Thank the Sumerians

Over five thousand years ago, the Sumerians in the area now known as southern Iraq appear to have been the first to develop a penchant for the numbers 12, 24, 60 and 360.

It is easy to see why. 12 is the first number that is evenly divisible by six smaller numbers:

12 = 1×12, 2×6, 3×4 .

24 is the first number that is evenly divisible by eight smaller numbers:

24 = 1×24, 2×12, 3×8, 4×6 .

60 is the first number than is evenly divisible by twelve smaller numbers:

60 = 1×60, 2×30, 3×20, 4×15, 5×12, 6×10 .

And 360 is the first number that is evenly divisible by twenty-four smaller numbers:

360 = 1×360, 2×180, 3×120, 4×90, 5×72, 6×60, 8×45, 9×40, 10×36, 12×30, 15×24, 18×20 .

And 360 in a happy coincidence is just 1.4% short of the number of days in a year.

We have 12 hours in the morning, 12 hours in the evening.

We have 24 hours in a day.

We have 60 seconds in a minute, and 60 minutes in an hour.

We have 60 arcseconds in an arcminute, 60 arcminutes in a degree, and 360 degrees in a circle.

The current equatorial coordinates for the star Vega are

α2019.1 = 18h 37m 33s
δ2019.1 = +38° 47′ 58″

Due to precession, the right ascension (α) of Vega is currently increasing by 1s (one second of time) every 37 days, and its declination (δ) is currently decreasing by 1″ (one arcsecond) every 5 days.

With right ascension, the 360° in a circle is divided into 24 hours, therefore 1h is equal to (360°/24h) = 15°. Since there are 60 minutes in an hour and 60 seconds in a minute, and 60 arcminutes in a degree and 60 arcseconds in an arcminute, it follows that 1m = 15′ and 1s = 15″.

Increasingly, you will see right ascension and declination given in decimal, rather than sexagesimal, units. For Vega, currently, this would be

α2019.1 = 18.62583h
δ2019.1 = +38.7994°

Or, both in degrees

α2019.1 = 279.3875°
δ2019.1 = +38.7994°

Or even radians

α2019.1 = 4.876232 rad
δ2019.1 = 0.677178 rad

Even though the latter three forms lend themselves well to computation, I still prefer the old sexagesimal form for “display” purposes, and when entering coordinates for “go to” at the telescope.

There is something aesthetically appealing about three sets of two-digit numbers, and, I think, this form is more easily remembered from one moment to the next.

For the same reason, we still use the sexagesimal form for timekeeping. For example, as I write this the current time is 12:25:14 a.m. which is a more attractive (and memorable) way to write the time than saying it is 12.4206 a.m. (unless you are doing computations).

That’s quite an achievement, developing something that is still in common use 5,000 years later.

Thank the Sumerians!

ZZ Ceti Stars

About 80% of all known white dwarf stars have hydrogen atmospheres, showing only hydrogen absorption lines in their spectra. These have been assigned the white dwarf spectral type of DA (presumably D for dwarf and A for the first, or most common, type of white dwarf). Arlo Landolt (1935-) was the first to discover variability in a white dwarf by observing the mv=15.0 DA white dwarf star named HL Tau 76 (not to be confused with HL Tau!), in front of a dark nebula in Taurus (LDN 1521C = MLB 3-13), in December 1964. This star now has the standard variable star designation V411 Tauri.

A second DA white dwarf, mv=14.2 Ross 548 in Cetus, was discovered to be variable by Barry Lasker (1939-1999) and Jim Hesser in 1970, and in 1972 it was assigned the variable star designation ZZ Ceti.

By 1976, seven luminosity-variable DA white dwarfs had been discovered, and John T. McGraw and Edward L. Robinson stated in an ApJ paper

We suggest that the recently proposed ZZ Ceti class of variable stars be reserved for the DA variables in Table 1 and specifically exclude the DB variables since the mechanism of variation is almost certainly different.

McGraw & Robinson, Astrophysical Journal, Vol. 205, p. L155-L158 (1976)

So, why wasn’t this new class of luminosity-variable DA white dwarfs named after V411 Tau, the first of its class discovered? Why are they called ZZ Ceti stars, after the second such star discovered, instead? In each constellation, variable stars are given one- or two-letter designations in order of discovery, and when the letter designations run out, the letter “V” is used followed by a number. The first “V” star is V335, the 335th variable star to be discovered in a constellation. Well, V411 Tau was the 411th variable star discovered in Taurus, and as a matter of tradition, no class of variable stars is ever named after a “V” designation. So, the honor fell to the runner-up, ZZ Ceti. Besides, ZZ Cet is a little brighter than V411 Tau, so not a bad choice.

ZZ Ceti stars, also known as DAV stars (as in DA Variable), are multimodal pulsating white dwarfs having periods ranging from 70 seconds to 25 minutes. But the amplitude of the brightness variations is tiny to small, ranging from less than 0.001 magnitude up to 0.3 magnitudes.

