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:
I’m still struggling to do simple astronometry even on a well-known variable star like RRLyrae. If you could measure its brightness for several nights without any breaks, you should in theory get a light curve like this:
I don’t. I’m still trying to figure out why my light curve for RRLyrae is so flat.
In 2004, during a two-week astronomy summer class at Mount Wilson, with a professional astronomer on hand guiding me at every step of the way over a couple of nights, I got light curves looking like pieces of the good example above. (Why only pieces? Because you can’t image a star in the daytime or when it’s cloudy or if the star is on the other side of our planet!)
A couple of weeks or so ago, inspired by an exoplanet light curve taken by a 9th grader with a Seestar, I had the opportunity to run my tiny automated Seestar S50 for 8 hours outside at Hopewell Observatory, which is a nice, safe location, connected to wall power. The weather was perfect for it. The scope is about the size of a large cookie tin on a tripod. It did nothing but take ten-second photos of a small region around RRLyrae from whenever stars came out until dawn.
Afterwards I then had to start analyzing those 972 images. My first step was to learn how to use YET ANOTHER astro-imaging package, called AstroImageJ. It’s quite impressive, but It pisses me off that every few years I have to learn an entirely new piece of software, and just throw out nearly everything I learned regarding anything software-related over the past 60 years!
I eventually figured out how to get AIJ to verify that the little scope was in fact looking at my chosen star — and it was.
I then asked AIJ to compare the brightness of RRLyrae to the brightness of five or six other stars of similar brightness that happened to be located in the same field of view, for each image. (Today’s computers quickly do all sorts of math on the values of certain pixels in certain rings around certain stars, at lightning speeds, but the human computer of 1899, Williamina Fleming, who discovered this star, had to do it completely manually by comparing the size of the spots on a glass photographic plate. My hat is off to you, Ms Fleming, and all the other unsung female computers!
Here is a screenshot of the very last image in the series I took. The RA and Dec are the coordinates of RRLyrae, which AIJ has circled in green. The stars circled in red are comparison stars. That 20.28′ legend is in arc-minutes, 60 of which equal one degree. So the field of view is a bit over half a degree across and roughly a degree vertically.
To my surprise, my results were totally different from what I expected to find.
The blue dots are RRLyrae’s brightness on some scale that the computer cooked up, and the pink ones are from one of the known comparison stars. The x-axis goes from roughly 0.48 to 0.64, or 0.16, which is 1/6 of a day, or 4 hours.
The cases where both the blue and pink dots drop down below 1.0 are garbage caused by some glitch and should be ignored. But one thing is for sure: there is no sawtooth spike in my data for RRLyrae’s brightness during those 8 or 9 hours!
Four possible reasons are:
I’ve made a great scientific discovery! (probably not correct)
2. Wrong star? (I don’t think so. Checked and re-checked)
3. Perhaps those 8 hours happened to correspond to a flat place in the light curve (Possible — I just noticed that these images end before midnight, but I thought it kept working until dawn! Must re-check!)
4. The pixels all are too saturated, ie were exposed for too long,, which fills up the pixel with too many electrons. (This is possible, I guess, but each of these were merely 10 second-long exposures, which doesn’t sound very long to me, but maybe I’m missing something important).
Saturation is what the following graphic seems to indicate:
If it is indeed saturation that is making all the stars not change brightness, then what do I do?
I don’t think I can control the gain or ISO inside SeeStar, but I can ask for shorter time exposures, I think, by trying a time lapse and asking for shorter exposures, if possible. I just need to have time and a location to let it run all night without anybody disturbing it, making a time lapse of the sky.
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.
Habitable worlds exist. Do they? It seems overwhelmingly likely, given that there are probably a trillion planets in the Milky Way alone, but for now we don’t know. Perhaps there are many near-miss planets like Venus and Mars, but extremely few true Earth analogs. For instance, life might require a particular rock/ice ratio, a large moon, and a specific style of plate tectonics. That level of specificity seems unlikely to me, but that’s just my random opinion. Until we find another planet with truly Earthlike conditions, we cannot say for sure that this is true.
Alien life exists. Does it? Honestly, we have no idea. There are many strong arguments suggesting that the fundamental biochemistry of self-replication is practically inevitable given the right conditions. But we don’t know how common those conditions are (see above), and even then we don’t know if there is some extremely low-probability gap that hinders the emergence of even simple microbial life.
Intelligent life exists. Does it? This one is a complete unknown. Keep in mind that there was no intelligent, self-aware life on Earth for 99.999% of its existence. Maybe the emergence of intelligence here was a rare fluke, unlikely to be reproduced anywhere else. Rat-level intelligence seems to have existed for at least 200 million years without any indication that higher level intelligence would confer a big evolutionary advantage. (There are all kinds of speculations about why intelligent life could not emerge until now on Earth, but these are just-so stories, trying to paint an explanation on top of a truth that we already know.)
Intelligent species want to “colonize” the galaxy. Do they? Life does have a tendency to explore every available ecological niche, and humans sure do like to spread out. From our example of one Earth, it seems likely that this is a general tendency of life everywhere, but we are doing an awful lot of extrapolating here. Maybe other types of intelligence have other motivations that have nothing to do with expansion.
Intelligent species become technological species. Do they? It’s certainly true for humans, but dolphins have a high level of intelligence and they are not trying to build spaceships. Crows, chimps, and bonobos are also capable of simple tool use, but they don’t appear to have experienced any evolutionary pressure to become true technological species.
Technological species can travel a significant fraction of the speed of light. (I assume you mean something like more than 1% of light speed.) Can they? Extrapolating from human technology, that seems extremely likely. Then again, the fastest spacecraft we have ever built would take about 300,000 years to reach the next star. Nobody is going to be colonizing the galaxy at that rate. You have to accept that speculative but unproven technologies are both feasible and practical for more advanced technological civilizations. Maybe intelligent life is out there, but in isolated pockets.
Intelligent, technological, space-faring species survive for a long time. Do they? Oh boy, we have no idea at all if this is true. Earth is 4.5 billion years old. Life has been around 4 billion years. Land species have been around 400 million years. Rat-level intelligence has maybe been around 200 million years. Our species has been around for about 100 thousand years. We have been capable of spaceflight for less than 100 years. It may seem inconceivable that humans could go extinct—but even if we last another 100,000 years, that may not be nearly enough time to spread across the galaxy, even if we develop the means to do it and maintain the will to do it. If intelligent species typically last less than 100,000 years, thousands of them could have come and gone in our galaxy without us ever knowing.
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.
Dr Rob Zellem posed this question last night (9-13-2025) to NCA members and visitors at their monthly meeting at the University of Maryland Observatory.
Are we alone in the universe, or are there exoplanets with life of some sort, and even some advanced civilizations out there?
Dr Zellem said the correct answer right now is, maybe. We just don’t have enough data to tell.
He reminded us that Giordano Bruno and Isaac Newton both correctly predicted that other stars would have planets around them. We now know that just about every single star is born with a retinue of planets, asteroids, dust, and comets, so there are at least as many planets as there are stars in our galaxy and all the others as well. Previous speakers to NCA have noted that many of these objects end up getting flung out into the vast frozen emptiness of interstellar space in a giant random game of ‘crack the whip’. No life can exist out there.
