Choral Hymns from the Rig Veda

Gustav Holst (1874-1934) is, of course, best known for The Planets, but I continue to discover other compositions by Holst which are truly remarkable and unjustifiably neglected.

I listened to an out-of-print compact disc this evening that features some Holst rarities: Hymn to Dionysus, Choral Hymns of the Rig Veda, and Two Eastern Pictures. Fortunately, there are still used copies available of this 1985 UK release, so I was able to purchase the disc: Unicorn Digital DKP(CD) 9046. These performances are by the Royal Philharmonic Orchestra and the Royal College of Music Chamber Choir, conducted by Sir David Willcocks (1919-2015), and the legendary harpist Osian Ellis (1928-). What a gem of a recording this is! Seek it out!

The standout work on this disc is a (nearly) complete recording of the Choral Hymns from the Rig Veda, written in four groups between 1908 and 1912. The Rig Veda is the oldest scripture of the Hindu religion. Not satisfied with existing English translations, Holst learned Sanskrit so that he could provide his own translation.

Choral Hymns from the Rig Veda, op. 26

First Group, for chorus and orchestra (H. 96)
   I.   Battle Hymn
   II.  To the Unknown God
   III. The Funeral Hymn [not included in this recording]

Second Group, for women's chorus and orchestra (H. 98)
   I.   To Varuna (God of the Waters)
   II.  To Agni (God of Fire)
   III. Funeral Chant

Third Group, for women's chorus and harp (H. 99)
   I.   Hymn to the Dawn
   II.  Hymn to the Waters
   III. Hymn to Vena (Sun rising through the mist)
   IV.  Hymn of the Travellers

Fourth Group, for men's chorus and orchestra (H. 100)
   I.   Hymn to Agni [not included in this recording]
   II.  Hymn to Soma (the juice of a herb)
   III. Hymn to Manas (the spirit of a dying man)
   IV.  Hymn to Indra [not included in this recording]

I also very much enjoyed the final work on this recording, Two Eastern Pictures, written in 1911.

Two Eastern Pictures, for women’s voices and harp (H. 112)

I.  Spring
II. Summer

I certainly hope that this fine recording will be reissued soon, and that live performances of these works are in the offing.

Happy Birthday, AAAA!

The first meeting of the Ames Area Amateur Astronomers (AAAA) took place 40 years ago today: Saturday, June 2, 1979. Central Junior High Earth Science teacher Jack Troeger and Welch Junior High Earth Science Teacher Ron Bredeson held the first meeting in Jack’s classroom in the building that is now the Ames City Hall. This was a great start to a great astronomy club. Here’s to the next 40 years!

And, we just passed another important milestone in AAAA history. The grand opening of the original McFarland Park Observatory took place 35 years ago on Memorial Day, Monday, May 28, 1984. Back then, the pavement ended at the intersection of Dayton Rd. & County Road E-29, northeast of Ames, Iowa, and it was gravel the rest of the way.

The first McFarland Park Observatory with its second telescope, a 12.5-inch Newtonian & Cassegrain telescope. The first telescope was a 13.1-inch Coulter Odyssey Dobsonian.
Observatory manager Jim Doggett and AAAA president David Oesper inside the original McFarland Park Observatory. Lower right photo is Julie Oesper and Katie Dilks watching the spectacular aurora borealis display the evening of November 8, 1991.

The AAAA purchased a backyard-observatory silo-top dome from Glen Hankins in Nevada on Saturday, September 27, 1980, and then-Ranger (and later Story County Conservation Director) Steve Lekwa of McFarland Park was instrumental in allowing the AAAA to build its observatory at its present site at McFarland Park. The much-improved replacement roll-off-roof observatory, named after club members and benefactors Bertrand & Mary Adams, was completed in 2000. The only part of the original observatory structure that remains is the telescope pier!

A Shroud of Satellites

The first five Iridium satellites were launched on May 5, 1997, and by 2002 there were 66 operational satellites, providing consistent global satellite phone coverage. These satellites have the interesting property that their antenna panels sometimes reflect sunlight down to the Earth’s surface, causing what came to be known as “Iridium flares”, delighting terrestrial observers—myself included. During an Iridium flare event, the satellite suddenly appears and gradually brightens and then dims to invisibility as it moves slowly across a section of sky over several seconds. Many of these events reach negative magnitude, with some getting as bright as magnitude -9.5.

