## Black Hole Conundrums

Last night I re-watched the excellent two-hour PBS NOVA special Black Hole Apocalypse, and this time I jotted a few questions down.

• Has Gaia DR2 improved our knowledge of the distance to the O-star black hole binary system Cygnus X-1 (6000 ly) and the mass of the black hole (15M)?
• Are there any known pulsar black hole binary systems?
• Could LIGO (and now Virgo in Italy) detect a stellar-mass black hole infalling into a supermassive black hole at the center of the Milky Way galaxy or another galaxy?
• Do supermassive black holes play a role in galaxy formation?  If so, how does a supermassive black hole interact with dark matter?
• Wouldn’t material infalling into a black hole undergo extreme time dilation and from our vantage point take millions or even billions of years to cross the event horizon?  If so, don’t all black holes—even supermassive ones—form from rapid catastrophic events such as core-collapse supernovae and black hole collisions?

Gaia DR2 (Gaia Data Release 2) has indeed measured the distance to the Cygnus X-1 system.  The “normal” star component of Cygnus X-1 (SIMBAD gives spectral type O9.7Iabpvar) is the 8.9-magnitude star HDE 226868.  Gaia DR2 shows a parallax of 0.42176139325365936 ± 0.032117130282281664 mas (not sure why they show so many digits!).

The distance to an object in parsecs is just the reciprocal of the parallax angle in arcseconds, but since the parallax angle is given in milliarcseconds, we must divide parallax into 1000.  This gives us a best-estimate distance of 2,371 parsecs or 7,733 light years.  Adding and subtracting the uncertainty to the parallax value and then doing the arithmetic above gives us a distance range of 2,203 to 2,566 parsecs or 7,186 to 8,371 light years.  (To get light years directly, just divide the parallax in millarcseconds into 3261.564.)

This is 20% to 40% further than the distance to Cygnus X-1 given in the NOVA program, and looking at the source for that distance (Reid et al. 2011) we find that the Gaia DR2 distance (7,186-8,371 ly) is outside the range given by Reid’s VLBA radio trigonometric parallax distance of 5,708-6,458 ly.  It remains to be seen what effect the Gaia DR2 distance, if correct, will have on the estimate of the mass of the black hole.

The estimate of the mass of the black hole in Cygnus X-1 is calculated using modeling which requires as one of its input parameters the distance to the system.  This distance is used to determine the size of the companion star which then constrains the scale of the binary system.  Because the Cygnus X-1 system is not an eclipsing binary, nor does the companion star fill its Roche equipotential lobe, traditional methods of determining the size of the companion star cannot be used.  However, once we use the distance to the system to determine the distance between the black hole and the companion star, as well as the orbital velocity of the companion star, we can determine the mass of the black hole.

Now, moving along to the next question, have any pulsar black-hole binary systems been discovered yet?  The answer is no, not yet, but the hunt is on because  such a discovery would provide us with an exquisite laboratory for black hole physics and gravity.  Something to look forward to!

Could LIGO ( and Virgo) detect a stellar-mass black hole infalling into a supermassive black hole at the center of the Milky Way galaxy or another galaxy?  No.  That would require a space-based system gravitational wave detector such as the Laser Interferometer Space Antenna (LISA)—see “Extreme mass ratio inspirals” in the diagram below.

The above diagram illustrates that gravitational waves come in different frequencies depending on the astrophysical process that creates them.  Ground-based detectors such as LIGO and Virgo detect “high” frequency gravitational waves (on the order of 100 Hz) resulting from the mergers of stellar-mass black holes and neutron stars.  To detect the mergers of more massive objects will require space-based gravitational wave observatories (millihertz band) or pulsar timing arrays (nanohertz band) in the case of  supermassive black holes binaries within merging galaxies.  The future of gravitational wave astronomy looks very bright, indeed!