My calculations here: It is estimated that there are literally trillions (10^12) of galaxies, each with millions (10^6) or billions (10^9) of stars. Let’s start with our own galaxy, the Milky Way, with maybe 200 billion stars (maybe more). I will assume that life needs a nice, calm, long-lived G class yellow star, which only make up 7.6% of all stars. Roughly 50% to 70% of those stars are in binary systems, which I fear will reduce the chances of having a planet survive in the Goldilocks zone. Perhaps one-third to two-thirds of those G stars have a planet in their habitable zone. We have no idea how likely life is to get started, but after reading Nick Lane’s The Vital Question it sounds pretty complicated to me, so I’ll use a range of estimates: somewhere between 10% and 80% of them develop some form of life. We know that on Earth, the only form of life that existed during the vast majority of the existence of the Earth was unicellular microbes. Four-footed tetrapods like ourselves have only occupied about 1% of the life of our planet, and we humans have only had the telescope for just over 400 years, out of the 400,000,000 years since four-footed animals evolved, which is one in a million. Low estimate:
If my low-end estimates are correct, then there are about five or so exo-planets somewhere in our galaxy with a civilization formed by some sort of animal that can look out into outer space. High estimate:
In that case, there are well over a hundred civilizations in our galaxy — but the Milky Way is huge, hundreds of thousands of light-years across! Most of our exoplanet detections have been within the nearest 100 light years, and we have no way of detecting most exoplanets at all because the planes of their orbits point the wrong way.
NOTE: Jim Kaiser pointed out that I made a dumb mistake: a hundred billion is ten to the 11th power, not ten to the 14th power. Fixed now.
Even so, Zellem pointed out that thanks to incredible advances in sensitivity of telescopes and cameras, we are now closer than ever to being able to answer the title question: Are We Alone.
Plus, any amateur astronomer can take useful measurements of exoplanet transits with any telescope, and any digital camera. Following the directions on NASA’s Planet Watch webpage, you can take your data, in your back yard or from a remote observatory, process it the best you can, send it in, and be credited as a co-author on any papers that are published about that particular exoplanet. Then, later, a massive space telescope can be aimed at the most promising exoplanets during their transits. Astronomers can use their extremely sensitive spectroscopes to detect the atmospheres of those bodies and look for signs of life. They do not want to waste extremely valuable telescope time waiting for a transit that doesn’t recur!
Some day we will be in a situation where scientists will be able to say that based on their measurements, the signal indicates a very good chance of life at least a bit like ours, with similar chemistry on some planet. They will also state what the chances are that they are wrong, and indicate what further steps could be made to disprove or confirm their claim.
Zellem noted that both the Doppler-shift method and the transit methods are quite biased in favor of large exoplanets that are close to their suns.
I asked the speaker how likely it would be for observers from some exoplanet to detect the planet Mercury, but couldn’t do the math in my head and didn’t have paper and pencil to write anything down at the time. But now I do.
The closer Mercury is to the Sun, the larger the possible viewing angle.
Using a calculator to find the arc-tangent of that ratio (865,000 miles solar diameter, divided by the smallest and also by the largest distances between them, namely 28,500,000 and 43,500,000 miles) gave me an angle between 2 and 3 degrees, depending. So there is a circular wedge of our galaxy where observers on some other planet might view a transit of our innermost planet. Where is that wedge in our galaxy?
The following sky diagram has the Ecliptic in pink. Only observers within a degree or so of that curvy line could detect that Sol has planets.
So what fraction of the sky can ever hope to catch a transit of Mercury? Only about 1% or 2% of the sky — not much.
Turning things around, this means that we can ourselves only detect, via transits, a very small portion of all extra-solar planetary systems – those whose planes are pointing almost directly at us, and those with large planets that are very close to their stars. (Any planet so close to a star is not a very good candidate for life, in my opinion.)
The biggest obstacle is the sheer distances between stars. At the speed of our very fastest space craft (the Parker Solar Probe), which only goes 0.064% of the speed of light, it would take about 6250 years to reach our closest stellar neighbors near Proxima Centauri. One way. Which probably explains why, if all these other civilizations do exist, we do not appear so far to have been visited by any other extraterrestrial civilization.
At the meeting, someone in the audience was pretty sure that yes, we have already been visited by aliens. I talked with him outside after the meeting. His main evidence was a 2020 New York Times article concerning the upcoming release of classified data about mysterious flying objects (now called UAPs rather than UFOs). In the article, one Eric Davis claimed (without producing any evidence) that some items have been retrieved from various places by the US military that couldn’t be made here on earth. That is of course true of every single asteroid or meteorite ever discovered, since we can’t reproduce the conditions in which they were formed, so his claim is not very helpful. No technological devices clearly of alien manufacture have ever been publicly produced by him or anybody else for testing.
(It’s pretty obvious that American and other military forces spend a lot of money producing objects that go very fast and are highly maneuverable — and which they want to keep secret.)
There are in fact many, many unsolved mysteries in science (eg, the nature of dark matter and dark energy, and exactly how the nucleus arose in eukaryotes). Many of the unidentified sky or water phenomena that have been witnessed do not have clear explanations so far, but the simplest explanation is usually the correct one. Reputable scientists require a lot more than hearsay evidence before they make bold claims.
When I show people things in the sky with a telescope, I want to help them to realize how lucky we are to live on a nice, warm, wet little planet in a relatively safe part of a medium-large galaxy.
I also want them to realize that if we aren’t careful, we could turn this planet into one of those many varieties of deadly hell that they are viewing in the eyepiece.
We should be very thankful that this planet got formed in a solar system that had sufficient oxygen, silicon, iron, nitrogen, and carbon for life as we know it. We are fortunate that all of those ‘metals’ I just listed (as astronomers call them) got cooked up in cycle after cycle of stars that went boom or whooshed their outer layers into the Milky Way. We are lucky to be alive at the far multicellular side of the timeline of life on Earth*, and that no star has gone supernova in our neighborhood recently or aimed a gamma-ray burst directly at us.
We are exceedingly lucky that a meteorite wiped out the dinosaurs 65 million years and allowed our ancestors, the mammals, to take over. We can rejoice that most of us in the USA can have our physical needs (food, shelter, clean water, clean air, and communication) taken care of by just turning a knob or a key, or pushing a button, instead of hauling the water or firewood on our backs. (There are, obviously, many folks here and abroad who live in tents and who have essentially none of those nice things. We could do something about that, as a society, if we really wanted to.)
I am often asked whether there is life elsewhere. My answer is that I am almost positive that there are lots of planets with some form of life in every single galaxy visible in an amateur telescope. But there is no possible way for us humans to ever visit such a planet. Nor can aliens from any exoplanet ever visit us, whether they be single-celled organisms or something you would see in a Sci-Fi movie.
Yes, it is possible to send a handful of people to Mars, if we are willing to spend enormous sums of money doing so, and if the voyagers are willing to face loss of bone and muscle mass, and the dangers of lethal radiation, meteorites, accidental explosions, and freezing to death. If they do survive the voyage, then by all means, let them pick up some rocks and bring them back for analysis before they die.
But wait: we already have robots that can do that! Plus, robots won’t leave nearly as many germs behind as would a group of human beings. And we already know a lot about how Mars looks, because of all the great photos sent back by ESA, JAXA, NASA and others for some decades now. You can see photos taken by NASA at JMARS, which I highly recommend. (https://jmars.asu.edu/ )
While one can justify sending a few brave folks to Mars for a little while, it is completely insane to think that we can avoid our terrestrial problems by sending large populations there. Mars is often colder than Antarctica, is close to waterless, has poisonous perchlorates in its soil, no vegetation whatsoever, and no atmosphere to speak of. How would millions or billions of exiles from Earth possibly live there? Do you seriously think they can gather enough solar energy to find and melt sufficient water to drink and cook and bathe and grow plants and livestock in the huge, pressurized, aluminum cans they would need to live in? No way.