The next generation of Iridium satellites began launching in 2017, but these satellites are constructed in such a way that they do not produce flares. Gradually, the original Iridium satellites are de-orbiting (or being de-orbited), so eventually there will be no more Iridium flares.

The Iridium flares haven’t been much of a nuisance to astronomers because the number of events per night for a given observer have been in the single digits.

But now we’re facing too much of a good thing. The first volley of 60 Starlink satellites was launched on May 24, with 12,000 expected to be in orbit by 2028. These satellites will provide broadband internet service to the entire planet. Though the Starlink satellites aren’t expected to produce spectacular flares like the first generation of the Iridium satellites, they do reflect sunlight as any satellite does, and the sheer number of them in relatively low Earth orbit is sure to cause a lot of headaches for astronomers and stargazers throughout the world.

I estimate that about 468 of the 12,000 satellites will be above your horizon at any given moment, but how many of them will be visible will depend on their altitude (both in terms of distance above the Earth’s surface and degrees above the horizon), and where they are relative to the Earth’s shadow cone (they have to be illuminated by sunlight to be seen).

And Starlink will not be the only swarm of global broadband internet satellites, as other companies and countries plan to fly their own satellite constellations.

This situation illustrates yet another reason why we need a binding set of international laws that apply to all nations and are enforced by a global authority. The sooner we have this the better, as our survival may depend upon it. How else can we effectively confront anthropogenic climate change and the precipitous decline in biodiversity?

As for these swarms of satellites, two requirements are needed now to minimize their impact on astronomy:

  1. Build the satellites with minimally reflective materials and finishes
  2. Fly one internationally-managed robust constellation of global broadband internet satellites, and require competing companies and nations to utilize them, similar to the co-location often required for terrestrial communication towers

I’d like to close this piece with a few questions. Will future “stargazers” go out to watch all the satellites and generally ignore the real stars and constellations because they are too “boring”? Will professional astronomers increasingly have to move their operations off the Earth’s surface to the far side of the Moon and beyond? Will we continue to devalue the natural world and immerse ourselves ever more deeply into our human-invented virtual environments?

Milutin Milanković

Serbian engineer, mathematician, and scientist Milutin Milanković was born 140 years ago on this date in 1879, in the village of Dalj on the border between Croatia and Serbia—then part of the empire of Austria-Hungary. He died in 1958 in Beograd (Belgrade), then in Yugoslavia and today in Serbia, at the age of 79.

Milanković is perhaps most famous for developing a mathematical theory of climate based on changes in the Earth’s orbit and axial orientation. There are three basic parameters that change with time—now known as the Milankovitch cycles—that affect the amount of solar energy the Earth receives and how it is distributed upon the Earth.

I. Orbital eccentricity of the Earth changes with time

The eccentricity (e) tells you how elliptical an orbit is. An eccentricity of 0.000 means the orbit is perfectly circular. A typical comet’s orbit, on the other hand, is very elongated, with an eccentricity of 0.999 not at all uncommon. Right now, the Earth’s orbital eccentricity is 0.017, which means that it is 1.7% closer to the Sun at perihelion than its semimajor axis distance (a), and 1.7% further from the Sun at aphelion than its semimajor axis distance.

The greater the eccentricity the greater the variation in the amount of solar radiation the Earth receives throughout the year. Over a period of roughly 100,000 years, the Earth’s orbital eccentricity changes from close to circular (e = 0.000055) to about e = 0.0679 and back to circular again. At present, the Earth’s orbital eccentricity is 0.017 and decreasing. We now know the Earth’s orbital eccentricity changes with periods of 413,000, 95,000, and 125,000 years, making for a slightly more complicated variation than a simple sinusoid, as shown below.

II. Tilt of the Earth’s axis changes with time

The tilt of the Earth’s polar axis with respect to the plane of the Earth’s orbit around the Sun—called the obliquity to the ecliptic—changes with time. The Earth’s current axial tilt is 23.4°, but it ranges between about 22.1° and 24.5° over a period of about 41,000 years. Greater axial tilt means winter and summer become more extreme. Presently, the axial tilt is decreasing, and will reach a minimum around 11,800 A.D.

