case I want to try brighter variable stars again like RR Lyrae.
I very impressed that Seestar absolutely nails the locations of every single one of these targets! I’m also pleased that AstroImageJ allows quick and easy plate-solving!
18 Tuesday Nov 2025
Posted in astronomy, astrophysics, History, Hopewell Observatorry, Math, Optics, Uncategorized
Tags
Hopewell Observatory, light curve, Math, photometry, saturation, Seestar, Telescope, variable star
This graph gives me confidence that defocusing will solve my overflow problem. It’s a profile of the number of photons/electrons captured (vertical axis) versus the distance from what I thought was the exact center of the star RR Lyrae aka HD 182989.
(It is amazing how fast the computer works this out! I’m used to my middle school or high school students working things out like this by hand at first — it’s a very slow and tedious process! Let us give a tip of the hat to Williamina Fleming, who was the first person to notice and record that RR Lyrae was a variable star. She did so by examining glass plates on which were little dark spots made by stars’ light striking particles of suspended silver nitrate, without a blink comparator! Wow!)
Notice that there is one
If I defocus the camera a bit, that saturated value would get spread out over an airy disk that might look like this:
14 Tuesday Oct 2025
Posted in astronomy, astrophysics, History, Math, nature, science, Uncategorized
Tags
aliens, civilization, evolution, exoplanets, life, philosophy, science, science-fiction, space travel, Speed of light
Someone else’s take on this topic.
We’ve all been brainwashed by years of Star Wars, Star Trek, Marvel Universe, Avatar, etc, to think that space should be teeming with intelligent civilizations, most of them vaguely like ourselves, working with and against each other to carve up the galaxy. As a result, it’s easy to overlook the huge assumptions embedded in your question.
So there’s not one answer, but a whole set of overlapping possible answers why we don’t see evidence of any alien civilizations around us. And that doesn’t even consider more exotic possibilities, such as the idea that they might be here but just undetectable to us or deliberately hidden from our primitive eyes.
02 Saturday Nov 2024
Posted in astronomy, astrophysics, Math, Optics, science, Telescope Making
Tags
astronomy, ATM, data, FigureXP, foucault, measurement, millies-lacroix, paraboloid, Telescope
Alan Tarica, Pratik Tambe, Tom Crone and I have been pulling our hair out for a couple of years, trying to use cameras and software to measure the ‘figure’ of the telescope mirrors that we and others produce in our telescope-making class.
There has been progress, and there has been frustration.
I think we finally succeeded!
Some of the difficulties have been described in previous posts. In brief, we want our mirrors to be really, really close to a perfect paraboloid. There are many ways of doing those measurements and seeing whether one is close enough, but none of those methods are easy!
(By the way, one needs the entire mirror to be within one-tenth of a wave-length of green light of that ideal paraboloid! That’s extremely tiny, and equivalent to the thickness of a pencil over a ten-mile diameter!)
I think I can finally report a victory. My evidence is this graph that I made just now, using data that Alan and I gathered last night with our setup, which consists of a surveillance camera coupled to an old 35mm SLR film camera lens, which is mounted on a linear actuator screw connected to a stepper motor controlled by an Arduino and a Python app developed by Pratik.
Something seemed to be always a bit — or a lot — ‘off’.
Until today, when I converted everything to millimeters and used the criterion set out by Adrien Millies-Lacroix in an article he wrote in Sky & Telescope back in 1976.
The blue dots just above the x-axis are the measurements for this one particular mirror with a diameter of 8″ and a radius of curvature of 77 inches.
The dotted blue curve in the middle of the image is the best-fit parabola for those dots. Notice that the R-squared value (variance) for that curve is not great: 0.3599.
But that variance isn’t important. What is important is the green and orange blobs and curves above and below the blue ones.
The green and orange curves are the upper and lower allowable limits for the measurements of this particular mirror, using the
Clearly, the blue dots are all well within the green and orange curves.
Which means that this mirror is sufficiently parabolized.
The fact that the blue dots don’t fit the dotted line perfectly, and behave pretty oddly at positive or negative 80 millimeters, both agree with the fact that we can see on the photos that the surface of this mirror is rather rough, as you can see in the images below. Note also that the image labeled ‘Step 6’ found not one, but two null zones on the right, indicated by two vertical blue lines.
So, finally, we have an algorithm that gives good measurements! What I still want to do is to automate all the spreadsheet calculations that I just did today. Perhaps we can upload them to something like FigureXP by Dave Rowe and James Lerch.
Thanks very much to all those who have helped, whom I should look up and name here.
Caveat: This method can give really ridiculous measurements close to the center and close to the edge.
PS: if anybody wants the raw data, just email me at gfbrandenburg at gmail dot com.
15 Tuesday Aug 2023
Posted in Math, teaching, Uncategorized
Tags
Some probability situations are quite confusing!
There is a pretty well-known paradox which goes something like this:
You hear that the Smith and Jones families each have two children.
You are told that the older Smith child is a girl, and that at least one of the Jones children is a girl.
