Lunar Maria

António Cidadão, of Oeiras, Portugal, many years ago produced a wonderful set of images showing the location of each mare on the Moon. His website has not been updated since 1999 and the contact email address provided there is no longer valid, and even after a thorough Google search I can find no way to contact him to ask permission to link images here to his site. Even worse, because his hosting site is not secure (http: instead of https:), WordPress does not allow me to link directly to his images so I had to put copies into my media library. Please know that the images shown below are all copyrighted by António Cidadão.

Each image shows north is up and west is to the left. This is direction of increasing longitude and therefore west on the Moon, but in our sky, east is to the left. In other words, these annotated images of the Moon are correctly oriented as they would appear to the unaided eye in the sky in the northern hemisphere. In the rest of this article, we will use the moon-centric east-west convention that Cidadão indicates in his image diagrams.

Let’s take a look at each of the lunar maria from moon-west to moon-east. Their fanciful names were mostly given (and codified in 1651) by the Italian astronomer Giovanni Battista Riccioli (1598-1671). Riccioli chose names related to weather, as it was then believed that the Moon, the closest celestial body to the Earth, exerted an influence on the Earth’s weather. This is perhaps not at all surprising given that the phenomenon of tides had been known since antiquity.

Most of the nearside west portion of the Moon is covered by a mare that is so large that it is given a unique designation: Oceanus for “ocean”.

Oceanus Procellarum, the “Ocean of Storms”

Oceanus Procellarum contains the famously bright crater Aristarchus and the associated Aristarchus Plateau. In the image above you will notice what appears to be a tiny mare close to the limb of the Moon west of the southern part of Oceanus Procellarum. This is the lava-flooded crater Grimaldi.

Mare Orientale, the “Eastern Sea”

South of Grimaldi and straddling the lunar limb is Mare Orientale. It is difficult to see because most of it is on the lunar farside, though libration can sometimes bring its oblique visage into view. The name Orientale, meaning “eastern”, describes its location on the eastward-facing limb of the Moon as seen from Earth, rather than its westward direction as seen from the surface of the Moon.

Mare Humorum, the “Sea of Moisture”

Mare Humorum is located just south of Oceanus Procellarum. It is round and inviting, though no spacecraft has ever landed there.

Mare Nubium, the “Sea of Clouds”

Mare Nubium is east of Mare Humorum. The large crater Bullialdus flanks the western edge of Mare Nubium, and Rupes Recta (the “Straight Wall”) flanks its eastern edge.

Mare Cognitum, the “Sea That Has Become Known”

Mare Cognitum lies between Mare Nubium and Oceanus Procellarum. It was named in 1964 after the Ranger 7 probe took the first U.S. close-up pictures of the Moon’s surface prior to crashing there.

Mare Insularum, the “Sea of Islands”

Mare Insularum is north of Mare Cognitum. Its current name was bestowed upon it in 1976 by lunar geologist Don Wilhelms (1930-). The crater Kepler on its western edge separates Mare Insularum from Oceanus Procellarum. The crater Copernicus is on the northeast side of its western lobe.

Mare Vaporum, the “Sea of Vapors”

Mare Vaporum is the mare closest to the center of the Moon’s nearside. The bright crater Manilius lies towards its northeastern edge and the volcanic crater Hyginus and its associated rille (Rima Hyginus) are immediately to its south.

Mare Imbrium, the “Sea of Rains”

Mare Imbrium was created 3.9 billion years ago when an asteroid some 150 miles across crashed into the Moon. This ancient feature is so large that it forms the right eye of the “Man in the Moon” we see when looking at a full or nearly full moon with our unaided eyes.

Mare Frigoris, the “Sea of Cold”

Mare Frigoris lies north and northeast of Mare Imbrium. The dark crater between them is Plato. It is the mare closest to the north pole of the Moon.

Mare Serenitatis, the “Sea of Serenity”

Now we begin our tour of the eastern hemisphere of the Moon’s nearside. Mare Serenitatis has the distinction of being the landing site of the last human mission to the Moon, Apollo 17, in 1972. It was also the landing site of the Soviet unmanned spacecraft Luna 21 just one month later.

Mare Tranquillitatis, the “Sea of Tranquility”

Mare Tranquillitatis is perhaps the most famous of the lunar maria, as it was there that humans first set foot on the surface of the Moon in 1969. The Apollo 11 landing site is located near its southwest corner.