V411 Tau has a dozen detected pulsation modes. In order of amplitude (in millimagnitudes), they are (without error bars):

Period (seconds)Amplitude (mmag)

ZZ Cet has eleven detected pulsation modes. In order of amplitude, they are (without error bars):

Period (seconds)Amplitude (mmag)

ZZ Ceti stars are not radial pulsators, that is they do not undergo radial oscillations (changes in size). White dwarf stars typically have diameters of only 0.9 to 2.2 that of the Earth, so they are much smaller than “normal” stars. As short as the pulsation periods are, they are not short enough if the cause were radial pulsations. Instead, the pulsations are due to shock waves traversing the atmosphere of the ultradense star. The slow rotation of these stars often causes closely spaced “double periods” such as we see in ZZ Cet.

The brightest (and closest) ZZ Ceti star yet discovered is DN Draconis, shining at visual magnitude 12.2. DN Dra pulsates with an amplitude of just 0.006 magnitude (6 millimagnitudes), and its pulsation period is 109 seconds.

What ZZ Ceti star has the largest amplitude? As they say, “it’s complicated”. Even though references to a maximum amplitude as high as 0.3m can be found in the literature, I was unable to find any ZZ Ceti stars with amplitudes greater than 0.12m. Moreover, pulsation modes of ZZ Ceti stars can come and go, so one observer may observe a higher amplitude but the next may not. Though pulsation modes can and do appear and disappear over time, there is also the changing additive nature of many pulsation modes to consider from one observing run to the next.

Patterson et. al (1991) report mv=13.0 ZZ Psc having a pulsation amplitude of 0.116m and period 614.9s in blue light. Mukadam et al. (2004) report mv=15.2 UCAC4 448-059643 (in the constellation Serpens) having a pulsation amplitude of 0.121m and period 873.2s in blue light.

One challenge in the literature is that pulsation amplitudes are variously given in units of milli-modulation amplitude (mma), milli-magnitudes (mmag), percent, or parts per thousand. Here are the unit conversions:

1\:mma = \frac{1}{2.5\log_{10}e}\:mmag = 0.1\% = 1\:ppt

The study of the pulsation modes of white dwarfs and other stars is called asteroseismology. I hope this article has piqued your interest in learning more about this rapidly developing and fascinating field!

Bognár, Z., Sódor, Á. 2016, Information Bulletin on Variable Stars,6184
Castanheira, B. G. & Kepler, S. O. 2008, MNRAS, 385, 430
De Gerónimo, F. C., Althaus, L. G., Córsico, et al. 2017, A&A, 599, A21
Dolez, N., Vauclair, G., Kleinman, S. J., et al. 2006, A&A, 446,237
Giammichele, N., Fontaine, G., Bergeron, P., et al. 2015, ApJ, 815, 56
Haro, G., and Luyten, W. J. 1961, Bol. Obs. Tonantzintlay Tacubaya, 3, 35
Kepler, S. O., Robinson, E. L., Koester, D., et al. 2000, ApJ, 539, 379
Kukarkin, B. V., Kholopov, P. N., Kukarkina, N. P., et al. 1972, IBVS, 717, 1
Landolt, A. U. 1968, ApJ, 153, 151
Lasker, B. M. & Hesser, J. E., 1971, ApJ, 163, L89
Lynds, B. T. 1962, ApJS, 7, 1
McGraw J. T. & Robinson E. L., 1976, ApJ, 205, L155
Mukadam, A. S., Mullally, F., Nather, R. E., et al. 2004, ApJ,607, 982
Myers, P. C., Linke, R. A., & Benson, P. J. 1983, ApJ, 264,517
Patterson, J., Zuckerman, B., Becklin E. E., et al. 1991, ApJ, 374, 330

A Warm Day on Pluto

The coldest weather I’ve ever experienced occurred January 30-31, 2019. Here in Dodgeville, Wisconsin, I measured a low temperature the morning of Wednesday, January 30, 2019 of -31.0° F and a high that day of -14.4° F. It was even colder the following night. On Thursday, January 31, 2019 the low temperature was -31.9° F.

Thanks to the National Weather Service, we had advance notice of the arrival of the Arctic polar vortex that was to bring the coldest weather to Wisconsin in a generation. Concerned about the effect this would have on my observatory electronics, I started running my warming room electric heater continuously from 8:30 p.m. CST Monday, January 28 until 9:45 a.m. CST Friday, February 1. Of course, I left the warming room door open to the telescope room to ensure that some of the heat would reach the telescope and its associated electronics.

During this time, I made a number of temperature measurements from an Oregon Scientific weather station inside the house, connected by 433 MHz radio frequency signals to temperature sensors inside the observatory and on the north side of my house.

Here are those observations:

And here is graph plotting both temperatures at each time:

Air (north side of house) and Observatory (inside the observatory) temperatures January 28-February 1, 2019.