I wish there was some way to get around the laws of physics, and that we could actually visit other exoplanets. But there isn’t, and we can’t. I’ve seen estimates that accelerating a medium-sized spaceship to a mere 1% of the speed of light would require the entire energy budget of the entire human population of the planet for quite some time. (For example, see https://physics.stackexchange.com/questions/447246/energy-requirements-for-relativistic-acceleration )
Let us assume, for the sake of argument, that you could actually generate enough energy to accelerate that spaceship with nuclear fusion or something else that doesn’t violate the laws of physics as far as we know.
The next problem is the distance. It’s a bit over 4 light years to the nearest known exoplanet in a straight line, (compared with under 2 light-seconds for the Moon or about 35 light minutes for Jupiter). The table below gives the number of planets lying each extra solar system that are thought to be terrestrial (as opposed to gas giants) and to be within their stars’ habitable zones. Nobody knows if there is any life on any of those planets right not, but it is possible that astronomers may one day figure out a very effective way to test for extra-solar life. Let us suppose that a few of the ones in this list do have breathable atmospheres and are neither too cold nor too hot, have a fair amount of liquid water, and are protected from nasty radiation by magnetic fields and belts.
Unfortunately, a one-way trip to Proxima or Alpha Centauri for any possible spaceship, at one percent of the speed of light, (3,000 km per second), in a straight line, and pretending that you don’t need years and years to both accelerate and decelerate, would take over four centuries. And that’s for the very closest one! All the other planetary systems are many multiples of that distance! See this or this table:
Our fastest spacecraft so far, the Parker Solar Probe, reaches the insanely fast speed of 190 km/sec, but that’s still fifteen times slower than my hypothetical 1% of c. At the speed of Parker, it would take around six thousand years to reach the Proxima Cen planetary system! If all goes well!
Do you seriously think that a score or so generations of humans would all agree, century after century, that they, and their descendants — born and raised in a big metal box rushing through space — for the entire 400 years, would consent to live in a large metal box with no gravity to speak of, subject to who knows how many blasts of gamma rays, x-rays, and super-high-energy cosmic particles? What are the chances that each single generation would agree to stay the course and that not a single meteorite going the other direction, over a course of four centuries, would happen to smash into the space ship and instantly disable all the life support systems and kill all the passengers, quickly or slowly?
And how do you keep alive all the animals we would need to feed us upon arrival? I guess you compost all the poop from all the cattle, chickens, and so on. But do you also bring zillions of insects and tons of plant seeds as well, knowing full well that if you do so, then you lose the vast majority of the information you could have learned about an actual, functioning, extra-solar ecosystem like nothing we can possibly imagine.
The argument is made that perhaps the travelers would be put into suspended life. If that were possible, and nothing went wrong, upon arrival, they could take a triumphant group selfie and put it into a radio message back to Earth saying, “Hi, we made it, wish you were here…” That reply will of course take four years to reach Earth. Would people back on Earth still remember the handful of people who began the trip out, made over four centuries earlier? What will the humans back on earth remember about the absolutely prodigious effort expense that their ancestors had made to build and power that rocket, 20 generations or so earlier?
Let us suppose they have the tremendous luck to find, after 4 to 10 centuries of travel, a nice warm exoplanet with water, oxygen-producing life, and air that we can breathe.
Unfortunately, there is an overwhelming chance that there would be no humanoids or any other Sci-Fi characters. The chances are that creatures that look like insects, crustaceans, fish and salamanders are the most highly-organized life forms – at best; after all, for most of the existence of life on earth, it was single-celled organisms! Our travelers would have to have to build an entire urban and agricultural infrastructure *from scratch*, with no help. They could only do that if the plants and animals they brought from Earth are able to flourish.
The return trip, if desired, would of course take another four or more centuries, if the handful of travelers can find a proper power source and if they can figure out how to create, completely from scratch, an entire agricultural and industrial instructure. They would have to figure out where the natural resources of that planet (wood? minerals? energy sources?) are located, and how they can make use of them, to build something like the incredibly precise absolutely enormous rocket-building industries we have here, on a hypothetical planet that has never even had any mammals living on it.
If these voyagers should run into any technical problem while doing trying to build a modern civilization from nothing, fat chance of getting a prompt reply from Earth, since the question would take years to reach its home base back here!
Yes, the very closest exoplanets are a mere 4 LY away, but the others are all much, much farther away, so one-way trips for ones within 10 parsecs, i.e., in our tiny corner of our galaxy, at one percent of the speed of light, would require a thousand to three thousand years to reach. Each way.
Forget it. Just send a radio message, and see if we get a reply. Oh, wait – we’ve been doing that for several decades so far. No reply so far.
Speaking of radio – it’s only 120 years since Marconi first sent a very crude radio message from a ship to a station on land, and now we routinely use enormous parts of the entire electromagnetic spectrum for all sorts of private and public purposes, including sending messages like this one. Astronomers are able to gather amazing amounts of information via the longest radio waves to the very shortest gamma rays and make all sorts of inferences about worlds we have never seen at optical wavelengths. In addition, we have begun detecting gravity waves from extremely distant and powerful events with devices whose accuracy is quite literally unbelievable.
There is no planet B. We must, absolutely must, take care of this one, lest we turn into one of those freezing or burning variations of hell that we see through our eyepieces. Think I’m being alarmist? We now know this nice little planet Earth is more fragile than we once believed. It has been discovered that life was almost completely wiped out on this planet several times. The Chixculub impact I mentioned earlier, the Permian extinction and Snowball Earth are just three such events.
More recently, folks thought it was impossible for people to cause the extinction or near-extinction of the unbelievably huge flocks and herds and schools that once roamed the earth: passenger pigeons, buffaloes, cod, salmon, redwoods, elms, chestnuts, elephants, rhinos, tropical birds, rainforests, and so on, but we did, and continue to do so. The quantities of insects measured at site after site around the world have plummeted by 30 to 70% and more, over just a few decades, and so have the numbers of migratory birds observed on radar feeds. Light pollution, the bane of us amateur and professional astronomers, seems to be partly responsible for both the insect and bird population declines. The rise in the levels of atmospheric carbon dioxide and global temperatures are very scary.
In addition, we are dumping incredible amounts of plastic into the oceans, and rising water temperatures are causing coral reefs around the world to bleach themselves and die, while melting glaciers are causing average sea levels rise and threaten more and more low-lying cities.
What’s more, only a very tiny fraction of our planet’s mass is even habitable by humans: the deepest mine only goes down a few miles, and people die of altitude sickness when they climb just a few miles above sea level. Most of the planet is covered by ocean, deserts, and ice cap. By volume, the livable part of this planet is infinitesimal, and the temperatures on it are rising at an alarming rate.
Will we be able to curb the burning and leaking of fossil fuels sufficiently so as to turn around the parts of global warming caused by increases in carbon dioxide and methane? I am not optimistic, given that the main emitters have kept essentially none of the promises that they have been making to those various international gatherings on climate, and graphs like this one, taken from: https://ourworldindata.org/fossil-fuels
I have been wondering whether we may need to reduce temperatures more directly, by putting enough sulfur compounds into the stratosphere. We have excellent evidence that very violent volcanic eruptions have the power to lower global temperatures with the sulfates they put into the stratosphere. It would not be great for ground-based astronomy if such compounds were artificially lofted high into the atmosphere to lower global temperatures, and we won’t know for sure exactly which areas of the planet would benefit and which would be harmed, but at least it’s an experiment that can be stopped pretty easily, since the high-altitude sulfates would dissipate in a few years. High-altitude sulfur compounds do not seem to cause the obvious harm that SO2 does at the typical altitude of a terrestrial coal-burning power plant.
Adding iron to the oceans to increase the growth of phytoplankton, which then consumes CO2, dies, and settles to the bottom of the ocean, has been tried a number of times, but doesn’t seem to have a very large effect.