Mare Nectaris, the “Sea of Nectar”

Mare Nectaris lies south of Mare Tranquillitatis. This small, isolated, and nearly circular mare sports a prominent crater, Theophilus, at its northwest corner.

Mare Fecunditatis, the “Sea of Fertility”

East of Mare Nectaris lies Mare Fecunditatis. Superposed upon Mare Fecunditatis is the striking crater pair Messier and Messier A with two prominent rays evocative of a comet’s tail. Named after the famous French comet hunter Charles Messier (1730-1817), these craters and their associated rays were formed from a grazing impact from the east.

Mare Crisium, the “Sea of Crises”

Mare Crisium is a round and isolated mare that makes it easy to remember why it is called the “Sea of Crises”. The Soviet Luna 24 unmanned sample return mission landed there in 1976. The six ounces of lunar materials it brought back to Earth are the last lunar samples scientists have received.

Mare Anguis, the “Serpent Sea”

Mare Anguis lies just northeast of Mare Crisium and is called the “Serpent Sea” for its serpentine shape rather than the more fanciful name “Sea of Serpents” referred to by some science fiction authors.

Mare Undarum, the “Sea of Waves”

Mare Undarum lies southeast of Mare Crisium. Its uneven texture and lack of uniform smoothness appears to justify its name as “the sea of waves”.

Mare Spumans, the “Foaming Sea”

Mare Spumans lies south of Mare Undarum and east of Mare Fecunditatis. The bright crater Petit on the western side of this tiny mare evinces a bit of foam on “the foaming sea”.

Mare Australe, the “Southern Sea”

Mare Australe hugs the southeastern limb of the lunar nearside. Though obliquely viewed from Earth and wrapping around to the lunar farside, favorable libration makes it visible in its entirety on occasion.

Mare Smythii, “Smyth’s Sea”

Mare Smythii on the eastern limb of the Moon is one of two lunar maria named after people. The lucky honoree is English hydrographer and astronomer William Henry Smyth (1788-1865). The lunar equator passes through Mare Smythii.

Mare Marginis, the “Sea of the Edge”

Mare Marginis lies east of Mare Crisium, right along the lunar limb. The crater Goddard on the northeast side of Mare Marginis exhibits bright deposits on its northeastern side. This crater and its associated deposits can only be seen from Earth during favorable librations.

Mare Humboldtianum, the “Sea of Alexander von Humboldt”

Mare Humboldtianum lies along the northeastern limb of the Moon and is the other lunar mare named after a person. The German astronomer Johann Heinrich von Mädler (1794-1874) named this feature after German geographer and explorer Alexander von Humboldt (1769-1859).

This completes our tour of the 21 maria on the nearside of the Moon.

References

António Cidadão’s Home-Page of Lunar and Planetary Observation and CCD Imaging, Moon-“Light” Atlas.  Retrieved 22 April 2020.
http://www.astrosurf.com/cidadao/moonlight_mare_oceanus.htm

Ewen A. Whitaker, Mapping and Naming the Moon: A History of Lunar Cartography and Nomenclature (Cambridge University Press, 2003).

BepiColombo Passes Earth

The BepiColombo spacecraft flew by the Earth last night, the first of nine gravity-assist maneuvers it will make to slow it down so that it can go into orbit around the planet Mercury on 5 December 2025. This was the only Earth gravity assist. There will be a Venus flyby later this year and next year, and six Mercury flybys from 2021-2025.

BepiColombo passed 7,877 miles over the South Atlantic Ocean at 0425 UT on 10 April 2020 at its closest approach to Earth, and I was able to image it from my backyard observatory in Dodgeville, Wisconsin at 0600 UT at a distance (range) of 21,760 miles.

BepiColombo passing through the constellation Crater 10 Apr 2020 0600 UT as seen from Dodgeville, WI

North is up and East to the left in the video frame, so BepiColombo is moving in a northwesterly direction. The two stars in the field are 3UC 145-134561 (12.2m, north) and 3UC 144-138354 (12.7m, south). The predicted equatorial coordinates (epoch of date) at 0600 UT from JPL Horizons were α = 11h 38m 03.90s, δ = -18° 08′ 25.4″. Please note when using JPL Horizons to generate ephemerides for spacecraft and minor planets passing close to the Earth that you should use the ICRF coordinates (astrometric) and not the apparent coordinates. They can be significantly different!