III. Orientation of the Earth’s axis changes with time

The Earth’s axis precesses or “wobbles” with a period of around 26,000 years about the north and south ecliptic poles. This changes what latitude of the Earth is most directly facing the Sun when the Earth is closest to the Sun each year. Currently, the southern hemisphere has summer when the Earth is at perihelion.

Milanković used these three cycles to predict climate change. His ideas were largely ignored until 1976, when a paper by James Hays, John Imbrie, and Nicholas Shackleton in the journal Science showed that Milanković’s mathematical model of climate change was able to predict major changes in climate that have occurred during the past 450,000 years.

These Milankovitch cycles are important to our understanding of climate change over much longer periods than the climate change currently being induced by human activity. Note the extremely rapid increase of greenhouse gas concentrations (CO2, CH4, and N2O) in our atmosphere over the past few decades in the graphs below.

The world population has increased by 93% since 1975. In 1975, it was about 4 billion and by 2020 it is expected to be 7.8 billion.

Stevens Point

I visited Stevens Point, Wisconsin for the first time over the Memorial Day weekend and, I have to say, this community of 26,000 is impressive. A great place to stay while you’re there is the Baymont Inn & Suites at 247 Division St. N. It is a short and pleasant walk to the University of Wisconsin – Stevens Point campus, the Schmeeckle Reserve (wow!), and the Green Circle Trail. Michele’s Restaurant is only a few blocks down the street. Great food!

I miss living in a college town. It is energizing to interact on a daily basis with well educated, intellectually curious, and cosmopolitan people who are passionate about their work. I lived in Ames, Iowa—where Iowa State University is located—for nearly 30 years, and I feel more at home in Stevens Point, a smaller community, than I do now in Ames. I think Stevens Point is the nicest community I have visited since leaving Ames in 2005. Definitely would be willing to live there someday. UW-Stevens Point even has a physics & astronomy department, an observatory, and a planetarium. Perhaps I could help out in retirement.

Some towns have a lot going for them even without a college or university—around here, Mineral Point and Spring Green come to mind. Some towns are at somewhat of a disadvantage because they have a name that is not particularly attractive. For example, Dodgeville, where I currently live and work, has a moniker that isn’t all that inviting. But there is no place so nice to live as a college town—for people like me, at least.

My primary civic interests are in gradually developing a well planned network of paved, off-road bike paths, walking trails through natural areas, a center for continuing education, a community astronomical observatory, and a comprehensive and well-enforced outdoor lighting ordinance to restore, preserve, and protect our nighttime environment and view of the night sky. Living in a community like Dodgeville, I don’t get the sense that there is enough interest or political will to make any of these things happen. I can’t do it alone.


George F. R. Ellis writes in Issues in the Philosophy of Cosmology:

9.2 Issue H: The possible existence of multiverses
If there is a large enough ensemble of numerous universes with varying properties, it may be claimed that it becomes virtually certain that some of them will just happen to get things right, so that life can exist; and this can help explain the fine-tuned nature of many parameters whose values are otherwise unconstrained by physics.  As discussed in the previous section, there are a number of ways in which, theoretically, multiverses could be realized.  They provide a way of applying probability to the universe (because they deny the uniqueness of the universe).  However, there are a number of problems with this concept.  Besides, this proposal is observationally and experimentally untestable; thus its scientific status is debatable.

My 100-year-old uncle—a lifelong teacher and voracious reader who is still intellectually active—recently sent me Max Tegmark’s book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, published by Vintage Books in 2014. I could not have had a more engaging introduction to the concept of the Multiverse. Tegmark presents four levels of multiverses that might exist. They are

Level I Multiverse: Distant regions of space with the same laws of physics that are currently but not necessarily forever unobservable.

Level II Multiverse: Distant regions of space that may have different laws of physics and are forever unobservable.

Level III Multiverse: Quantum events at any location in space and in time cause reality to split and diverge along parallel storylines.

Level IV Multiverse: Space, time, and the Level I, II, and III multiverses all exist within mathematical structures that describe all physical existence at the most fundamental level.