I agree that large-scale injection of sulfates into the stratosphere is scary. I also agree that there is a whole lot of unknown unknowns out there and inside of us, and we are being very short-sighted, as usual.
We have mapped the far side of the moon better than we have mapped the floors of Earth’s oceans – yet permits are being filed right now to begin deep-ocean dredging for manganese nodules, which will enrich some folks greatly. Unfortunately, that dredging is bound to utterly destroy those slow-growing ecosystems, before we even know what’s down there in the first place!
We continue to dump unbelievable amounts of plain old trash, fish nets, fishing lines, live ammunition, modern warships and hazardous chemicals into the oceans.
While the waters and atmosphere of the USA are much, much cleaner now than they were when I was a kid in the 50s and 60s, places like Delhi or Beijing are so polluted that folks can barely see the sun on a clear day.
If dark matter and dark energy really do exist, that means that scientists have absolutely no idea what 96% of the universe is made of!
If dark matter and dark energy don’t exist, then that means that astrophysicists don’t understand long-distance gravity and physics nearly as well as they thought. The late Vera Rubin (a past NCA member who should have won a Nobel for her careful measurements of the rotational measurements of galaxies that led to the Dark Matter hypothesis) once told me when we were co-chaperoning a field trip to the Smithsonian for the Carnegie Institution for Science’s Saturday program for middle-schoolers, that she thought that the entire question is perfectly open. I think she’s still correct.
If the Big Bang is real, then how come the Webb is seeing fully-formed galaxies as far back in time as it can see?
Do the alternative theories to the Big Bang (eg, Burbridge’s hypothesis that matter is being created in the centers of active galactic nuclei) make any sense?
But — does anybody have better solutions?
Can we engineer our way out of the mess we are making on this planet – the only home that humans will ever have?
There is cause for optimism:
Our NCA speaker this month, Deborah Shapley, will tell how, almost exactly a century ago, astronomers finally figured out that the Milky Way was just one of many billions of other galaxies. Since that time, the amount of astronomical information gathered has been staggering, as has the efficacy of the instruments!
After scientists figured out what was causing the ozone hole, every single agency and government in the entire world passed and enforced regulations that banned those chlorofluorocarbons that were used in almost everything from air conditioners to hair spray. Since that time, there has been almost complete compliance and agreement, and the ozone hole continues to shrink, as you can see here.
I have vivid memories about how smoggy and stinky the air used to be on a typical summer day in almost any American city of my youth. A fat-rendering plant right here in Georgetown (DC) stank worse than a hundred skunks, and is now gone. I know a paper mill in West Virginia whose fumes had long killed almost all the vegetation downwind of the factory. Nearby, acid drainage from an abandoned coal mine turned a stream so acidic that the rocks (and water) were amazing shades of orange, reds, and yellow. The rivers of this national often flowed with raw sewage, trash, and mine waste. Some, like the Cuyahoga, even caught fire, repeatedly (see https://www.smithsonianmag.com/history/cuyahoga-river-caught-fire-least-dozen-times-no-one-cared-until-1969-180972444/ ). The passage and actual enforcement of the Clean Air and the Clean Water Acts have cleaned up the air and water in this country to an amazing degree in my lifetime (I’m over 70). The cleanup of the Potomac and Anacostia Rivers in that period has also been tremendous. However, my friends who grew up in India and China tell me that the air and water pollution over there is worse than I can possibly imagine and is not improving at all.
When I was young, it appeared that nearly every adult I knew chain-smoked cigarettes and drank a lot of alcohol, and the bars, restaurants, dormitories, private houses, classrooms, buses and airplanes everywhere were filled with tobacco smoke. Despite the lies and obfuscation of the tobacco industry, not only legislation but also public opinion is such that today, I seldom encounter the nasty smell of tobacco smoke anywhere, even on people’s clothing on the bus or subway, and the number of drunk-driving fatalities is way down as well.
During my youth, the various nuclear powers exploded literally hundreds of nuclear weapons in the open air and underwater, spewing Strontium-90 and other radionucleides into things like cow or human milk, and doing untold destruction to the oceans nearby. While the number of world-wide nuclear explosions per year has dropped tremendously since then, they still continue, and may start up again on a larger scale.
Some noteworthy experiments re stopping global warming are listed in this month’s National Geographic. One of them, which has promise but also obvious drawbacks, involves dumping large quantities of finely ground-up alkaline rocks and minerals like olivine counteract the increasing acidification of the seas being caused by the absorption of so much carbon dioxide. Will these experiments work? I don’t know.
But let us not turn this planet – the only home we will ever know – into one of the barren, freezing or boiling versions of hell we see in the eyepieces of a telescope.
I have raised pigs, and I noticed that they never foul their own beds, if they are given any room to move around. Let’s be better than pigs and stop trying to extract riches in the short run while destroying the lovely planet we all love in the long run!
Heaven is not somewhere else.
It’s right here, if we can keep it that way and fix the damage we have done.
* For five-sixths of the roughly 3.7-billion-year time line of life on earth, all living things were single-celled microbes (or microbes living together in colonies). We mammals have only been important for the last 1.7% of that time, (ie since the dinosaurs died out 66 million years ago), the first known writing system was invented a few millennia ago, and Marconi only sent the first ship-to-shore radio message 130 years ago, which is an infinitesimally small fraction of 3.7 billion. Home radios only became popular 100 years ago.
Assuming that planets and stars are created at random times in the history of the universe, and assuming that a certain amount of enrichment of the interstellar medium by many generations of dead stars is necessary before life can begin at all, then it looks to me like the odds are not at all good for intelligent life of any sort to exist right now on any random planet we may study. And, unfortunately, if they do exist, we will never meet them. If there is an incredibly advanced civilization somewhere within 100 light years that can actually detect those first radio signals, then they just received our first messages. If they do respond, we won’t get the answer for another century or two!
For example, take a look at this time line of life on earth at a linear scale. If a hypothetical space traveler should somehow arrive on the 3rd rock from our Sun at a random moment in time over the past 4.5 billion years, then that’s like tossing a dart at this graph while blindfolded, and seeing where it lands. Notice the kind of organisms dominating during most of the past 4 billion years! The chances that they would happen to arrive here in the past few centuries or so, when we humans began to really understand science, are vanishingly small!
My original title began with “Space Travel is Impossible” — which is obviously false, because it is an incontrovertible fact of history that a handful of American astronauts, at enormous expense, did in fact land on the Moon and return. I remember the event well; I was working in a factory in Waltham, Mass that summer as part of the SDS Summer Work-In.
I should have written, “Space Travel to Exoplanets Is Impossible”.
But you could make the case that traveling to the Moon is barely even space travel! The distance to the moon is less than the total mileage on my last two automobiles (a Subaru Forester and a Toyota Prius) added together. Or, at the speed of light, the Moon is about 1.5 light-seconds away, the Sun about 8 light-minutes, Jupiter 34 light-minutes, and Saturn is about 85 light minutes this month. But the very nearest star-planet system to us is over four YEARS away, and the distances to the vast majority of exoplanets are measured in light-decades, light-centuries, or light-millennia.
I remember the Space Race! Both the USA and the Soviets poured incredible sums of cash, labor, raw materials, and brain power into that race, while, frankly, millions of people around the world starved or were killed in proxy wars between those two powers, representing two ideological and political opposing blocks. The incredibly expensive and dangerous race to win global prestige by being the first power bloc to reach the various goals has, so far, at its apogee, carted a handful of men to the near side of our Moon, less than two light-seconds away! And some people think we can easily travel to exoplanets that are light-decades or light-centuries away!
Several people have helped me with this applied geometry problem, but the person who actually took the time to check my steps and point out my error was an amazing 7th grade math student I know.