The integration time in the video above is 7.5 frames per second, or 0.13 second per frame. The field size is 17 x 11 arcminutes.

Here’s the video light curve of BepiColombo as it passed through the field. It was fairly constant in brightness with no obvious variability amidst the noisy measurements.

A New Infinite Series, Convergent and Irrational

Infinite series are a log of func. All kidding aside, you may have heard of the sum of reciprocal squares.

\sum\limits_{n=1}^{\infty}\frac{1}{{n}^2}=\frac{1}{{1}^2}+\frac{1}{{2}^2}+\frac{1}{{3}^2}+\frac{1}{{4}^2}+\frac{1}{{5}^2}+\frac{1}{{6}^2}+\frac{1}{{7}^2}+\cdots

The sum of this slowly convergent series is approximately equal to 1.644934. Is there anything special about this number? Italian mathematician Pietro Mengoli (1626-1686) first posed the question in 1644 (published 1650), what is the exact sum of this infinite series? This problem was not solved until 90 years later by Swiss mathematician Leonhard Euler (1707-1783) in 1734 (published 1735). Euler proved that the exact sum is

\sum\limits_{n=1}^{\infty}\frac{1}{{n}^2}=\frac{{\pi}^2}{6}

There’s that number pi, the most famous of the irrational numbers, showing up once again in mathematics, ostensibly having nothing at all to do with circles. What’s an irrational number? It is any real number that cannot be expressed as a ratio of two integers. The decimal digits of an irrational number neither terminate nor end in a repeating sequence (e.g. 1/3 = 0.3333… or 9/11 = 0.81818181…).

Determining the exact value of the sum of reciprocal squares infinite series is known as the Basel Problem, named after the hometown of Euler (who solved it) and the Bernoulli family of mathematicians (who were not able to solve it).

My admired colleague in England, Abdul Ahad, has come up with a variant of the sum of reciprocal squares where every third term starting with n = 4 is subtracted rather than added.

\frac{{\pi}^2}{6} -2\sum\limits_{n=1}^{\infty}\frac{1}{{\left (3n+1  \right )}^2}=\frac{1}{{1}^2}+\frac{1}{{2}^2}+\frac{1}{{3}^2}-\frac{1}{{4}^2}+\frac{1}{{5}^2}+\frac{1}{{6}^2}-\frac{1}{{7}^2}+\cdots

Ahad has shown that this new series is convergent and sums to an irrational number, approximately equal to 1.40146804. The infinite sum portion of the above expression is approximately equal to 0.12173301 and is also an irrational number. Multiplying by 2 gives us an irrational number, and subtracting from π2/6, which is itself irrational, results in our final result being irrational.

Interestingly, almost all real numbers are irrational, strange as they are.

References

Ahad, Abdul. “An interesting series.” M500 Magazine 278, 8-9 (2017). http://m500.org.uk/wp-content/uploads/2018/11/M278WEB.pdf.

Ahad, Abdul. “A New Infinite Series with Proof of Convergence and Irrational Sum.” Res Rev J Statistics Math Sci, Volume 4, Issue 1 (2018). http://www.rroij.com/open-access/a-new-infinite-series-with-proof-of-convergence-and-irrational-sum.pdf.

Comet ATLAS (C/2019 Y4)

Comet C/2019 Y4 ATLAS was discovered on December 28, 2019 and is named after the observational program that discovered it: Asteroid Terrestrial-impact Last Alert System (ATLAS). It could become a naked-eye comet—if it doesn’t disintegrate as it gets closer to the Sun. Here’s an ephemeris for the remainder of April and May.

Comet ATLAS (C/2019 Y4) 10 Apr 2020 0224 UT 4 minute exposure 300mm f/5.6 Dodgeville WI

Jean Sibelius: An Introduction

The young Finnish composer Jean Sibelius (1865-1957) wanted to be a virtuoso violinist but it was in composition that his greatest talent lay. All his life, he was deeply connected to the natural world, and this love of Nature is expressed in much of his music.

Jean Sibelius in 1913

I know of no better introduction to the music of Jean Sibelius than the two CD set of his Symphonies No. 1, 2, and 4, and Finlandia and the Karelia Suite by Vladimir Ashkenazy conducting the Philharmonia Orchestra.

Decca 455 402-2

The earliest composition featured on this recording is the Karelia Suite, completed in 1893; the latest is the pensive Symphony No. 4, completed in 1911. All of the music on these discs is splendid, the performances inspired, and the recordings immersive.