Assuming that boys and girls are equally likely to be born (I know this is not quite true, but let’s pretend) in any given pregnancy, what are the chances that the Smiths have two girls? How about the Joneses?
Most people would say that those probabilities are equal: 50% in both cases.
But they are not. In fact, it is much less likely that the Joneses have two daughters!
Here is why:
In any family with two children, there is an older sibling and a younger one.
In the Smith family, you know that the older child is a girl, but you know nothing about their younger child, so the younger one is equally likely to be male or female. So the chances that the Smiths have two daughters is indeed 1/2, or 50%.
In the Jones family, all we know is that there is at least one girl. Let’s look at a diagram that shows all of the equally-likely possibilities in any family with two children:
With the Smith family, we can rule out cases 1 and 2, leaving us cases 3 and 4.
However, with the Jones family, we can only rule out case number 1. Cases 2, 3, and 4 — which are all equally likely — are all possible outcomes for the Joneses. Notice that only in case number 4 do the Jones have two daughters. So with the Joneses, the chances that there are two daughters is only 1 in 3, or 33.3%.
And that result is a lot lower than 50%!
Weird, right?
24 Sunday Oct 2021
I had the pleasure of helping lead a field trip for 9th grade Geometry students at School Without Walls SHS that we call ‘Math on the Mall’ assisting with two colleagues from the SWW math faculty.
One of our goals is for the students to see how beautifully and geometrically this city was laid out by Pierre l’Enfant, Andrew Ellicott, and Benjamin Banneker about 230 years ago.
While there are lots of myths written and repeated about Banneker’s actual contribution, the fact is that he was the astronomer, who was responsible for determining due north, exactly, and the exact latitude and longitude of the southern tip of the original 10-mile-square piece of land. With no Internet or SatNav or even a telegraph or steam engine, but with a very nice refractor and highly accurate clock that he was entrusted with, but with no landmarks to measure from, he was able to do so, in 1790.
I was sad to see that exactly none of the students know which way was north – in a city where the numbered streets near the Mall and the rest of DC’s historic downtown were almost all laid out perfectly north-south, and the streets whose names begin with letters or words like ‘Newark’, and the streets along the Mall, are all laid out perfectly east-west. Very few of them had ever seen the Milky Way, though most had heard of Polaris or the North star.
Hopefully they will remember that in the future as they do more navigation on their own in this great city.
I challenged them to try to figure out why the angle of elevation of the North Star is the same as their latitude. Here is a diagram illustrating the problem:
This diagram is intended to help you understand why the North Star’s elevation above your horizon always gives you your latitude (if you live north of the Equator.
The big circle represents the Earth. The center of the earth is at E. The equator is AD.
YOU, the observer, are standing outside on a clear night. You see Polaris in the direction of ray BG. Line HCE is the Earth’s axis, and it also points at Polaris – which is so far away, and seems so tiny, but yet is also so large, that yes, parallel rays BG and CH do, for all practical purposes, point at the same point in the sky. Ray ED starts at the center of the Earth, passes through you at B, and goes on to the zenith (the part of the sky that is directly overhead). The horizon (BF) and the zenith (ray EB) are perpendicular. Also, line HCE (the earth’s axis) is perpendicular to its equator (segment AED).
Using some sort of angle measuring device, if you are out on the National Mall at night, you can very carefully measure the angle of elevation of the North Star above the local horizon, and you should ideally find that angle, FBG, is about 38.9 degrees, but we could also call it X degrees.
Prove (i.e. explain) why your latitude (which is angle AEB) measures the same as angle FBG.
What are the givens?
=========================================================
Full disclosure: My daughter graduated from SWW two decades ago, and I taught there as well for a year and for 10 years at a school that is now associated with it: Francis (then JHS now a middle school).
The kids were nice back then, and they still are. I thought the teachers did a great job.
This is a DC public high school that you have to apply to.
Benjamin Banneker was an amazing person. There are a lot of myths that have been attached to his work and accomplishments, which I am guessing might be because those people didn’t actually understand the math and astronomy that he did accomplish. The best book on him is by Silvio Bedini.
‘Math on the Mall’ was originated by Florence Fasanelli, Richard Thorington, and V. Frederick Rickey around 1990. I participated as a math teacher in a couple of those tours led by FF. Later, I wanted to take my students on a similar tour that would include a trip to see a number of the works of the geometer and artist Maurice C. Escher, and couldn’t find my copy of their work, so I made up my own, and added to it using the work of FF, RT, and VFR and suggestions from teachers and students. Later on, the Mathematical Association of America made something similar, which you can find here.
My version was on the website of the Carnegie Institution for Science for a number of years. See page 56 on this link. I need to find someone to cut out some of my excess verbiage and then trot it out to a publisher.
29 Sunday Aug 2021
Posted in astronomy, Hopewell Observatorry, Math, Optics, Telescope Making
Tags
ATM, barium, Bausch & Lomb, Bureau of Standards, flint, glass, Hopewell Observatory, Math, mystery glass, Optics, Schott, Snell's Law, Telescope
Many years ago, the late Bob Bolster, a founding member of Hopewell Observatory and an amazing amateur telescope maker, got hold of a large piece of glass, perhaps World War Two military surplus left over from the old Bureau of Standards.