And here is a plot of the temperature difference vs. the outside Air temperature:

Temperature difference vs. Air temperature with a linear regression line

There seems to be a general trend that the colder it was outside the observatory, the bigger was the temperature difference between inside the observatory and outside the observatory. Why is that? The electric heater is presumably putting out a constant amount of heat, so you might think that the temperature difference would remain more or less constant as the temperature goes up and down outside. It doesn’t.

There are a number of factors influencing the temperature inside the observatory. First, there is the thermal mass of the observatory itself, and some heating of the inside of the observatory should occur when the sun is shining on it. There is the wind speed and direction to consider. There may be some heating through the concrete slab from the ground below. It seems to me that thermodynamics should be able to explain the general downward trend in ΔT as the outside air temperature increases. Can you help by posting a comment here?

You’ll notice three outliers in the graph above where ΔT is quite a bit lower than the regression line. The points (-22.0,16.6) and (-10.5,10.1) were consecutive measurements just 76 minutes apart (8:32 a.m. and 9:48 a.m.), the first readings I made after the lowest overnight temperature of -31.9° F on 1/31. The point (8.2,7.6) was my first reading on 1/28 at 8:42 p.m., soon after turning the space heater in the observatory on. The points (-16.4,25.2), (-17.9,26.0), (-19.5,26.3), (-25.1,27.2), and (-26.9,27.4) all are above the regression line and are consecutive readings between 8:29 p.m. on 1/29 and 3:20 a.m. on 1/30 before the -31.0° F low on the first really cold night.

My weather station keeps track of the daily high and low temperatures, but not the time at which those temperatures occur. On 1/30 when the outside low temperature of -31.0° F was recorded, the low inside the observatory was -4.0° F (though not necessarily at the same time). ΔT = 27.0°. The high temperature that day was -14.4° F and 6.4° F inside the observatory (ΔT = 20.8°). The next night, 1/31, the low temperature was -31.9° F and -6.2° F inside the observatory (ΔT = 25.7°).

So, despite the many factors which influence the temperature differential between outside and inside the observatory, the clear trend of smaller ΔT at warmer outside temperature begs for an explanation. Can you help?

Turnkey System for Occultations

Finally, a turnkey system is available for recording stellar occultations by asteroids and trans-Neptunian objects (TNOs)! All you need besides the kit is a telescope and a PC. A big thank you to Ted Blank and IOTA for putting this together!

Occultation Recording Kit

  • Highly sensitive RunCam Night Eagle Astro Edition video camera
  • 0.5x focal reducer & adapters to attach camera to 1¼-inch eyepiece holder
  • IOTA VTI (Video Time Inserter) V3
  • StarTech SVID2USB23 USB video capture device
  • Instruction manual
  • Cost: $518

We need more observers in the Midwest (everywhere, really) to give us more chords across the asteroids and TNOs, thus increasing the scientific value of the observations. Right now, we are desperately in need of observers in Iowa (where I lived for many years and will always be home to me), and we have precious few active observers in Wisconsin (yours truly), Minnesota (Steve Messner), and Illinois (Bob Dunford, Aart Olsen, Randy Trank).

If you have an interest in pursuing this interesting and rewarding speciality that gives you the opportunity to make a valuable scientific contribution, feel free to post a comment here and I’ll be happy to help!

Lost in Math: A Book Review

I recently finished reading a thought-provoking book by theoretical physicist Sabine Hossenfelder, Lost in Math: How Beauty Leads Physics Astray. Hossenfelder writes in an engaging and accessible style, and I hope you will enjoy reading this book as much as I did. Do we have a crisis in physics and cosmology? You be the judge. She presents convincing arguments.

The basic premise of Hossenfelder’s book is that when theoretical physicists and cosmologists lack empirical data to validate their theories, they have to rely on other approaches—”beauty”, “symmetry”, “simplicity”, “naturalness“, “elegance”—mathematics. Just because these approaches have been remarkably successful in the past is no guarantee they will lead to further progress.

One structural element that contributes to the book’s appeal is Hossenfelder’s interviews with prominent theoretical physicists and cosmologists: Gian Francesco Giudice, Michael Krämer, Gordon Kane, Keith Olive, Nima Arkani-Hamed, Steven Weinberg, Chad Orzel, Frank Wilczek, Garrett Lisi, Joseph Polchinski, Xiao-Gang Wen, Katie Mack, George Ellis, and Doyne Farmer. And, throughout the book, she quotes many other physicists, past and present, as well. This is a well-researched book by an expert in the field.

I also like her “In Brief” summaries of key points at the end of each chapter. And her occasional self-deprecating, brief, soliloquies, which I find reassuring. This book is never about the care and feeding of the author’s ego, but rather giving voice to largely unspoken fears that theoretical physics is stagnating. And an academic environment hell-bent on preserving the status quo isn’t helping matters, either.