Ashkenazy seems to have an innate understanding of Sibelius, and his conducting and interpretations shine here throughout.

As with many (most?) of the greatest composers, Sibelius faced a number of challenges and personal demons throughout his life. Though he lived a long and productive life, he wrote almost no new music after his brilliant tone poem Tapiola in 1926, 31 years before his death. He did complete a Symphony No. 8, but threw the score into his fireplace in 1945. Sibelius once remarked, “If I cannot write a better symphony than my Seventh, then it shall be my last.”

To find out more about the life and music of Jean Sibelius, I’d like to direct your attention to an excellent two-part documentary film by Christopher Nupen, completed in 1984. It is available through the classical music streaming channel medici.tv (highly recommended) and Amazon.

Shadows Cast by Starlight

Henry Norris Russell (1877-1957) received his Ph.D. at Princeton in 1899 at just 21 years of age. Three years later—in 1902 when he was 24 years old and years before his discovery of the color-luminosity relationship now known as the Hertzsprung-Russell (H-R) diagram—Russell had an interesting article published in the journal Popular Astronomy that shows him already to be a meticulous and perspicacious observational astronomer. This article, completed 118 years ago this day, is reprinted below.


SHADOWS CAST BY STARLIGHT.

HENRY NORRIS RUSSELL.

FOR POPULAR ASTRONOMY.

It has long been known that Venus casts a distinct shadow; and the same thing has sometimes been observed in Jupiter’s case. More recently, it has been stated in the daily press* that shadows cast by Sirius have been seen at the Harvard Observatory in Jamaica, though it was then said that they could probably be seen only where the air is exceptionally clear.

The writer began to investigate this subject, quite independently, last November, and has found that the shadows cast by a number of the brighter fixed stars can be seen without difficulty under ordinary circumstances, provided proper precautions are taken to exclude extraneous light, and to secure the maximum sensitiveness of the observer’s eyes.

* Interview with Professor W.H. Pickering, New York Tribune, Jan. 18, 1902.

The most convenient method of observation is as follows: Choose a window from which the star is visible, while as little light as possible enters from terrestrial sources. Darken the room completely, with the exception of this window. Open the window, and screen down its aperture to an area of a square foot or less. Hold a large piece of white paper in the path of the star’s rays, as far from the opening as possible. The image of the opening will then appear on the paper.

It cannot, however, be well seen until the observer has spent at least ten minutes in the dark, (to rest his eyes from the glare of ordinary lights). The paper should be held within a foot or so of the eyes, as the faint patch of starlight is most easily visible when its apparent area is large. The shadow of any convenient object may now be made to fall on the screen, and may be observed. By holding the object near the window and noticing that its shadow is still sharp, the observer may convince himself that the light which casts the shadow really comes from the star.

By the method above described, the writer has succeeded in distinguishing shadows cast by the following stars, (which are here arranged in order of brightness):

Mag.Mag.
α Canis Majoris (Sirius)– 1.4ζ Orionis1.9
α Bootis (Arcturus)0.0β Tauri1.9
α Aurigae (Capella)0.2γ Geminorum2.0
β Orionis (Rigel)0.3β Canis Majoris2.0
α Canis Minoris (Procyon)0.5α Hydrae2.0
α Orionis* (Betelgeuse)0.8?α Arietis2.0
α Tauri (Aldebaran)1.0κ Orionis2.2
β Geminorum (Pollux)1.1β Leonis2.2
α Virginis (Spica)1.2γ Leonis2.2
α Leonis (Regulus)1.4δ Orionis2.4
ε Canis Majoris1.5η Canis Majoris2.4
α Geminorum (Castor)1.6ζ Argus2.5
ε Orionis1.8α Ceti2.7
δ Canis Majoris1.915 Argus2.9
γ Orionis1.9

* Variable

The groups of stars comprised in the Pleiades and the sword of Orion also cast perceptible shadows. With a wide open window the belt of Orion should be added to this class.

Most of the observations on which this list is based were made at Princeton on February 7th, and 8th, and March 6th, 1902. The first of these nights is recorded as not remarkably clear, the others as very clear. Whenever there was any doubt of the reality of an observed patch of starlight, it was located at least three times, and it was verified each time that the star was really visible from the spot where its light had been located. Many more stars might have been added to the 29 in the foregoing list, had not unfriendly street lamps confined the observations to less than half the sky.