Do supermassive black holes play a role in galaxy formation?  Probably.  We are not yet able to explain how supermassive black holes form, especially so soon after the Big Bang.  Does dark matter play a major role?  Probably.  The formation of supermassive black holes, their interaction with dark matter, and their role in galaxy formation are all active topics or current research.  Stay tuned.

To succinctly restate my final and most perplexing question, “How can anything ever fall into a black hole as seen from  an outside observer?”  A lot of people have asked this question.  Here’s the best answer I have been able to find, from Ben Crowell:

The conceptual key here is that time dilation is not something that happens to the infalling matter.  Gravitational time dilation, like special-relativistic time dilation, is not a physical process but a difference between observers.  When we say that there is infinite time dilation at the event horizon we don’t mean that something dramatic happens there.  Instead we mean that something dramatic appears to happen according to an observer infinitely far away.  An observer in a spacesuit who falls through the event horizon doesn’t experience anything special there, sees her own wristwatch continue to run normally, and does not take infinite time on her own clock to get to the horizon and pass on through.  Once she passes through the horizon, she only takes a finite amount of clock time to reach the singularity and be annihilated.  (In fact, this ending of observers’ world-lines after a finite amount of their own clock time, called geodesic incompleteness, is a common way of defining the concept of a singularity.)

When we say that a distant observer never sees matter hit the event horizon, the word “sees” implies receiving an optical signal.  It’s then obvious as a matter of definition that the observer never “sees” this happen, because the definition of a horizon is that it’s the boundary of a region from which we can never see a signal.

People who are bothered by these issues often acknowledge the external unobservability of matter passing through the horizon, and then want to pass from this to questions like, “Does that mean the black hole never really forms?” This presupposes that a distant observer has a uniquely defined notion of simultaneity that applies to a region of space stretching from their own position to the interior of the black hole, so that they can say what’s going on inside the black hole “now.”  But the notion of simultaneity in GR is even more limited than its counterpart in SR.  Not only is simultaneity in GR observer-dependent, as in SR, but it is also local rather than global.

References
K. Liu, R. P. Eatough, N. Wex, M. Kramer; Pulsar–black hole binaries: prospects for new gravity tests with future radio telescopes, Monthly Notices of the Royal Astronomical Society, Volume 445, Issue 3, 11 December 2014, Pages 3115–3132, https://doi.org/10.1093/mnras/stu1913

Mingarelli, Chiara & Joseph W. Lazio, T & Sesana, Alberto & E. Greene, Jenny & A. Ellis, Justin & Ma, Chung-Pei & Croft, Steve & Burke-Spolaor, Sarah & Taylor, Stephen. (2017). The Local Nanohertz Gravitational-Wave Landscape From Supermassive Black Hole Binaries. Nature Astronomy. 1. 10.1038/s41550-017-0299-6.
https://doi.org/10.1038/s41550-017-0299-6
https://arxiv.org/abs/1708.03491

Jerome A. Orosz et al 2011 ApJ 742 84
https://doi.org/10.1088/0004-637X/742/2/84

Mark J. Reid et al 2011 ApJ 742 83
https://doi.org/10.1088/0004-637X/742/2/83

Brian C. Seymour, Kent Yagi, Testing General Relativity with Black Hole-Pulsar Binaries (2018)
https://arxiv.org/abs/1808.00080

J. Ziółkowski; Determination of the masses of the components of the HDE 226868/Cyg X-1 binary system, Monthly Notices of the Royal Astronomical Society: Letters, Volume 440, Issue 1, 1 May 2014, Pages L61–L65, https://doi.org/10.1093/mnrasl/slu002

## Perseids Ahoy!

Already early this week you will see an occasional Perseid meteor gracing the sky, but next weekend the real show begins.  The absolute peak of this year’s Perseids is favorable to observers in North America, and with no moonlight interference we are in for a real treat—provided you escape cloudy weather.  I highly recommend “going mobile” if the weather forecast 24-48 hours before the peak night indicates less than ideal conditions at your location.

The Perseids this year are expected to peak Sunday night August 12/13.   Highest observed rates will likely be between 2 a.m. and 4 a.m. Monday, August 13.  Here’s a synopsis of the 2018 Perseids.