Anthropic Principle

Do we live in a universe fine-tuned for life? If so, is it the only possible universe that would support life? Recent work indicates that there may be more than one set of parameters that could lead to a life-supporting universe.

Beauty is in the Eye of the Beholder

Is our sense of what is “beautiful” a reliable guide to gaining a deeper understanding of nature? Or does it sometimes lead us astray? We know from history that it does.

In the past, symmetries have been very useful. Past and present, they are considered beautiful

When we don’t have data to guide our theory development, aesthetic criteria are used. Caveat emptor.

Experiment and Theory

Traditionally, experiment and observation have driven theory. Now, increasingly, theory drives experiment, and the experiments are getting more difficult, more expensive, and more time consuming to do—if they can be done at all.


The rapid expansion of the universe at the time of the Big Bang is known as cosmic inflation, or, simply, inflation. Though there is some evidence to support inflation, that evidence is not yet compelling.


Mathematics creates a logically consistent universe all its own. Some of it can actually be used to describe our physical universe. What math is the right math?

Math is very useful for describing nature, but is math itself “real”, or is it just a useful tool? This is an ancient question.

Memorable Quotations

“I went into physics because I don’t understand human behavior.” (p. 2)

“If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.” (p. 9)

“In our search for new ideas, beauty plays many roles. It’s a guide, a reward, a motivation. It is also a systematic bias.” (p. 10)

On artificial intelligence: “Being unintuitive shouldn’t be held against a theory. Like lack of aesthetic appeal, it is a hurdle to progress. Maybe this one isn’t a hurdle we can overcome. Maybe we’re stuck in the foundations of physics because we’ve reached the limits of what humans can comprehend. Maybe it’s time to pass the torch.” (p. 132)

“The current organization of academia encourages scientists to join already dominant research programs and discourages any critique of one’s own research area.” (p. 170)


The idea that our universe of just one of a great many universes is presently the most controversial idea in physics.

Particles and Interactions

What is truly interesting is not the particles themselves, but the interactions between particles.


Physicists and astrophysicists are sloppy philosophers and could stand to benefit from a better understanding of the philosophical assumptions and implications of their work.

Physics isn’t Math

Sure, physics contains a lot of math, but that math has traditionally been well-grounded in observational science. Is math driving physics more than experiment and observation today?

Quantum Mechanics

Nobody really understands quantum mechanics. Everybody’s amazed but no one is happy. It works splendidly well. The quantum world is weird. Waves and particles don’t really exist, but everything (perhaps even the universe itself) is describable by a probabilistic “wave function” that has properties of both and yet is neither. Then there’s the many-worlds interpretation of quantum mechanics, and quantum entanglement

Science and the Scientific Method

In areas of physics where experiments are too difficult, expensive, or impossible to do, some physicists seem to be abandoning the scientific method as the central pillar of scientific inquiry. Faith in beauty, faith in mathematics, faith in naturalness, faith in symmetry. How is this any different than religion?

If scientists can evaluate a theory using other criteria than that theory’s ability to describe observation, how is that science?


Some areas of physics haven’t seen any new data for decades. In such an environment, theories can and do run amok.

Standard Model (of particle physics)

Ugly, contrived, ad hoc, baroque, overly flexible, unfinished, too many unexplained parameters. These are some of the words used to describe the standard model of particle physics. And, yet, the standard model describes the elementary particles we see in nature and their interactions with extraordinary exactitude.

String Theory

String theory dates back at least to the 1970s, and its origins go back to the 1940s. To date, there is still no experimental evidence to support it. String theory is not able to predict basic features of the standard model. That’s a problem.

Triple Threat: Crises in Physics, Astrophysics, and Cosmology?

Physics: Sure, the Large Hadron Collider (LHC) at CERN gave us the Higgs boson, but little else. No new physics. No supersymmetry particles. Embarrassments like the diphoton anomaly. Do we need a bigger collider? Perhaps. Do we need new ideas? Likely.

Astrophysics: We’ve spent decades trying to understand what dark matter is, to no avail. No dark matter particles have been found.

Cosmology: We have no testable idea as to what dark energy is. Plenty of theories, though.

See Hossenfelder’s recent comments on the LHC and dark matter in her op-ed, “The Uncertain Future of Particle Physics” in the January 23, 2019 issue of The New York Times.

The book concludes with three appendices:

  • Appendix A: The Standard Model Particles
  • Appendix B: The Trouble with Naturalness
  • Appendix C: What You Can Do To Help

Hossenfelder gives some excellent practical advice in Appendix C. This appendix is divided into three sections of action items:

  • As a scientist
  • As a higher ed administrator, science policy maker, journal editor, or representative of a funding body
  • As a science writer or member of the public

I’m really glad she wrote this book. As an insider, it takes courage to criticize the status quo.

Hossenfelder, S., Lost in Math: How Beauty Leads Physics Astray, Basic Books, New York (2018).
Hossenfelder, Sabine. “The Uncertain Future of Particle Physics.” The New York Times 23 Jan 2019.