As many of the stars observed were at a low altitude, it may be concluded that a star of the 3rd magnitude, if near the zenith, would cast a perceptible shadow.

In attempting to get a shadow from these faint stars, the opening of the window should be narrowed to a width of a few inches, so as to cut off as much as possible of the diffused light of the sky. Care should be taken not to look at the sky while observing, as it is bright enough to dazzle the eyes for some little time.

By observing these precautions, the writer has been able to detect shadows cast by Sirius, Arcturus and Capella on moonlight nights,—in the case of Sirius, even when the Moon shone into the room.

The actual brightness of the screen, even when illuminated by Sirius, is very small in comparison with that of the “dark” background of the sky, as seen by the naked eye. White paper reflects about 80 per cent of the incident light. From photometric considerations, a disk of this material 1° in apparent diameter, illuminated perpendicularly by Sirius, should send us about 1/16,000 as much light as the star.

But, according to Professor Newcomb’s determination*, an area of sky 1° in diameter, remote from the Milky Way, sends us 9/10 as much light as a 5th magnitude star, or about 1/400 of the light of Sirius. Hence the sky is about 40 times as bright, area for area, as the paper illuminated by Sirius. The illumination of the paper by a 1st magnitude star is about 1/400 as bright, and by a 3d magnitude star less than 1/2000 as bright, area for area, as the “dark” background of the sky.

* Astrophysical Journal, December 1901.

This faint light, as might be anticipated, shows no perceptible color. The light of the white stars β and γ Orionis and the red star α Orionis does not differ sensibly in quality; but the light of the red star appears much fainter than the star’s brightness, as directly seen, would lead one to anticipate. On the screen, the light of α Orionis is much fainter than that of β, and only a little brighter than that of γ, while by direct vision α is much nearer to β than to γ in brightness. As β is 1 ½ magnitudes brighter than γ, it appears that, as measured by the intensity of its light on a screen, α Orionis is at least half a magnitude, perhaps a whole magnitude, fainter than when compared with the neighboring white stars by direct vision.

Such a result might have been anticipated à priori, since, in the ease of such faint lights as are here dealt with, the eye is sensitive to the green part of the spectrum alone, and this is relatively brighter in the spectrum of a white star than of a red one.

A much more interesting example of the accordance of theoretical prediction with observation is afforded by another phenomenon discovered by the writer, which is not hard to observe.

A surface illuminated by a planet—Venus for example—appears uniformly and evenly bright, but in the case of a fixed star, there are marked variations in brightness, so that the screen appears covered with moving dark markings.

This was predicted many years ago by Professor Young, in discussing the twinkling of the stars. He says*: “If the light of a star were strong enough, a white surface illuminated by it would look like the sandy bottom of a shallow, rippling pool of water illuminated by sunlight, with light and dark mottlings which move with the ripples on the surface. So, as we look toward the star, and the mottlings due to the irregularities of the air move by us, we see the star alternately bright and faint; in other words, it twinkles.”

General Astronomy, page 538 (edition of 1898).

It would be difficult to give a better description of the observed phenomenon than the one contained in the first part of the above quotation. It need only be added that the dark markings are much more conspicuous than the bright ones. This agrees with the fact that a star more frequently seems to lose light while twinkling than to gain it.

Sirius is the only star whose light is bright enough to make these light and dark mottlings visible without great difficulty, though the writer has seen them in the light of Rigel and Procyon. With Sirius they have been seen every time the star’s light has been observed on a moonless night. They are much more conspicuous when the star is twinkling violently than on nights when the air is steady. In the latter case there are only faint irregular mottlings, whose motion produces a flickering effect. More usually there appear also ill-defined dark bands, two or three inches wide. These are never quite straight nor parallel but usually show a preference for one or two directions, sometimes dividing the screen into irregular polygons. On some nights they merely seem to oscillate, but on others they have a progressive motion, which may be at any angle with their own direction. The rate of motion is very variable, but is greatest on windy nights,—another evidence of the atmospheric origin of the bands.

The best nights for observing these bands occur when the stars are twinkling strongly, and there is not much wind. The directions given above for observing shadows should be somewhat modified in this case.

If the room is not at the same temperature as the outer air, the window should be kept closed, as otherwise most of what is seen will be due to the air-currents near it. It is also desirable to have an area of star-light at least a foot square to see the bands in, so that a good sized part of the window should be left clear.