Fri/Sat
Aug 10/11
respectable activity
Sat/Sun
Aug 11/12
strong activity

Sun/Mon

Aug 12/13

very strong activity

Mon/Tue
Aug 13/14
strong activity
Tue/Wed
Aug 14/15
respectable activity

## Largest Satellites of Our Solar System

Here is a table of the 12 largest satellites in our solar system.  In addition to the size of each satellite, its home planet, its median distance from that planet, and discovery information, its median distance from its home planet is given in terms of the median lunar distance from the Earth.  Remarkably, Pluto’s moon Charon is just 0.05 lunar distances from Pluto, only 19,591 km.  Only one other of the largest satellites orbits closer to its home planet than the Moon orbits around the Earth, and that is Neptune’s moon Triton at 92% of the Earth-Moon distance.  At the other end of the scale, Saturn’s moon Iapetus orbits Saturn over nine times further away than the Moon orbits the Earth.

Now let’s look at the orbital eccentricity of each of the largest moons, and the orbital inclination relative to the equator of its home planet.

Our familiar Moon is really an oddball: it has the greatest orbital eccentricity of all the largest satellites, and, with the exception of Triton and Iapetus, by far the greatest orbital inclination relative to the equator of its home planet.  Triton is the oddball among oddballs as it is the only large satellite in our solar system that has a retrograde orbit: it orbits Neptune in a direction opposite the planet’s rotation.  Iapetus has an orbital inclination relative to Saturn’s equator almost as much as the Moon’s orbital inclination relative to the Earth’s equator, but this anomaly can perhaps be forgiven because Iapetus orbits so very far away from Saturn.  Its orbital period is over 79 days.

Note that the Moon’s orbital inclination relative to the equator of the Earth varies between 18.33˚ and 28.60˚.  This occurs because the intersection between the plane of the Moon’s orbit around the Earth and the plane of the Earth’s orbit around the Sun precesses westward, making an entire circuit every 18.6 years.

## 88 Constellations, One Musical Instrument

Of all the constellations in our sky, only one is a musical instrument: Lyra the Lyre.  A lyre is a stringed harplike instrument used to accompany a singer or reader of poetry, especially in ancient Greece.  One wonders what strange and lonely enchantments await the contemplative listener as Lyra wheels through our zenith these short summer nights.

## Nova Scuti 2018

Nova Scuti 2018 (or N Sct 2018, for short) was discovered by prolific nova finder Yukio Sakurai of Japan on June 29, 2018.  His discovery image at 13:50:36 UT showed the nova shining at magnitude 10.3 (unfiltered CCD magnitude), using only a 180-mm f/2.8 lens plus a Nikon D7100 digital camera.  One of his many discoveries is named after him: Sakurai’s Object.

What is a nova?  A classical nova is a close binary star system that includes a white dwarf and a “normal” star.  The white dwarf siphons material off the other star until a critical density and temperature is reached in the atmosphere of the white dwarf, and a thermonuclear detonation occurs.

Nova Scuti 2018 will eventually receive a variable star designation (V507 Sct?).  Here are some typical nova light curves.

Nova Scuti 2018 is located fortuitously close to the 4.7-magnitude star Gamma (γ) Scuti.

Here is a time sequence of images I’ve acquired of Nova Scuti 2018.  Comparing with the star chart above, can you find the nova?

## Caffau’s Star

A 17th-magnitude dwarf star in Leo $4,445^{+529}_{-427}$ ly distant has the lowest metallicity of any star yet discovered.  Stars with very low metallicity are designated as extremely metal-poor (EMP).

SDSS J102915+172927 (aka UCAC3 215-112497, UCAC4 538-051259, Gaia DR2 3890626773968983296, or just J1029+1729 for short) was identified by Elisabetta Caffau and her team in 2011 to have a global metallicity of Z ≤ 6.9 × 10-7 which means that the star is 99.999931% hydrogen and helium.  Looking at this another way, the global metallicity of our Sun is 0.0134 (98.66% hydrogen and helium), so Caffau’s Star has only about 1/19,000th the abundance of elements heavier than helium in comparison to the Sun.