There seems little question that our universe is very much larger than the part that we can observe. The vast majority of our universe is so far away that light has not yet had time to reach us from those regions. Whether we choose to call the totality of these regions the universe or a Level I multiverse is a matter of semantics.

Is our universe or the Level I multiverse infinite? Most likely not. That infinity is a useful mathematical construct is indisputable. That infinite space or infinite time exists is doubtful. Both Ellis and Tegmark agree on this and present cogent arguments as to why infinity cannot be associated with physical reality. Very, very large, or very, very small, yes, but not infinitely large or infinitely small.

Does a Level II, III, and IV multiverse exist? Tegmark thinks so, but Ellis raises several objections, noted above and elsewhere. The multiverse idea remains quite controversial, but as Tegmark writes,

Even those of my colleagues who dislike the multiverse idea now tend to grudgingly acknowledge that the basic arguments for it are reasonable. The main critique has shifted from “This makes no sense and I hate it” to “I hate it.”

I will not delve into the details of the Level II, III, and IV multiverses here. Read Tegmark’s book as he adroitly takes you through the details of eternal inflation, quantum mechanics and wave functions and the genius and tragic story of Hugh Everett III, the touching tribute to John Archibald Wheeler, and more, leading into a description of each multiverse level in detail.

I’d like to end this article with a quote from Max Tegmark from Mathematical Universe. It’s about when you think you’re the first person ever to discover something, only to find that someone else has made that discovery or had that idea before.

Gradually, I’ve come to totally change my feelings about getting scooped. First of all, the main reason I’m doing science is that I delight in discovering things, and it’s every bit as exciting to rediscover something as it is to be the first to discover it—because at the time of the discovery, you don’t know which is the case. Second, since I believe that there are other more advanced civilizations out there—in parallel universes if not our own—everything we come up with here on our particular planet is a rediscovery, and that fact clearly doesn’t spoil the fun. Third, when you discover something yourself, you probably understand it more deeply and you certainly appreciate it more. From studying history, I’ve also come to realize that a large fraction of all breakthroughs in science were repeatedly rediscovered—when the right questions are floating around and the tools to tackle them are available, many people will naturally find the same answers independently.

Ellis, G.F.R., Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.

Tegmark, Max. Our mathematical universe : my quest for the ultimate nature of reality. New York: Alfred A. Knopf, 2014.

“You passed your exam in many parallel universes—but not in this one.”

Scintillating Stars But Not Planets

Aristotle (384 BC – 322 BC) may have been the first person to write that stars twinkle but planets don’t, though our understanding of twinkling has evolved since he explained that “The planets are near, so that the visual ray reaches them in its full vigour, but when it comes to the fixed stars it is quivering because of the distance and its excessive extension.”

John Stedman (1744-1797), a controversial and complicated figure to be sure, writes the following dialog between teacher and student in The Study of Astronomy, Adapted to the capacities of youth (1796):

PUPIL.  How is the twinkling of the stars in a clear night accounted for?

TUTOR.   It arises from the continual agitation of the air or atmosphere through which we view them; the particles of air being always in motion, will cause a twinkling in any distant luminous body, which shines with a strong light.

PUPIL.  Then, I suppose, the planets not being luminous, is the reason why they do not twinkle.

TUTOR.   Most certainly.  The feeble light with which they shine is not sufficient to cause such an appearance.

Still not quite right, but closer to our current understanding. Our modern term for “twinkling” is atmospheric scintillation, which is changes in a star’s brightness caused by curved wavefronts focusing or defocusing starlight.

Scintillation is caused by refractive index variations (due to differences in pressure, temperature, and humidity) of “pockets” of air passing in front of the light path between star and observer at a typical height of about 5 miles. These pockets are typically about 3 inches across, so from the naked eye observer’s standpoint, they subtend an angle of about 2 arcseconds.

The largest angular diameters of stars are on the order of 50 milliarcseconds1 (R Doradus, Betelgeuse, and Mira), and only seventeen stars have an an angular diameter larger than 1 milliarcsecond. So, it is easy to see how cells of air on the order of 2 arcseconds across moving across the light path could cause the stars to flicker and flash as seen with the unaided eye.