If Sirius is unavailable, Arcturus and Vega are probably the best stars in whose light to attempt to see the bands.

PRINCETON, N. J., March 24, 1902.

Rhapsody on a Theme of Paganini

The remarkable composer and virtuoso pianist Sergei Rachmaninoff (1873-1943) wrote five works for piano and orchestra. The first four were his piano concertos.

Piano Concerto No. 1 in F♯ minor, Op. 1 (1891; revised 1917)

Piano Concerto No. 2 in C minor, Op. 18 (1901)

Piano Concerto No. 3 in D minor, Op. 30 (1909)

Piano Concerto No. 4 in G minor, Op. 40 (1926; revised 1941)

His 2nd and 3rd piano concertos are especially beautiful, and are among the finest examples of this genre in the entire repertory.

Then, in 1934, eight years after his final piano concerto, he wrote his final work for piano and orchestra, Rhapsody on a Theme of Paganini. It is a set of 24 variations in a single movement lasting 23 to 25 minutes. Its point of departure is the last of the 24 Caprices for Solo Violin, written between 1802 and 1817 by the great violinist Niccolò Paganini (1782-1840). Here is a performance of Caprice No. 24.

Kyoko Yonemoto playing Caprice No. 24 in A minor by Niccolò Paganini

And, oh, what Rachmaninoff does with this theme by Paganini! Energetic, scintillating, lush, virtuosic—these are just a few of the words that describe this incredibly dynamic and exciting work. It is the perfect introduction to Rachmaninoff’s music, and arguably his finest work—at least in terms of what he accomplishes in a mere two dozen minutes.

There are many fine recordings of this remarkable piece. I have several. Here they are, in order of duration.

23:00 Gary Graffman (1928-), New York Philharmonic, Leonard Bernstein (1918-1990)

23:01 Cecile Licad (1961-), Chicago Symphony, Claudio Abbado (1933-2014)

23:16 Adilia Alieva (living; birth year unknown), Orchestra Sinfonica do Samremo, Walter Proost (living; birth year unknown)

23:36 Vladimir Ashkenazy (1937-), London Symphony, André Previn (1929-2019)

23:44 Stephen Hough (1961-), Dallas Symphony, Andrew Litton (1959-)

24:56 Daniil Trifonov (1991-), Philadelphia Orchestra, Yannick Nézet-Séguin (1975-)

As you can see even from this small sample, a piece of music can be played with widely varying tempos and, of course, interpretations. The Trifonov recording is the latest addition to my collection, and you’ll note that it is a full 1m12s longer than the next longest interpretation, another great recording by pianist Stephen Hough.

I was bowled over by this Trifonov recording, and it is my current favorite. There is so much to savor here, and yet I never get the sense that the tempo is too slow. Time is certainly relative when it comes to music!

Give this recording of Rhapsody on a Theme of Paganini a listen! Truly outstanding.

Deutsche Grammophon 479 4970 GH

Counting Stars

Looking in all directions, how many stars are there brighter than a particular visual magnitude? Here’s an empirical formula that gives an approximation. It can be used over the range mv = +4.0 to +25.0.

\textup{S} = 10^{-0.0003\,\textup{m}^{3} + 0.0019\,\textup{m}^{2} + 0.484\,\textup{m} + 0.795}

where S is the approximate number of stars brighter than apparent visual magnitude m in the entire sky