It involves optical testing for the making of telescope mirrors, which is something I find fascinating, as you may have guessed. Towards the end of this very long post, you can see the corrections, if you like.
Optics themselves are amazingly mysterious. Is light a wave, or a particle, or both? Why can nothing go faster than light? We forget that humans have only very recently discovered and made use of the vast majority of the electromagnetic spectrum that is invisible to our eyes.
But enough on that. At the telescope-making workshop here in DC, I want folks to be able to make the best ordinary, parabolized, and coated mirrors possible with the least amount of hassle possible and at the lowest possible cost. Purchasing high-precision, very expensive commercial interferometers to measure the surface of the mirror is out of the question, but it turns out that very inexpensive methods have been developed for doing that – at least on Newtonian telescopes.
Tom Crone, a friend of mine who is also a fellow amateur astronomer and telescope maker, wondered how on earth we can report mirror profiles as being within a few tens of nanometers of a perfect paraboloid with such simple devices as a classic Foucault knife-edge test.
He told me his computations suggested to him that the best we could do is get it to within a few tenths of a millimeter at best, which is four orders of magnitude less precise!
I assured him that there was something in the Foucault test which produced this ten-thousand-fold increase in accuracy, but allowed that I had never tried to do the complete calculation myself. I do not recall the exact words of our several short conversations on this, but I felt that I needed to accept this as a challenge.
When I did the calculations which follow, I found, to my surprise, that one of the formulas I had been taught and had read about in many telescope-making manuals, was actually not exact, and that the one I had been told was inherently less accurate, was, in fact, perfectly correct! Alan Tarica sent me an article from 1902supposedly explaining the derivation of a nice Foucault formula, but the author skipped a few bunch of important steps, and I don’t get anything like his results. it took me a lot of work, and help from this rising 8th grader, to find and fix my algebra errors. I now agree with the results of the author , T.H.Hussey.
I am embarrassed glad to say that even after several weeks of pretty hard work, an exact, correct formula for one of the commonly used methods for measuring ‘longitudinal aberration’ still eludes me. was pointed out to me by a student who took the time to Let’s see if anybody can follow my work and helped me out on the second method.
But first, a little background information.
Isaac Newton and Leon Foucault were right: a parabolic mirror is the easiest and cheapest way to make a high-quality telescope.
If you build or buy a Newtonian scope, especially on an easy-to-build Dobsonian mount, you will get the most high-quality photons for the money and effort spent, if you compare this type with any other type of optics at the same diameter. (Optical designs like 8-inch triplet apochromats or Ritchey-Chrétiens, or Maksutovs, or modern Schmidt-Cassegrains can cost many thousands of dollars, versus a few hundred at most for a decent 8″ diameter Newtonian).
With a Newtonian, you don’t need special types of optical glass whose indices of refraction and dispersion, and even chemical composition, must be known to many decimal places. The glass can even have bubbles and striations, or not even be transparent at all! Any telescope that only has mirrors, like a Newtonian, will have no chromatic aberration (ie, you don’t see rainbows around bright stars) because there is no refraction – except for inside your eyepieces and in your eyeball. All wavelengths of light reflect exactly the same –but they bend (refract) through glass or other materials at different angles depending on the wavelength.
Another advantage for Newtonians: you don’t need to grind and polish the radii of curvature of your two or three pieces of exotic glass to exceedingly strict tolerances. As long as you end up with a nice parabolic figure, it really doesn’t matter if your focal length ends up being a few centimeters or inches longer or shorter than you had originally planned. Also: there is only one curved mirror surface and one flat one, so you don’t need to make certain that the four or more optical axes of your mirrors and/or lenses are all perfectly parallel and perfectly concentric. Good collimation of the primary and secondary mirrors to the eyepiece helps with any scope, but it’s not nearly as critical in a Newtonian, and getting them to line up if they get knocked out of whack is also much easier to perform.
With a Newtonian, you only need to get one surface correct. That surface needs to be a paraboloid, not a section of a sphere. (Some telescopes require elliptical surfaces, or hyperbolic or spherical ones, or even more exotic geometries. A perfect sphere is the easiest surface to make, by the way.)
In the 1850’s, Leon Foucault showed how to ‘figure’ a curved piece of glass into a sufficiently perfect paraboloid and then to cover it with a thin, removable layer of extremely reflective silver. The methods that telescope makers use today to make sure that the surface is indeed a paraboloid are variations and improvements on Foucault’s methods, which you can read for yourself in my translation.
Jim Crowley performing a Foucault test
It turns out that the parabolic shape does need to be very, very accurate. In fact, over the entire surface of the mirror, other than scratches and particles of dust, there should be no areas that differ from each other and from the prescribed geometric shape by more than about one-tenth of a wavelength of green light (which I will call lambda for short), because otherwise, instead of a sharp image, you just receive a blur, because the high points on the sine waves of the light coming to you would tend to get canceled out by the low points.
Huh?
Let me try to explain. In my illustrations below, I draw two sine waves (one red, one green) that have the same exact frequency and wavelength (namely, two times pi) and the same amplitude, namely 3. They are almost perfectly in phase. Their sum is the dark blue wave. In diagram A, notice that the dark blue wave has an amplitude of six – twice as much as either the red or green sine wave. This means the blue and green waves added constructively.
Next, in diagram B, I draw the red and green waves being out of phase by one-tenth of a wave (0.10 lambda) , and then in diagram C they are ‘off’ by ¼ of a wave (0.25 lambda). You will notice that in the diagrams B and C, the dark blue wave (the sum of the other two) isn’t as tall as it was in diagram A, but it’s still taller than either the red or green one.
One-quarter wave ‘off’ is considered the maximum amount of offset allowed. Here is what happens if the amount of offset gets larger than 1/4:
In diagram D, the red and green curves differ by 1/3 of a wave (~0.33 lambda), and you notice that the blue wave (which is the sum of the other two) is exactly as tall as the red and green waves, which is not good.
Diagram E shows what happens is what happens when the waves are 2/5 (0.40 lambda) out of phase – the blue curve, the sum of the other two, now has a smaller amplitude than its components!
And finally, if the two curves differ by ½ of a wave (0.5 lambda) as in diagram F, then the green and red sine curves cancel out completely – the dark blue curve has become the x-axis, which means that you would only see a blur instead of a star or a planet. This is known as destructive interference, and it’s not what you want in your telescope!
But how on earth do we achieve such accuracy — one-tenth of the wavelength of visible light (λ/10) over an entire surface? And if we do, what does it mean, physically? And why one-tenth λ on the surface of the mirror, when ¼ λ looked pretty decent? For that last question, the reason is that when light bounces off a mirror, any deviations are multiplied by 2. So lambda – about 55 nanometers or 5.5×10^(-8) m- is the maximum allowable depth or height of a bump or a hollow across the entire width of the mirror. That’s really small! How small? Really insanely small.
Let’s try to visualize this by enlarging the mirror. At our mirror shop, we generally help folks work on mirrors whose diameters are anywhere from 11 cm (4 ¼ inches) to 45 cm (18 inches) across. Suppose we could magically enlarge an 8” (20 cm) mirror and blow it up so that it has the same diameter as the original 10-mile (16 km) square surveyed in 1790 by the Ellicott brothers and Benjamin Banneker for the 1790 Federal City. (If you didn’t know, the part on the eastern bank of the Potomac became the District of Columbia, and the part on the western bank was given back to Virginia back in 1847. That explains why Washington DC is no longer shaped like a nice rhombus/diamond/square.)
So imagine a whole lot of earth-moving equipment making a large parabolic dish where DC used to be, a bit like the Arecibo radio telescope, but about 50 times the diameter, and with a parabolic shape, unlike the spherical one that Arecibo was built with.