Zodiacal Light 2019

In this year of 2019, the best dates and times for observing the zodiacal light are listed below. The sky must be very clear with little or no light pollution. The specific times listed are for Dodgeville, Wisconsin.

Tue. Jan. 226:39 p.m.7:03 p.m.West
Wed. Jan. 236:40 p.m.7:40 p.m.West
Thu. Jan. 246:41 p.m.7:41 p.m.West
Fri. Jan. 256:42 p.m.7:42 p.m.West
Sat. Jan. 266:43 p.m.7:43 p.m.West
Sun. Jan. 276:44 p.m.7:44 p.m.West
Mon. Jan. 286:45 p.m.7:45 p.m.West
Tue. Jan. 296:46 p.m.7:46 p.m.West
Wed. Jan. 306:48 p.m.7:48 p.m.West
Thu. Jan. 316:49 p.m.7:49 p.m.West
Fri. Feb. 16:50 p.m.7:50 p.m.West
Sat. Feb. 26:51 p.m.7:51 p.m.West
Sun. Feb. 36:52 p.m.7:52 p.m.West
Mon. Feb. 46:53 p.m.7:53 p.m.West
Tue. Feb. 56:55 p.m.7:55 p.m.West
Wed. Feb. 67:09 p.m.7:56 p.m.West
Thu. Feb. 217:14 p.m.8:14 p.m.West
Fri. Feb. 227:15 p.m.8:15 p.m.West
Sat. Feb. 237:16 p.m.8:16 p.m.West
Sun. Feb. 247:17 p.m.8:17 p.m.West
Mon. Feb. 257:19 p.m.8:19 p.m.West
Tue. Feb. 267:20 p.m.8:20 p.m.West
Wed. Feb. 277:21 p.m.8:21 p.m.West
Thu. Feb. 287:22 p.m.8:22 p.m.West
Fri. Mar. 17:23 p.m.8:23 p.m.West
Sat. Mar. 27:25 p.m.8:25 p.m.West
Sun. Mar. 37:26 p.m.8:26 p.m.West
Mon. Mar. 47:27 p.m.8:27 p.m.West
Tue. Mar. 57:28 p.m.8:28 p.m.West
Wed. Mar. 67:30 p.m.8:30 p.m.West
Thu. Mar. 77:31 p.m.8:31 p.m.West
Fri. Mar. 88:01 p.m.8:32 p.m.West
Fri. Mar. 228:50 p.m.9:24 p.m.West
Sat. Mar. 238:52 p.m.9:52 p.m.West
Sun. Mar. 248:53 p.m.9:53 p.m.West
Mon. Mar. 258:54 p.m.9:54 p.m.West
Tue. Mar. 268:56 p.m.9:56 p.m.West
Wed. Mar. 278:57 p.m.9:57 p.m.West
Thu. Mar. 288:59 p.m.9:59 p.m.West
Fri. Mar. 299:00 p.m.10:00 p.m.West
Sat. Mar. 309:01 p.m.10:01 p.m.West
Sun. Mar. 319:03 p.m.10:03 p.m.West
Mon. Apr. 19:04 p.m.10:04 p.m.West
Tue. Apr. 29:06 p.m.10:06 p.m.West
Wed. Apr. 39:07 p.m.10:07 p.m.West
Thu. Apr. 49:09 p.m.10:09 p.m.West
Fri. Apr. 59:10 p.m.10:10 p.m.West
Sat. Apr. 69:12 p.m.10:12 p.m.West
Sun. Apr. 710:03 p.m.10:13 p.m.West
Thu. Aug. 293:39 a.m.4:39 a.m.East
Fri. Aug. 303:40 a.m.4:40 a.m.East
Sat. Aug. 313:42 a.m.4:42 a.m.East
Sun. Sep. 13:43 a.m.4:43 a.m.East
Mon. Sep. 23:45 a.m.4:45 a.m.East
Tue. Sep. 33:46 a.m.4:46 a.m.East
Wed. Sep. 43:48 a.m.4:48 a.m.East
Thu. Sep. 53:49 a.m.4:49 a.m.East
Fri. Sep. 63:50 a.m.4:50 a.m.East
Sat. Sep. 73:52 a.m.4:52 a.m.East
Sun. Sep. 83:53 a.m.4:53 a.m.East
Mon. Sep. 93:55 a.m.4:55 a.m.East
Tue. Sep. 103:56 a.m.4:56 a.m.East
Wed. Sep. 113:57 a.m.4:57 a.m.East
Thu. Sep. 124:52 a.m.4:59 a.m.East
Fri. Sep. 275:11 a.m.5:18 a.m.East
Sat. Sep. 284:19 a.m.5:19 a.m.East
Sun. Sep. 294:20 a.m.5:20 a.m.East
Mon. Sep. 304:21 a.m.5:21 a.m.East
Tue. Oct. 14:23 a.m.5:23 a.m.East
Wed. Oct. 24:24 a.m.5:24 a.m.East
Thu. Oct. 34:25 a.m.5:25 a.m.East
Fri. Oct. 44:26 a.m.5:26 a.m.East
Sat. Oct. 54:27 a.m.5:27 a.m.East
Sun. Oct. 64:29 a.m.5:29 a.m.East
Mon. Oct. 74:30 a.m.5:30 a.m.East
Tue. Oct. 84:31 a.m.5:31 a.m.East
Wed. Oct. 94:32 a.m.5:32 a.m.East
Thu. Oct. 104:33 a.m.5:33 a.m.East
Fri. Oct. 114:43 a.m.5:34 a.m.East
Sat. Oct. 264:51 a.m.5:19 a.m.East
Sun. Oct. 274:53 a.m.5:53 a.m.East
Mon. Oct. 284:54 a.m.5:54 a.m.East
Tue. Oct. 294:55 a.m.5:55 a.m.East
Wed. Oct. 304:56 a.m.5:56 a.m.East
Thu. Oct. 314:57 a.m.5:57 a.m.East
Fri. Nov. 14:58 a.m.5:58 a.m.East
Sat. Nov. 24:59 a.m.5:59 a.m.East
Sun. Nov. 34:01 a.m.5:01 a.m.East
Mon. Nov. 44:02 a.m.5:02 a.m.East
Tue. Nov. 54:03 a.m.5:03 a.m.East
Wed. Nov. 64:04 a.m.5:04 a.m.East
Thu. Nov. 74:05 a.m.5:05 a.m.East
Fri. Nov. 84:06 a.m.5:06 a.m.East
Sat. Nov. 94:07 a.m.5:07 a.m.East
Sun. Nov. 104:34 a.m.5:08 a.m.East
Sun. Nov. 244:23 a.m.4:27 a.m.East
Mon. Nov. 254:24 a.m.5:24 a.m.East
Tue. Nov. 264:25 a.m.5:25 a.m.East
Wed. Nov. 274:26 a.m.5:26 a.m.East
Thu. Nov. 284:27 a.m.5:27 a.m.East
Fri. Nov. 294:28 a.m.5:28 a.m.East
Sat. Nov. 304:29 a.m.5:29 a.m.East
Sun. Dec. 14:30 a.m.5:30 a.m.East
Mon. Dec. 24:31 a.m.5:31 a.m.East
Tue. Dec. 34:32 a.m.5:32 a.m.East
Wed. Dec. 44:33 a.m.5:33 a.m.East
Thu. Dec. 54:34 a.m.5:34 a.m.East
Fri. Dec. 64:35 a.m.5:35 a.m.East
Sat. Dec. 74:35 a.m.5:35 a.m.East
Sun. Dec. 84:36 a.m.5:36 a.m.East
Mon. Dec. 94:37 a.m.5:37 a.m.East
Tue. Dec. 105:29 a.m.5:38 a.m.East