Apparent Visual Magnitude# of Stars
4.0552
4.1618
4.2690
4.3772
4.4863
4.5964
4.61,077
4.71,204
4.81,345
4.91,503
5.01,679
5.11,875
5.22,094
5.32,338
5.42,611
5.52,914
5.63,253
5.73,631
5.84,051
5.94,520
6.05,042
6.15,623
6.26,271
6.36,992
6.47,794
6.58,687
6.69,681
6.710,786
6.812,015
6.913,382
7.014,900
7.116,588
7.218,464
7.320,547
7.422,860
7.525,428
7.628,278
7.731,441
7.834,949
7.938,839
8.043,152
8.147,932
8.253,229
8.359,096
8.465,592
8.572,784
8.680,743
8.789,549
8.899,287
8.9110,055
9.0121,955
9.1135,104
9.2149,627
9.3165,662
9.4183,362
9.5202,891
9.6224,431
9.7248,181
9.8274,358
9.9303,200
10.0334,965
10.1369,938
10.2408,426
10.3450,768
10.4497,330
10.5548,514
10.6604,755
10.7666,528
10.8734,349
10.9808,780
11.0890,430
11.1979,963
11.21,078,096
11.31,185,610
11.41,303,349
11.51,432,229
11.61,573,241
11.71,727,456
11.81,896,035
11.92,080,230
12.02,281,392
12.12,500,983
12.22,740,574
12.33,001,863
12.43,286,675
12.53,596,976
12.63,934,877
12.74,302,651
12.84,702,734
12.95,137,742
13.05,610,480
13.16,123,951
13.26,681,371
13.37,286,180
13.47,942,053
13.58,652,916
13.69,422,957
13.710,256,640
13.811,158,721
13.912,134,260
14.013,188,640
14.114,327,575
14.215,557,134
14.316,883,749
14.418,314,236
14.519,855,805
14.621,516,082
14.723,303,122
14.825,225,420
14.927,291,933
15.029,512,092
15.131,895,815
15.234,453,520
15.337,196,142
15.440,135,142
15.543,282,516
15.646,650,811
15.750,253,128
15.854,103,131
15.958,215,053
16.062,603,700
16.167,284,449
16.272,273,253
16.377,586,632
16.483,241,673
16.589,256,016
16.695,647,847
16.7102,435,879
16.8109,639,337
16.9117,277,932
17.0125,371,840
17.1133,941,667
17.2143,008,417
17.3152,593,453
17.4162,718,451
17.5173,405,353
17.6184,676,315
17.7196,553,644
17.8209,059,737
17.9222,217,010
18.0236,047,823
18.1250,574,401
18.2265,818,743
18.3281,802,538
18.4298,547,061
18.5316,073,074
18.6334,400,717
18.7353,549,396
18.8373,537,665
18.9394,383,103
19.0416,102,189
19.1438,710,168
19.2462,220,923
19.3486,646,831
19.4511,998,631
19.5538,285,275
19.6565,513,790
19.7593,689,134
19.8622,814,048
19.9652,888,922
20.0683,911,647
20.1715,877,479
20.2748,778,904
20.3782,605,508
20.4817,343,852
20.5852,977,352
20.6889,486,170
20.7926,847,110
20.8965,033,523
20.91,004,015,228
21.01,043,758,439
21.11,084,225,707
21.21,125,375,873
21.31,167,164,044
21.41,209,541,573
21.51,252,456,065
21.61,295,851,393
21.71,339,667,742
21.81,383,841,658
21.91,428,306,130
22.01,472,990,684
22.11,517,821,499
22.21,562,721,546
22.31,607,610,744
22.41,652,406,140
22.51,697,022,107
22.61,741,370,568
22.71,785,361,232
22.81,828,901,853
22.91,871,898,516
23.01,914,255,925
23.11,955,877,722
23.21,996,666,815
23.32,036,525,723
23.42,075,356,932
23.52,113,063,265
23.62,149,548,260
23.72,184,716,557
23.82,218,474,290
23.92,250,729,483
24.02,281,392,450
24.12,310,376,189
24.22,337,596,778
24.32,362,973,766
24.42,386,430,550
24.52,407,894,751
24.62,427,298,570
24.72,444,579,131
24.82,459,678,812
24.92,472,545,544
25.02,483,133,105

How many stars are there in our Milky Way galaxy? Between 100 and 400 billion stars. Many stars are not very luminous, and can only be seen in the immediate solar neighborhood. That is one source of uncertainty.

How many galaxies are there in the observable universe? Something like two trillion (2 × 1012).

How many stars are in the observable universe? Something like a septillion (1024). A trillion trillion!

And, just so you know, our universe is probably much larger than the volume that we can observe.

How does the Universe love thee? Let us count the stars…

References

“How many stars are in the sky?”, Space Math, NASA Goddard Space Flight Center, accessed February 29, 2020, https://spacemath.gsfc.nasa.gov/weekly/6Page103.pdf.

Wikipedia contributors, “Galaxy,” Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Galaxy&oldid=942479372 (accessed February 29, 2020).

Wikipedia contributors, “Milky Way,” Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Milky_Way&oldid=942977760 (accessed February 29, 2020).