(Technical detail: since Arecibo was so big, there was no way to physically steer it around at desired targets in the sky. Since they couldn’t steer it, then a parabolic mirror would be useless except for directly overhead. However, a spherical mirror does NOT have a single focal point. So the scope has a movable antenna (or ‘horn’) which can move around to a variety of more-or-less focal points, which enabled them to aim the whole device a bit off to the side, so they can ‘track’ an object for about 40 minutes, which means that it can aim at targets around 5 degrees in any direction from directly overhead, but the resolution was probably not as good as it would have been if it had a fully steerable, parabolic dish. See the following diagrams comparing focal locations for spherical mirrors vs parabolic mirrors. Note that the spherical mirror has a wide range of focal locations, but the parabolic mirror has exactly one focal point.)
I’ll use the metric system because the math is easier. In enlarging a 20 cm (or 0.20 m) mirror all the way to 16 km (which is 16 000 m), one is multiplying 80,000. So if we take the 5.5×10-8 m accuracy and multiply it by eighty thousand you get 44 x 10-4 m, which means 4.4 millimeters. So, if our imaginary, ginormous 16-kilometer-wide dish was as accurate, to scale, as any ordinary home-made or commercial Newtonian mirror, then none of the bumps or valleys would be more than 4.4 millimeters too deep or too high. For comparison, an ordinary pencil is about 6.8 millimeters thick.
Wow!
So that’s the claim, but now let’s verify this mathematically.
I claim that such a 3-dimensional paraboloid, like the radio dish in the picture below, can be represented by the equation
where f represents the focal length. (For simplicity, I have put the vertex of the paraboloid at the origin, which I have called A. I have decided to make the x-axis (green, pointing to our right) be the optical and geometric axis of the mirror. The positive z-axis (also green) is pointed towards our lower left, and the y-axis (again, green) is the vertical one. The focal point is somewhere on the x-axis, near the detector; let’s pretend it’s at the red dot that I labeled as Focus.)
You may be wondering where that immediately previous formula came from. Here is an explanation:
Let us define a paraboloid as the set (or locus) of all points in 3-D space that are equidistant from a given plane and a given focal point, whose coordinates I will arbitrarily call (f, 0, 0). (When deciding on a mirror or radio dish or reflector on a searchlight, you can make the focal length anything you want.)
To make it simple, the plane in question will be on the opposite side of the origin; its equation is x = -f. We will pick some random point G anywhere on the surface of the parabolic dish antenna and call its coordinates (x, y, z). We will see what equation these conditions create. We then drop a perpendicular from G towards the plane with equation x = -f. Where this perpendicular hits the plane, we will call point H, whose coordinates are (-f, y, z). We need for distance GH (from the point to the plane) to equal distance from G to the Focus. Distance GH is easy: it’s just f + x. To find distance between G and Focus, I will use the 3-D distance formula:
Which, after substituting, becomes
To get rid of the radical sign, I will equate those two quantities, because FG = GH, omit the zeroes, and square both sides. I then get
Multiplying out both sides, we get
Canceling equal stuff on both sides, I get
Adding 2fx to both sides, and dividing both sides by 4f, I then get
However, 3 dimensions is harder than 2 dimensions, and two dimensions will work just fine for right now. Let us just consider a slice through this paraboloid via the x-y plane, as you see below: a 2-dimensional cross-section of the 3-dimensional paraboloid, sliced through the vertex of the paraboloid, which you recall is at the origin. We can ignore the z values, because they will all be zero, so the equation for the blue parabola is
or, if you solve it for y, you get
There is a circle with almost the same curvature as the paraboloid; its center, labeled CoC (for ‘Center of Curvature’) is exactly twice as far from the origin as the focal point. You can just barely see a green dotted curve representing that circle, towards the top of the diagram, just to the right of the blue paraboloid. center of the circle (and sphere). Its radius is 2f, which obviously depends on the location of the Focus.
D is a random point on that parabola, much like point G was earlier, and D’ being precisely on the opposite side of the optical axis. The great thing about parabolic mirrors is that every single incoming light ray coming into the paraboloid that is parallel to the axis will reflect towards the Focus, as we saw earlier. Or else, if you want to make a lamp or searchlight, and you place a light source at the focus, then all of the light that comes from it that bounces off of the mirror will be reflected out in a parallel beam that does not spread out.
In my diagram, you can see a very thin line, parallel to the x-axis, coming in from a distant star (meaning, effectively at infinity), bouncing off the parabola, and then hitting the Focus.
I also drew two red, dashed lines that are tangent to the paraboloid at point D and D’. I am calling the y-coordinate of point D as h (D has y-coordinate -h)and the x-coordinate of either one is
I used basic calculus to work out the slope of the red, dashed tangent line ID. (Quick reminder, if you forgot: in the very first part of most calculus classes, students learn that the derivative, or slope, of any function such as this:
is given by this:
So for the parabola with equation
the slope can be found for any value of x by plugging that value into the equation
Since
the exponent b is one-half. Therefore, the slope is going to be
which simplifies to
Now we need to plug in the x coordinate of point D, namely
we then get that the slope is
To find the equation of the tangent line, I used the point-slope formula y – y1=m(x – x1). ; plugging in my known values, I got the result
To find where this hits the y-axis, I substituted 0 for x, and got the result that the tangent line hits the y-axis at the point (0, h/2) — which I labeled as I — or one-half of the distance from the vertex (or origin) to the ‘height’ of the zone, or ring, being measured.
Line DW is constructed to be perpendicular to that tangent, so any beam of light coming from W that hits the parabola at point D will be reflected back upon itself. Perpendicular lines have slopes equal to the negative reciprocal of the other. Since the tangent has slope 2f/h, then line DW has slope -h/(2f).
Plugging in the known values into the point-slope formula, the equation for DW is therefore
Here, I am interested in the value of x when y = 0. Substituting, re-arranging, and solving for x, I get
Recall that point C is precisely 2f units from the origin, which means that the perpendicular line DW hits the x axis at a point that is the same distance from the center of curvature CoC as the point D is from the y-axis!
Or, in other words, CW = AT = DE. This means: if you are testing a parabolic mirror with a moving light source at point W, then a beam of light from W that is aimed at point D on the paraboloid will come right back to W, and the longitudinal readings of distance will follow the rule h2/(4f), where h is the radius of the zone, or ring, that you are measuring. Other locations on the mirror which do not lie in that ring will not have that property. This then is the derivation of the formula I was taught over 30 years ago by Jerry Schnall, and found in many books on telescope making – namely that for a moving light source, since R=2f,
where LA means ‘longitudinal aberration and the capital R is the radius of curvature of the mirror, or twice the focal length. So that’s exactly the same as what I computed.
HOWEVER, this formula [ LA=h^2/(2R) ] does not work at all if your light source is fixed at point C, the center of curvature of the green, reference sphere. In the old days, before the invention of LEDs, the light sources were fairly large and rather hot, so it was easier to make them stationary, and the user would move the knife-edge back and forth, but not the light source. The formula I was given for this arrangement by my mentor Jerry Schnall, and which is also given in numerous sources on telescope making was this:
that is, exactly twice as much as for a moving light source. I discovered to my surprise that this is not correct, but it took me a while to figure this out. I originally wrote the following:
But now I can confirm this, thanks in part to two of my very mathematically inclined 8th grade geometry students. Here goes, as corrected:
If one is using a fixed light source located at the center of curvature C, and a moving knife-edge, located at point E, the the rays of light that hit the same point D will NOT bounce straight back, because they don’t hit the tangent line at precisely 90 degrees. Instead, the angle of incidence CDW will equal the angle of reflection, namely WDE. I used Geometer’s sketchpad to construct line DE by asking the software to reflect line CD over the line DW.