The five planets that are easily visible to the unaided eye (Mercury, Venus, Mars, Jupiter, and Saturn) have angular diameters that range from 3.5 arcseconds (Mars, at its most distant) up to 66 arcseconds (Venus, at its closest). Since the disk of a planet subtends multiple air cells, the different refractive indexes tend to cancel each other out, and the planet shines with a steady light.

From my own experience watching meteors many nights with my friend Paul Martsching, our reclining lawn chairs just a few feet apart, I have sometimes seen a principal star briefly brighten by two magnitudes or more, with Paul seeing no change in the star’s brightness, and vice versa.

Stedman’s dialogue next turns to the distances to the nearest stars.

PUPIL.  Have the stars then light in themselves?

TUTOR.   They undoubtedly shine with their own native light, or we should not see even the nearest of them: the distance being so immensely great, that if a cannon-ball were to travel from it to the sun, with the same velocity with which it left the cannon, it would be more than 1 million, 868 thousand years, before it reached it.

He adds a footnote:

The distance of Syrius is 18,717,442,690,526 miles.  A cannon-ball going at the rate of 1143 miles an hour, would only reach the sun in about 1,868,307 years, 88 days.

Where Stedman comes up with the velocity of a cannon-ball is unclear, but the Earth’s rotational speed at the equator is 1,040 mph, close to Stedman’s cannon-ball velocity of 1,143 mph. He states the distance to the brightest star Sirius—probably then thought to be the nearest star—is 18,717,442,690,526 miles or 3.18 light years, a bit short of the actual value of 8.60 light years. The first measurements of stellar parallax lie 42 years in the future when Stedman’s book was published.

1 1 milliarcsecond (1 mas) = 0.001 arcsecond

Aristotle, De Caelo, Book 2, chap.8, par. 290a, 18
Crumey, A., 2014, MNRAS, 442, 2600
Dravins, D., Lindegren, L., Mezey, E., Young, A. T., 1997a, PASP, 109, 173
Ellison, M. A., & Seddon, H., 1952, MNRAS, 112, 73
Stedman, J., 1796, The Study of Astronomy, Adapted to the capacities of youth

In Praise of SAS

I’ve been writing programs in SAS since 1985. Back then, it was SAS 5.15 on an IBM mainframe computer (remember JCL, TSO, ISPF?) at the Iowa Department of Transportation. Today, it is SAS 9.4 under Windows 10 at home and Linux at work.

I love this language. It is elegant. It is beautiful. I’ve become an expert. I’ve never had a computational problem to solve, a data manipulation to do, a process to automate, or a report to write that I couldn’t do with SAS.

New features are being added all the time, and I am constantly learning and improving to keep up with it all. And the legacy code still runs just fine. Peace of mind. The company behind this success story is SAS Institute, based in Cary, North Carolina. SAS Institute has the best technical support of any company I have ever dealt with, and that is as true today as it was in 1985, and all the years in between. Again, peace of mind.

I’ve heard from multiple sources that SAS Institute is a fabulous place to work, and it shows in their software, their customer service, and the passion their employees have for making SAS software the best it can be—and helping us solve just about any analytics problem. Inspiring. And you won’t find a more passionate user community anywhere. At least not with any company that has been around as long as SAS has (since 1976).

SAS Institute is the world’s largest private software company, and being privately owned has much to do with their success and consistency, I believe. No greedy shareholders to please. They need answer only to their customers, and to their employees. That’s the way it should be.

Computer languages have come in and out of vogue over the years: FORTRAN, PL/I, Pascal, C, C++, Perl, Java, R, Python, etc., and with each new language that comes along, SAS absorbs the best elements and moves forward to the next challenge.

Python is currently very popular, as is open source in general, and I have no doubt that SAS will incorporate the most valuable functionality of Python and open source (already in progress) and keep tooling along like a well-oiled machine. In another ten years, SAS will be incorporating another new language that will have supplanted Python as the programming language du jour.

You’ve got to admire a company like that. In an era when everyone wants — even expects — “stuff for free”, the old adage “you get what you pay for” still applies. Yes, SAS is expensive—and I’m hoping their mature “core” product will come down in price—but I can’t complain too loudly because quality, longevity, and dependability costs money. It always has.