I have no idea what it is made out of. If Bob had any clue about its composition, he didn’t tell anyone.
Its diameter is 22 inches, and its thickness is about 3.25″. It has a yellowish tint, and it is very, very heavy.
If you didn’t know, telescope lenses (just like binocular or camera lenses) are made from a wide variety of ingredients, carefully selected to refract the various colors of light just so. Almost all glass contains quartz (SiO2), but they can also contain limestone (CaCO3), Boric oxide (B2O3), phosphates, fluorides, lead oxide, and even rare earth elements like lanthanum or thorium. This link will tell you more than you need to know.
If you are making lenses for a large refracting telescope, you need to have two very different types of glass, and you need to know their indices of refraction very precisely, so that you can calculate the the exact curvatures needed so that the color distortions produced by one lens will be mostly canceled out by the other piece(s) of glass. This is not simple! The largest working refractor today is the Yerkes, with a diameter of 40 inches (~1 meter). By comparison, the largest reflecting telescope made with a single piece of glass today is the Subaru on Mauna Kea, with a diameter of 8.2 meters (323 inches).
For a reflecting telescope, one generally doesn’t care very much what the exact composition of the glass might be, as long as it doesn’t expand and contract too much when the temperature rises or falls.
We weren’t quite sure what to do with this heavy disk, but we figured that before either grinding it into a mirror or selling it, we should try to figure out what type of glass it might be.
Several companies that produce optical glass publish catalogs that list all sorts of data, including density and indices of refraction and dispersion.
Some of us Hopewell members used a bathroom scale and tape measures to measure the density. We found that it weighed about 130 pounds. The diameter is 22 inches (55.9 cm) and the thickness is 3 and a quarter inches (8.26 cm). Using the formula for a cylinder, namely V = pi*r2*h, the volume is about 1235 cubic inches or 20,722 cubic centimeters. Using a bathroom scale, we got its weight to be about 130 lbs, or 59 kg (both +/- 1 or 2). It is possible that the scale got confused, since it expects two feet to be placed on it, rather than one large disk of glass.
However, if our measurements are correct, its density is about 2.91 grams per cc, or 1.68 ounces per cubic inches. (We figured that the density might be as low as 2.80 or as high as 3.00 if the scale was a bit off.)
It turns out that there are lots of different types of glass in that range.
Looking through the Schott catalog I saw the following types of glass with densities in that range, but I may have missed a few.
2.86 N-SF5
2.86 M-BAK2
2.89 N-BAF4
2.90 N-SF8
2.90 P-SF8
2.91 N-PSK3
2.92 N-SF15
2.93 P-SF69
2.94 LLF1
2.97 P-SK58A
3.00 N-KZFS5
3.01 P-SK57Q1
By comparison, some of the commonest and cheapest optical glasses are BAK-4 with density 3.05 and BK-7 with density 2.5.
Someone suggested that the glass might contain radioactive thorium. I don’t have a working Geiger counter, but used an iPhone app called GammaPix and it reported no gamma-ray radioactivity at all, and I also found that none of the glasses listed above (as manufactured today by Schott) contain any Uranium, Thorium or Lanthanum (which is used to replace thorium).
So I then rigged up a fixed laser pointer to measure its index of refraction using Snell’s Law, which says
Here is a schematic of my setup:
And here is what it looked like in practice:
I slid the jig back and forth until I could make it so that the refracted laser beam just barely hit the bottom edge of the glass blank.
I marked where the laser is impinging upon the glass, and I measured the distance d from that spot to the top edge of the glass.
I divided d by the thickness of the glass, in the same units, and found the arc-tangent of that ratio; that is the measure, b, of the angle of refraction.
One generally uses 1.00 for the index of refraction of air (n1). I am calling n2 the index of refraction of the glass. I had never actually done this experiment before; I had only read about doing it.
As you might expect, with such a crude setup, I got a range of answers for the thickness of the glass, and for the distance d. Even angle a was uncertain: somewhere around 49 or 50 degrees. For the angle of refraction, I got answers somewhere between 25.7 and 26.5 degrees.
All of this gave me an index of refraction for this class as being between 1.723 and 1.760.
This gave me a list of quite a few different glasses in several catalogs (two from Schott and one from Bausch & Lomb).
Unfortunately, there is no glass with a density between 2.80 and 3.00 g/cc that has an index of refraction in that range.
None.
So, either we have a disk of unobtanium, or else we did some measurements incorrectly.
I’m guessing it’s not unobtanium.
I’m also guessing the error is probably in our weighing procedure. The bathroom scale we used is not very accurate and probably got confused because the glass doesn’t have two feet.
A suggestion was made that this might be what Bausch and Lomb called Barium Flint, but that has an index of refraction that’s too low, only 1.605.
Mystery is still unsolved.
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