However, calculating an algebraic expression for the x-coordinate of point E was surprisingly complicated. See if you can follow along!
To find the x-coordinate of E, I will employ the tangent of angle TDE.
To make the computations easier, I will draw a couple of simplified diagrams that keep the essentials.
I also tried other approaches, and also got answers that made no sense. It looks like the formula in the 1902 article is correct, but I have not been able to confirm it.
I suspect I made a very stupid and obvious algebra mistake that anybody who has made it through pre-calculus can easily find and point out to me, but I have had no luck in finding it so far. I would love for someone did to point it out to me.
An alarming article about studies of bird deaths due to bright city lighting. A couple of quotes:
Every 11 September at dusk, in memory of the 2001 attacks, New York City mounts the Tribute in Light, an art installation in lower Manhattan. And every year, as twin towers of light bloom skyward, they attract thousands of migrating birds, sucking in warblers, seabirds, and thrushes—along with predators such as peregrine falcons eager to take advantage of the confusion. On each anniversary, bird conservationists wait below, counting and listening to disoriented chirps. If the observers report too many birds circling aimlessly in the beams, organizers flip off the lights.
In recent years, on-site observers have also used a complementary tool to quantify the orbiting birds: weather radar, which bounces off birds as well as raindrops. In 2017, a group led by Cornell University ornithologist Andrew Farnsworth found that during seven previous anniversaries, the once-a-year installation had attracted a total of about 1.1 million birds. Within 20 minutes of lighting up, up to 16,000 birds crammed themselves into a half-kilometer radius. But when the lights flicked off, the dense clouds of birds on the radar screen dissipated just as fast, a finding later confirmed by on-site thermal cameras.’
Later, discussing a single building, the author found that a
‘key factor was how many of the convention center’s windows had been illuminated. Each individual bright window left more dead birds for volunteers to find the next day. The correlation suggests halving the number of lit window bays would halve the number of bird strikes, the team estimated, saving thousands of birds at this one three-story building. “It really does seem that each window makes a difference,” van Doren says.’
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:
The Earth, Polaris, and You.
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.
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.
Recently, while preparing to give a talk at this year’s Stellafane telescope-makers’ convention, I was disappointed to discover that the National Capital Astronomers (NCA), which I’ve belonged to for about 30 years, specifically excluded Black members for nearly 3 decades: from about 1940 all the way up to1969.
But NCA didn’t start out being overtly racist. Our original 1937 founding document has no such language. It reads, in part,
“The particular business and objects of [the NCA] shall be the education and mutual improvement of its members in the science of Astronomy and the encouragement of an interest in this science among others. (…) The activities of this Association are designed for the enjoyment and cultural profit of all interested in astronomy, whether the member be a beginner, an advanced student, or one whose pursuit of the science is necessarily desultory.”
And today’s NCA home page reads, “All are welcome to join. Everyone who looks up to the sky with wonder is an astronomer and welcomed by NCA. You do not have to own a telescope, but if you do own one that is fine, too. You do not have to be deeply knowledgeable in astronomy, but if you are knowledgeable in astronomy that is fine, too. You do not have to have a degree, but if you do that is fine, too. WE ARE THE MOST DIVERSE local ASTRONOMY CLUB anywhere. Come to our meetings and you will find this out. WE REALLY MEAN THIS!”
But in the 1940’s, the original open-minded and scientific NCA membership policy changed. The January 1946 Star Dust listed a number of changes to be voted on by the membership in the club’s founding documents. (See https://capitalastronomers.org/SD_year/1946/StarDust_1946_01.pdf ) The organization voted to change article III of its constitution as follows:
From:
“only Caucasians over 16 years old are eligible for membership.”
To this:
“to include all ages (see by-laws), exclude only the Black race.”
While it may be shocking that a scientific organization like NCA had such a policy, people often forget how racist a nation the USA used to be, and for how long. If you look up actual pages of DC area newspapers from the 1950s, you will note that the classified advertisements were largely segregated both by race and by gender – want ads would very often specify male or female, single or married, White-only or Colored-only jobs, apartments, and so on.
Schools in DC, MD, and Virginia were mostly segregated, either by law or in practice, up until the late 1960s or early 1970s. The 1954 Brown v Board decision had very little real impact in most areas until much, much later. Queens (NYC), PG County (MD) and Boston (MA) had violent movements against integrating schools in the 1970s. I know because I attended demonstrations against those racists and have some scars to prove it.
While the Federal and DC governments offices were integrated immediately after the Civil War, that changed for the worse when Woodrow Wilson was elected President in 1912.
Many scientists in the USA and in Europe believed the pseudo-scientific ideas of racial superiority and eugenics that arose around 1900 and were still widespread 50 years ago – and even today, as recent events have sadly shown.
In The War Against the Weak: Eugenics and America’s Campaign to Create a Master Race, Edwin Black explains how august scientific institutions like the Carnegie Institution of Washington (CIW), the American Natural History Museum in New York, and a number of eminent statisticians and biologists for many decades supported the Eugenics Records Office (ERO) at Cold Spring Harbor. So did the fabulously wealthy Rockefeller and Harriman Foundations.
The ERO pushed the concept of the genetic superiority of the ‘Nordic’ race and helped to pass State laws sterilizing the ‘weak’ and forbidding interracial marriage. They were also successful in passing the 1924 Federal immigration law that severely cut back immigration from parts of the world where supposedly ‘inferior’ people lived – e.g. Eastern and Southern Europe. As a result, many Jews who would have loved to escape Hitler’s ovens by crossing the Atlantic never made it.
Hitler and his acolytes always acknowledged their ideological and procedural debt to American eugenical laws, literature, and propaganda. As we all know, Germany’s Nazis put those ideas to work murdering millions of Jews, Gypsies, Slavs and others.
It took more than three decades for the CIW to withdraw their support of the ERO. A CIW committee concluded in 1935 “that the Eugenics Record Office was a worthless endeavor from top to bottom, yielding no real data, and that eugenics itself was not a science but rather a social propaganda campaign with no discernable value to the science of either genetics or human heredity.” (Black, p. 390) The members pointedly compared the work of the ERO to the excesses of Nazi Germany. However, it took four more years for CIW to cut all their ties – shortly after Hitler invaded Poland in 1939, starting World War Two.
I don’t know exactly when the ‘Caucasian’-only policy became part of the NCA rules, but it seems to have been between the club founding in 1937, and October 1943 when volume 1, number 1 of Star Dust was printed. At one point, perhaps around 1940, NCA decided that only ‘Caucasians’ over 16 could join. But as indicated above, in 1946, the racial exclusion policy was narrowed to only exclude Black people. Apparently Jews, Italians, young people, Latin Americans, and Asians were eligible to join NCA from 1946 to 1969. But not African-Americans.
While researching my talk, I found that the NCA held amateur telescope-making classes at a number of all-white DC, MD, and VA high schools, from the 1940s through about 1970, both during the days of de jure segregation and the merely de-facto type: McKinley, Roosevelt, Central, Bladensburg, Falls Church, and McLean high schools are listed. While Star Dust mentions a telescope-making course at (the largely-Black) Howard University in 1946, there is no mention of any assistance for that course from NCA.
I also found no evidence in any issue of Star Dust from that era that anybody at the time raised any vocal objections to racial exclusion. Not in 1946, nor 23 years later when the rule prohibiting Black members was quietly dropped (in 1969) when a new constitution was adopted.
A few current or past NCA members confirmed to me that at some point, they noticed that racist language and privately wondered about it. One person told me that they definitely recalled some now-deceased NCA members who were openly racist and not shy about expressing those views. Others told me that they had never heard any discussion of the subject at all.