Comet Orbital Elements

The orbit of a comet can be defined with six numbers, called the orbital elements, and by entering these numbers into your favorite planetarium software, you can view the location of the comet at any given time reasonably near the epoch date. The epoch date is a particular date for which the orbital elements are calculated and therefore the most accurate around that time.

Different sets of six parameters can be used, but the most common are shown below. Example values are given for Comet Holmes (17P), which exhibited a remarkable outburst in October 2007, now almost 12 years ago.

Perihelion distance, q

This is the center-to-center distance from the comet to the Sun when the comet is at perihelion, its closest point to the Sun. For Comet Holmes, this is 2.05338 AU, well beyond the orbits of both the Earth and Mars.

Orbital eccentricity, e

This is a unitless number that is the measure of the amount of ellipticity an orbit has. For a circular orbit, e = 0. A parabolic orbit, e = 1. A hyperbolic orbit, e > 1. Many comets have highly elliptical orbits, often with e > 0.9. Short-period comets, such as Comet Holmes (17P), have more modest eccentricities. Comet Holmes has an orbital eccentricity of 0.432876. This means that at perihelion, Comet Holmes is 43.3% closer to the Sun than its midpoint distance, and at aphelion Comet Holmes is 43.3% further away from the Sun than its midpoint distance.

Date of perihelion, T

This is a date (converted to decimal Julian date) that the comet reached perihelion, or will next reach perihelion. For example, Comet Holmes reached perihelion on 2007 May 5.0284.

Inclination to the Ecliptic Plane, i

This is the angle made by the intersection of the plane of the comet’s orbit with the ecliptic, the plane of the Earth’s orbit. Comet Holmes has an inclination angle of 19.1143°.

Longitude of the ascending node, Ω

The intersection between the comet’s orbital plane and the Earth’s orbital plane forms a line, called the line of nodes. The places where this line intersects the comet’s orbit forms two points. One point defines the location where the comet crosses the ecliptic plane heading from south to north. This is called the ascending node. The other point defines the location where the comet crosses the ecliptic plane heading from north to south. This is called the descending node. 0° longitude is arbitrarily defined to be the direction of the vernal equinox, the point in the sky where the Sun in its apparent path relative to the background stars crosses the celestial equator heading north. The longitude of the ascending node (capital Omega, Ω) is the angle, measured eastward (in the direction of the Earth’s orbital motion) from the vernal equinox to the ascending node of the comet’s orbit. For Comet Holmes, that angle is 326.8532°.

Argument of perihelion, ω

The angle along the comet’s orbit in the direction of the comet’s motion between its perihelion point and its ascending node (relative to the ecliptic plane) is called the argument of perihelion (small omega, ω). For Comet Holmes, this angle is 24.352°.

If all the mass of the Sun and the comet were concentrated at a geometric point, and if they were the only two objects in the universe, these six orbital elements would be fixed for all time. But these two objects have physical size, and are affected by the gravitational pull of other objects in our solar system and beyond. Moreover, nongravitational forces can act on the comet’s nucleus, such as jets of material spewing out into space, exerting a tiny but non-negligible thrust on the comet, thus altering its orbit. Because of these effects, in practice it is a good idea to define a set of osculating orbital elements which will give the best positions for the comet around a particular date. These osculating orbital elements change gradually with time (due to gravitational perturbations and non-gravitational forces acting on the comet) and give the best approximation to the orbit at a given point in time. The further one strays from the epoch date for the osculating elements, the less accurate the predicted position of the comet will be.

For example, the IAU Minor Planet Center gives a set of orbital elements for Comet Holmes that has a more recent epoch date than the one given by the JPL Small-Body Database Browser. The MPC gives an epoch date of 2015 Jun 27.0, reasonably near the date of the most recent perihelion passage of this P = 6.89y comet (2014 Mar 27.5736). JPL, on the other hand, provides a default epoch date of 2010 Jan 17.0, nearer the date of the 2007 May 5.0284 perihelion and the spectacular October 2007 apparition. For the most accurate current position of Comet Holmes in your planetarium software, you’ll probably want to use the MPC orbital elements, since they are for an epoch nearest to the date when you’ll be making your observations.