Metallicity is usually expressed as the abundance of iron relative to hydrogen.   It is a logarithmic scale.  [Fe/H] = 0.0 for the Sun; positive numbers mean iron is more abundant and negative numbers mean iron is less abundant than in the Sun.

[Fe/H] = +2.0 means iron is 100 times more abundant than in the Sun

[Fe/H] = +1.0 means iron is 10 times more abundant than in the Sun

[Fe/H] = -1.0 means iron is 1/10 as abundant as in the Sun

[Fe/H] = -2.0 means iron is 1/100 as abundant as in the Sun

And so on.  Caffau’s Star has an iron abundance [Fe/H] = -5.0, or 1/100,000th that of the Sun.  Caffau’s Star is the only EMP star with [Fe/H] < -4.5 thus far detected that is not a carbon-enhanced metal-poor star (CEMP).  In fact, Caffau’s Star has no detectable carbon!  Nor nitrogen.  Nor lithium.

Caffau’s Star is probably almost as old as our Milky Way galaxy.  In order to have survived for 13 Gyr, its mass cannot be any larger than 0.8 M.

References
Aguado, D.S., Prieto, C.A., Hernandez, J.I.G., et al. 2018 ApJL, 854, L34
Aguado, D.S., Prieto, C.A., et al. 2018 ApJL, 852, L20
Aguado, D. S., González Hernández, J. I., et al. 2017, A&A, 605, A40
Bonifacio, P., Caffau, E., Spite, M., Spite, F., François, P., et al. 2018
(arXiv:1804.10419)
Caffau, E., Bonifacio, P., François, P., et al. 2011, NAT, 477, 67

## June Boötids

Some meteor showers give a more-or-less reliable performance the same time each year, but others have an occasional year with (sometimes substantial) activity punctuating many years with little or no activity.  The June Boötids, which may or may not be visible any night this week but most likely Wednesday morning or Wednesday evening if at all, is one such shower.  This year, however, any meteors that do occur will be compromised by the nearly-full moon.

One hallmark of the June Boötids is that they are unusually slow meteors, so they’re easy to identify if you see one.  Look for the meteors to emanate from a region of the sky a few degrees north of the top of the “kite” of Boötes.

Of the 38 meteor showers listed in the IMO‘s “Working List of Visual Meteor Showers”, the lowest V, which is the pre-atmospheric Earth-apparent meteor velocity, is 18 km/s.  The three showers with that velocity are the π Puppids (Apr 23, δ=-45°), June Boötids (Jun 27, δ=+48°), and Phoenicids (Dec 2, δ=-53°).  For those of us living in the northern U.S., the June Boötids is the only one of these three showers we are ever likely to see.

Outbursts of June Boötids activity approaching or even exceeding 100 meteors per hour (single observer hourly rate) occurred in 1916, 1921, 1927, 1998, and 2004.  When the next outburst will occur none can yet say.

In eight years between 2001 and 2014 inclusive, my friend and expert visual meteor observer Paul Martsching of Ames, Iowa observed fourteen 0-magnitude or brighter June Boötids, the brightest of which was -4 in 2004.  He has seen June Boötids activity as early as June 22nd and as late as July 1st.  Of the 44 June Boötids he has observed, 52% were white in color, 27% yellow, and 21% orange.

Though we’re always at the mercy of the weather and the Moon and a workaday world that does little to accommodate the observational astronomy amateur scientist, meteor watching is a rewarding activity.   Even when meteor activity is sparse, you have time to think, to study the sky, to experience the beauty of the night.

## 29769 (1999 CE28)

Early in the morning of Tuesday, May 29, 2018, I was fortunate enough to record a 3.2 second occultation of the 12.6 magnitude star UCAC4 359-140328 in Sagittarius by the unnamed asteroid 29769, originally given the provisional designation 1999 CE28.