Marfa Lights

Yes, I’ve seen the Marfa lights. Bernie Zelazny and I were coming back from doing a star party for a culinary group at El Cosmico in Marfa on April 7, 2011 when we decided to stop at the Marfa lights viewing station just off of US 67/90. For the first couple of minutes (Thursday evening around 11:00 p.m. or so) we saw nothing, but then, sure enough, a slowly moving white light appeared near a small tower with red lights, providing a good point of reference for the motion. The light gradually changed brightness, sometimes brighter, sometimes dimmer, moving left to right, then disappeared. Soon, another would appear: sometimes higher, sometimes lower, usually moving to the right, but sometimes to left. My first thought: distant headlights. Sometimes, more that one could be seen at the same time.

Quickly, I ran back to my car to get the 15 x 70 binoculars and binocular mount (an Orion Paragon Plus) and set them up to view the Marfa lights, which by now were happening frequently. When viewing each Marfa light through these powerful binoculars, the first thing I noticed is that I was not able to focus! No matter how I changed the focus of the binoculars, I could do no better than to see a round amorphous blob of light.

Next, I decided to see if any of the fixed distant lights would focus. First the red tower lights. Nope, red blobs. Then a distant ranch light to the left of the light dome of Ojinaga/Presidio. Nope, a while blob. Then, another distant ranch light. Another white blob. Then some distant headlights on US 67/90 near Marfa heading toward Alpine. The headlights were too far away to resolve, and in the binoculars they, too, were an unresolvable white blob. Next I moved the binoculars up a few degrees to look at some stars. Perfect focus! Back down to the ground lights and Marfa lights: out of focus blobs!

So, it appears to me that some atmospheric phenomenon is defocusing and distorting terrestrial lights in the distance. Perhaps some sort of superior mirage. I think the most likely explanation for the Marfa lights is distant vehicle headlights.

Next steps in the investigation of this curious phenomenon: Use a micrometer eyepiece in a low-power rich-field telescope to measure the angular sizes of the Marfa light blobs, as well as the angular sizes of the blobs from identifiable terrestrial lights. Determine the distance to the terrestrial light sources in the daytime (if possible) using triangulation. Better yet, determine the great circle distance to each terrestrial light source by obtaining GPS coordinates of each of those light sources, and the Marfa lights viewing station. Even better would be to shine a mobile light source at the Marfa lights viewing station from various GPS-determined locations at different distances on an evening when the Marfa lights are visible. Determine if the size of each known light blob is a function of distance. Using this information, estimate the distance to the Marfa light sources.

Also, note whether the angular size of each Marfa light is related to its altitude above the horizon.

More ideas: Take a series of 30-second digital camera exposures over the course of an evening to determine if the Marfa lights take preferred paths. The results might support or refute the vehicle headlights hypothesis. Determine if the Marfa lights paths change from night to night or during the course of one night.

Finally, I’d suggest using the same kind of wide-field spectroscopic equipment used to obtain meteor spectra to determine the spectral characteristics of the Marfa lights. This would tell us much about their chemical composition, temperature, and origin.

Forever Stamps

The United States Postal Service has issued a number of enticing forever stamps in recent years, and I’ve begun accumulating stamps faster than I use them. Sound familiar? If so, why not use them for extra postage items—even if you end up spending a little more than is required.

The current value of a forever stamp is 55¢. If you have a postal scale at home to weigh the envelopes you want to post, this handy guide will show you how many forever stamps to use for envelopes of different sizes and weights. (Mail within the U.S. only)

Standard Envelopes (≤11.5″ long, ≤6.125″ high, ≤0.25″ thick)
  • 0 to 1 ounce: 1 forever stamp
  • 1 to 4 ounces: 2 forever stamps
  • 4 to 8 ounces: 3 forever stamps
Large Envelopes (11.5-15″ L, 6.125-12″ H, or 0.25-0.75″ T)
  • 0 to 1 ounce: 2 forever stamps
  • 1 to 4 ounces: 3 forever stamps
  • 4 to 7 ounces: 4 forever stamps
  • 7 to 9 ounces: 5 forever stamps
  • 9 to 12 ounces: 6 forever stamps
  • 12 to 15 ounces: 7 forever stamps

If you are mailing a standard envelope that has one or more of the characteristics in DMM 101.1.2, add an ounce to the measured weight to cover the non-machinable surcharge.

If you are mailing a large envelope that is rigid, is non-rectangular, or is not uniformly thick, then take your envelope to the post office to mail because you will have to pay parcel prices.