The best nights to observe the zodiacal light at mid-northern latitudes occur when the ecliptic plane intersects the horizon at an angle of 60° or steeper. The dates above were chosen on that basis, with the Sun at least 18° below the horizon and the Moon below the horizon being used to calculate the times. An interval of time of one hour either before morning twilight or after evening twilight was chosen arbitrarily because it is the “best one hour” for observing the zodiacal light. The zodiacal light cone will be brightest and will reach highest above the horizon when the Sun is 18° below the horizon (astronomical twilight), but no less.

If you are interested in calculating the angle the ecliptic makes with your horizon for any date and time, you can use the following formula:

\cos I = \cos \varepsilon \sin \phi-\sin \varepsilon \cos \phi \sin \theta

where I is the angle between the ecliptic and the horizon, ε is  the obliquity of the ecliptic, φ is the latitude of the observer, and θ is the local sidereal time (the right ascension of objects on the observer's meridian at the time of observation).

Here’s a SAS program I wrote to do these calculations:

Meeus, J. Astronomical Algorithms. 2nd ed., Willmann-Bell, 1998, p. 99.

Total Lunar Eclipse 2019

We’ll be treated to a front-row seat for the total lunar eclipse this coming Sunday night and Monday morning, January 20/21, 2019! Here are the local circumstances for Dodgeville, Wisconsin.

Time (CST)EventAltitude
8:36:29 p.m.Penumbral Eclipse Begins40°
9:10 p.m.Penumbra first visible?46°
9:33:55 p.m.Partial Eclipse Begins50°
10:41:19 p.m.Total Eclipse Begins60°
11:12:18 p.m.Greatest Eclipse64°
11:43:18 p.m.Total Eclipse Ends66°
12:14:31 a.m.Moon crosses the celestial meridian67°
12:50:42 a.m.Partial Eclipse Ends66°
1:15 a.m.Penumbra last visible?64°
1:48:06 a.m.Penumbral Eclipse Ends60°

This is the first total lunar eclipse visible in its entirety from SW Wisconsin since September 28, 2015; the next such event won’t occur again until May 16, 2022. You’ll note in the table above, the Moon will be 64° above the horizon at mid-totality. The Moon has not been this high in our sky at mid-totality since November, 29, 1993 (66°), and it will not be this high again at mid-totality until January 21, 2048 (67°).