(As one who grew up in DC and Montgomery County, and attended essentially-segregated public schools there, I am sorry that neither I nor my family actively spoke up at the time, even though a farm adjacent to ours in Clarksburg was owned by a Black family [with no school-age children at the time]. Amazing how blind one can be! The racists of those days were not shy about committing violence to achieve their ends. Fear might be one reason for silence.)
One possibility is that some of the early NCA meetings might have been held at private residences; perhaps some of the racist members insisted in preventing non-‘Caucasian’ or ‘Black’ people from attending. It is too bad the other NCA members didn’t take the other route and stay true to the original ideas of the club, and tell the racist members to get lost.
Very ironic: the late George Carruthers, a celebrated Naval Research Labs and NASA scientist, and an instrument-maker for numerous astronomical probes and satellites, gave a talk to the NCA in September of 1970 – not too long after the NCA apparently dropped its racist membership rules (April, 1969). So, a mere year and a half before he gave his talk, he could not have legally joined the organization. Nor could he have done so when he was making his own telescopes from scratch as a teenager in the 1940s. See https://en.wikipedia.org/wiki/George_Robert_Carruthers on the life and work of this great African-American scientist and inventor.
To NCA’s credit, we have done better in the past few decades at encouraging participation in telescope viewing parties, telescope making, and lectures by members of all races and ethnic groups. However, I often find that not very many NCA members bring telescopes to viewing events, or show up to judge science fairs, in mostly-minority neighborhoods. Often, it’s just me. That needs to change. We need to encourage an interest in science, astronomy, and the universe in children and the public no matter their skin color or national origin, and we need to combat the racist twaddle that passes for eugenics.
I anticipate that NCA will have a formal vote repudiating the club’s former unscientific and racist policies and behavior. I hope we will redouble our efforts to promote the study of astronomy to members of all ethnic groups, especially those historically under-represented in science.
We could do well to note the words that Albert Einstein wrote in 1946, after he had been living in the US for a decade, and the same year that NCA confirmed that Black people could not join:
“a somber point in the social outlook of Americans. Their sense of equality and human dignity is mainly limited to men of white skins. Even among these there are prejudices of which I as a Jew am clearly conscious; but they are unimportant in comparison with the attitude of the “Whites” toward their fellow-citizens of darker complexion, particularly toward Negroes.
The more I feel an American, the more this situation pains me. I can escape the feeling of complicity in it only by speaking out.
Many a sincere person will answer: “Our attitude towards Negroes is the result of unfavorable experiences which we have had by living side by side with Negroes in this country. They are not our equals in intelligence, sense of responsibility, reliability.”
I am firmly convinced that whoever believes this suffers from a fatal misconception. Your ancestors dragged these black people from their homes by force; and in the white man’s quest for wealth and an easy life they have been ruthlessly suppressed and exploited, degraded into slavery. The modern prejudice against Negroes is the result of the desire to maintain this unworthy condition.
The ancient Greeks also had slaves. They were not Negroes but white men who had been taken captive in war. There could be no talk of racial differences. And yet Aristotle, one of the great Greek philosophers, declared slaves inferior beings who were justly subdued and deprived of their liberty. It is clear that he was enmeshed in a traditional prejudice from which, despite his extraordinary intellect, he could not free himself.
What, however, can the man of good will do to combat this deeply rooted prejudice? He must have the courage to set an example by word and deed, and must watch lest his children become influenced by this racial bias.
I do not believe there is a way in which this deeply entrenched evil can be quickly healed. But until this goal is reached there is no greater satisfaction for a just and well-meaning person than the knowledge that he has devoted his best energies to the service of the good cause.”
I am indebted to Morgan Aronson, Nancy Byrd, Richard Byrd, Geoff Chester, Jeff Guerber, Jay Miller, Jeffrey Norman, Rachel Poe, Todd Supple, Wayne Warren, Elizabeth Warner, and Harold Williams for documents, memories, and/or technical support.
The Hopewell Observatory had available a finely-machined antique, brass-tube 6″ f./14 achromatic refractor.
The mount and drive were apparently made by John Brashear, but we don’t know for sure who made the tube, lens, focuser or optics.
We removed a lot of accumulated green or black grunge on the outside of the tube, but found no identifying markings of any sort anywhere, except for the degrees and such on the setting circles and some very subtle marks on the sides of the lens elements indicating the proper alignment.
The son of the original owner told me that the scope and mount were built a bit over a century ago for the American professional astronomer Carl Kiess. The latter worked mostly on stellar and solar spectra for the National Bureau of Standards, was for many years on the faculty of Georgetown University, and passed away in 1967. A few decades later, his son later donated this scope and mount to National Capital Astronomers (of DC), who were unable to use it. NCA then later sold it to us (Hopewell Observatory), who cleaned and tested it.
The attribution of the mount to Brashear was by Bart Fried of the Antique Telescope Society, who said that quite often Brashear didn’t initial or stamp his products. Looking at known examples of Brashear’s mounts, I think Fried is probably correct. Kiess’s son said he thought that the optics were made by an optician in California, but he didn’t remember any other details. His father got his PhD at UC Berkeley in 1913, and later worked at the Lick Observatory before settling in the DC area. The company that Brashear became doesn’t have any records going back that far.
When we first looked through the scope, we thought the views were terrible, which surprised us. However, as we were cleaning the lens cell, someone noticed subtle pencil marks on the edges of the two lens elements, indicating how they were supposed to be aligned with each other. Once we fixed that, and replaced the 8 or so paper tabs with three blue tape tabs, we found it produced very nice views indeed!
The focuser accepts standard 1.25″ eyepieces, and the focuser slides very smoothly (once we got the nasty, flaky corrosion off as delicately as possible and sprayed the metal with several coats of clear polyurethane). The workmanship is beautiful!
Top: tiller for hand control of right ascension. Middle: counterweight bar (machined by me to screw into the mount) with clamps to hold weights in place. Bottom: detail of 1.25″ rack-and-pinion focuser.
We have not cleaned the mechanical mount, or tried it out, but it does appear to operate: the user turns a miniature boat tiller at the end of a long lever to keep up with the motions of the stars.
The mount and cradle (with size 12 feet for scale)
The counterweight rod was missing, so I machined a replacement, which has weight holder clamps like you see in gymnasiums. Normal Barbell-type weights with 1 inch holes fit well and can be adjusted with the clamps.
Unfortunately, the whole device is rather heavy, and we already own a nice 6″ f/15 refractor made by Jaegers, as well as some Schmidt-Cassegrain telescopes that also have long focal lengths. Putting this scope on its own pedestal, outside our roll-off roof, with adequate protection from both the elements and from vandals, or figuring out a way to mount it and remove it when needed, are efforts that we don’t see as being wise for us.
Did I mention that it’s heavy? The OTA and the mount together weigh roughly 100 pounds.
However, it’s really a beautiful, historic piece with great optics. Perhaps a collector might be interested in putting this in a dome atop their home or in their office? Or perhaps someone might be interested in trading this towards a nice Ritchey Chretien or Corrected Dal-Kirkham telescope of moderate aperture?
Anybody know what might be a fair price for this?
Guy Brandenburg
President
The Hopewell Observatory
Some more photos of the process and to three previous posts on this telescope.
Partway through cleaning the greenish, peeling, grimy layer and old duct tape residue with a fine wire brush at low speed to reveal the beautiful brass OTA.This shows the universal joint that attaches to the ’tiller’ and drives the RA axisDo you see the secret mark, not aligned with anything?Aluminum lens cover and cell before cleaningLens cell and cover, with adjustment screws highlighted, after cleaningIt works!
Guy's Math & Astro Blog 