The first hint of shading will occur on the left (eastward-facing) edge of the Moon around 9:10 p.m. The first sliver of the full Moon enters the umbral shadow of the Earth at 9:33 p.m., so you’ll want to be watching by then. The entire Moon will be immersed in the umbral shadow of the Earth 67 minutes later at 10:41 p.m. This means that if you were anywhere on the nearside of the Moon you would see the dark Earth (except for city lights) completely covering the Sun, with a spectacular “ring of fire” all the way round the limb of the Earth refracting orangish-red light through our atmosphere—the combined light of all the world’s sunrises and sunsets at that moment.

This, of course, will continue as the Moon penetrates deeper into the umbral shadow of the Earth, reaching its closest to the center of the Earth’s shadow at mid-eclipse at 11:12 p.m.

The best place in the world to view this total lunar eclipse (assuming it is clear) will be Guantánamo Province in Cuba. Just 8 miles north of the municipality of El Salvador, Cuba, the Moon will be directly overhead at mid-eclipse.

There has been an unfortunate tendency of the mainstream media in recent years to use the term “Blood Moon” to describe a total lunar eclipse. Why must we use imagery so often associated with violence, death, and destruction in our discourse? The color of a total lunar eclipse depends upon the condition and transparency of the Earth’s atmosphere during the eclipse, and it can range from orange to coppery to red, and rarely even gray or brownish, so why not say orangish-red and leave it at that?

Direct Imaging of Exoplanets Through Occultations

Planetary orbits are randomly oriented throughout our galaxy. The probability that an exoplanet’s orbit will be fortuitously aligned to allow that exoplanet to transit across the face of its parent star depends upon the radius of the star, the radius of the planet, and the distance of the planet from the star. In general, planets orbiting close-in are more likely to be seen transiting their star then planets orbiting further out.

The equation for the probability of observing a exoplanet transit event is

p_{tra} = \left (\frac{R_{\bigstar}+R_{p}}{a} \right )\left (\frac{1}{1-e^{2}} \right )

where ptra is the transit probability, R* is the radius of the star, Rp is the radius of the planet, a is the semi-major axis of the planetary orbit, and e is the eccentricity of the planetary orbit 

Utilizing the data in the NASA Exoplanet Archive for the 1,463 confirmed exoplanets where the above data is available (and assuming e = 0 when eccentricity is unavailable), we find that the median exoplanet transit probability is 0.0542. This means that, on average, 1 out of every 18 planetary systems will be favorably aligned to allow us to observe transits. However, keep in mind that our present sample of exoplanets is heavily biased towards large exoplanets orbiting close to their parent star. Considering a hypothetical sample of Earth-sized planets orbiting 1 AU from a Sun-sized star, the transit probability drops to 0.00469, which means that we would be able to detect only about 1 out of every 213 Earth-Sun analogs using the transit method.

How might we detect some of the other 99.5%? My admired colleague in England, Abdul Ahad, has written a paper about his intriguing idea: “Detecting Habitable Exoplanets During Asteroidal Occultations”. Abdul’s idea in a nutshell is to image the immediate environment around nearby stars while they are being occulted by asteroids or trans-Neptunian objects (TNOs) in order to detect planets orbiting around them. While there are many challenges (infrequency of observable events, narrow shadow path on the Earth’s surface, necessarily short exposure times, and extremely faint planetary magnitudes), I believe that his idea has merit and will one day soon be used to discover and characterize exoplanets orbiting nearby stars.

Ahad notes that the apparent visual magnitude of any given exoplanet will be directly proportional to the apparent visual magnitude of its parent star, since exoplanets shine by reflected light. Not only that, Earth-sized and Earth-like planets orbiting in the habitable zone of any star would shine by reflected light of the same intrinsic brightness, regardless of the brightness of the parent star. He also notes that the nearer the star is to us, the greater will be a given exoplanet’s angular distance from the occulted star. Thus, given both of these considerations (bright parent star + nearby parent star = increased likelihood of detection), nearby bright stars such as Alpha Centauri A & B, Sirius A, Procyon A, Altair, Vega, and Fomalhaut offer the best chance of exoplanet detection using this technique.

Since an exoplanet will be easiest to detect when it is at its greatest angular distance from its parent star, we will be seeing only about 50% of its total reflected light. An Earth analog orbiting Alpha Centauri A would thus shine at visual magnitude +23.7 at 0.94″ angular distance, and for Alpha Centauri B the values would be +24.9 and 0.55″.

Other considerations include the advantage of an extremely faint occulting solar system object (making it easier to detect faint exoplanets during the occultation event), and the signal boost offered by observing in the infrared, since exoplanets will be brightest at these wavelengths.

A distant (and therefore slow-moving) TNO would be ideal, but the angular size of the TNO needs to be larger than the angular size of the occulted star. However, slow-moving objects mean that occultation events will be rare.

The best chance of making this a usable technique for exoplanet discovery would be a space-based observatory that could be positioned at the center of the predicted shadow and would be able to move along with the shadow to increase exposure times (Ahad, personal communication). It would be an interesting challenge in orbital mechanics to design the optimal base orbit for such a spacecraft. The spacecraft orbit would be adjusted to match the position and velocity of the occultation shadow for each event using an ion drive or some other electric propulsion system.

One final thought on the imaging necessary to detect exoplanets using this technique. With a traditional CCD you would need to begin and end the exoplanet imaging exposure(s) only while the parent star is being occulted. This would not be easy to do, and would require two telescopes – one for the occultation event detection and one for the exoplanet imaging. A better approach would be to use a Geiger-mode avalanche photodiode (APD). Here’s a description of the device captured in 2016 on the MIT Lincoln Labs Advanced Imager Technology website:

A Geiger-mode avalanche photodiode (APD), on the other hand, can be used to build an all-digital pixel in which the arrival of each photon triggers a discrete electrical pulse. The photons are counted digitally within the pixel circuit, and the readout process is therefore noise-free. At low light levels, there is still noise in the image because photons arrive at random times so that the number of photon detection events during an exposure time has statistical variation. This noise is known as shot noise. One advantage of a pixel that can digitally count photons is that if shot noise is the only noise source, the image quality will be the best allowed by the laws of physics. Another advantage of an array of photon counting pixels is that, because of its noiseless readout, there is no penalty associated with reading the imager out frequently. If one reads out a thousand 1-ms exposures of a static scene and digitally adds them, one gets the same image quality as a single 1-s exposure. This would not be the case with a conventional imager that adds noise each time it is read out.

Ahad, A., “Detecting Habitable Exoplanets During Asteroidal Occultations”, International Journal of Scientific and Innovative Mathematical Research, Vol. 6(9), 25-30 (2018).
MIT Lincoln Labs, Advanced Imager Technology, Retrieved March 17, 2016.
NASA Exoplanet Archive
Winn, J.N., “Exoplanet Transits and Occultations,” in Exoplanets, ed. Seager, S., University of Arizona Press, Tucson (2011).

My Music Recorded in 1976

Leaving Behind the Tears

All songs written, performed, and recorded by David Oesper

Recorded January – August 1976

Remixed August 20, 1976

Special thanks to Bob Gebhardt for loaning me his open reel tape deck in 1976.

Special thanks also to Jake Ewalt for his skillful analog to digital transfer in July 2002.

1. Hope1. Here With You
2. Leaving Behind the Tears2. Memories
3. Misled Again3. So Long
4. Reaching Out For Love4. Did I Tell You
5. Rock Star5. The Day You Left Me
6. Time Out6. Far Away Somewhere
7. You Should Have Seen7. Moments With You
8. I’m Thinking About You8. Hometown Boogie
9. Destiny9. He’s Gone
10. Picking Up the Pieces10. Hold On
11. Life11. If That Is All
12. For All Time12. In the End
13. Idol13. I’ll Come Back
14. Rock of the Country14. You’re the One
15. Pathless Roads15. No Other Person
16. You Get In Your Own Way

Probing the Proton

We have known since 1968 that protons are not elementary particles and are comprised of three persistent quarks: two up quarks with charge +⅔e, and one down quark with charge -⅓e, where e is the charge of the electron (which is an elementary particle).

But in a brilliant illustration of E = mc2, we now know that very little of the proton’s 938 MeV rest mass comes from the rest mass of its component up and down quarks.

The mass composition of a proton is:

½% up quark rest mass (¼% × 2)

½% down quark rest mass

8% sea quarks (virtual quark-antiquark pairs created  by the strong nuclear force)

23% quark-gluon interaction energy (the trace anomaly)

32% kinetic energy of the up and down quarks

36% momentum energy of the massless gluons that hold the up and down quarks together within the proton

We thus see that just 1% of the rest mass of a proton is provided by the rest mass of its three component valence quarks (2 up + 1 down), and the other 99% is interaction energy!

Even though protons are in the nucleus of every atom of matter in the universe, we still do not fully understand them.  For example, there is the proton radius puzzle, the proton spin puzzle, and the significant question of proton decay.

E. Conover. How the proton’s mass adds up. Science News. Vol. 194, December 22, 2018, p. 8.
E. Conover. There’s still a lot we don’t know about the proton. Science News. Vol. 191, April 29, 2017, p. 22.
Y.B. Yang et al. Proton mass decomposition from the QCD energy momentum tensor. Physical Review Letters. Vol. 121, November 23, 2018, p. 212001. doi: 10.1103/PhysRevLett.121.212001.