Not only is this the first time this asteroid has been observed to pass in front of a star, it is the smallest asteroid I have ever observed passing in front of a star.  At an estimated diameter of 14.7 miles, had I been located just 7.4 miles either side of the centerline of the shadow path, I would have missed this event altogether!  This is also the first positive event I’ve recorded for an (as yet) unnamed asteroid, and the first positive event I’ve recorded for an asteroid having more than a four-digit number (29769).

As you can see in the map above, the predicted shadow path was quite a ways northwest of my location.  Even though I used the Gaia DR2 position for UCAC4 359-140328 for the path prediction, the existing orbital elements for asteroid 29769 did not yield a correspondingly accurate position for the asteroid.

Though a single chord across an asteroid does not give us any definitive information about its overall size and shape, it does give us a very accurate astrometric position that will be used to improve the orbital elements for this asteroid.

The central moment of this occultation event was 6:00:02.414 UT on May 29, 2018, which was about 20 seconds later than predicted.  The astrometric equatorial coordinates for the star UCAC4 359-140328 referenced to the J2000 equinox (using Gaia DR2 with proper motion applied) are

UCAC4 359-140328
α = 18h 21m 01.6467
δ = -18° 20′ 46.282″

Using JPL Horizons (with the extra precision option selected), the astrometric equatorial coordinates for the asteroid 29769 (1999 CE28), again referenced to the J2000 equinox, are

29769 (1999 CE28)
α = 18h 21m 01.6388
δ = -18° 20′ 46.320″

As we can see above, the actual position of the asteroid at the time of the event was 0.0079 seconds of time east and 0.038 seconds of arc north of its predicted position.  This observation will provide a high quality astrometric data point for the asteroid that will be used to improve its orbit.  Gratifying!

As of this writing, there are 523,584 minor planets that have sufficiently well enough determined orbits to have received a number.  Of these, only 21,348 have received names (4.1%).  So, I guess you could say there is quite a backlog of numbered asteroids awaiting to receive names.  The IAU should consider naming some minor planets after the most productive asteroid occultation observers around the world.  There aren’t very many of us, and this would certainly be an encouragement to new and existing observers.

## Project Gutenberg

Over 56,000 historical books and other documents, most published prior to 1923, are available online for downloading or browsing at Project Gutenberg (http://www.gutenberg.org), with more being added all the time. A quick search of the term “astronomy” yields the following:

The Discovery of a World in the Moone: Or, A Discovrse Tending To Prove That ‘Tis Probable There May Be Another Habitable World In That Planet (1638)
John Wilkins (1614-1672)

The Study of Astronomy, Adapted to the capacities of youth (1796)
John Gabriel Stedman (1744-1797)

The Martyrs of Science, or, The lives of Galileo, Tycho Brahe, and Kepler (1841)
David Brewster (1781-1868)

Lectures on Astronomy (1854)
The Wit and Humor of America, Volume V. (1911)
George Horatio Derby (1823-1861), writing under the name of John Phoenix
Marshall Pinckney Wilder (1859-1915), editor

Letters on Astronomy: In which the Elements of the Science are Familiarly Explained in Connection with Biographical Sketches of the Most Eminent Astronomers (1855)
Denison Olmsted (1791-1859)

The Uses of Astronomy: An Oration Delivered at Albany on the 28th of July, 1856 (1856)
Edward Everett (1794-1865)

Cosmos: A Sketch of the Physical Description of the Universe, Vol. 1 (1858)
Alexander von Humboldt (1769-1859)

Curiosities of Science, Past and Present: A Book for Old and Young (1858)
John Timbs (1801-1875)

Astronomy for Young Australians (1866)
James Bonwick (1817-1906)

Meteoric astronomy: A treatise on shooting-stars, fire-balls, and aerolites (1867)
Daniel Kirkwood (1814-1895)

Popular Books on Natural Science: For Practical Use in Every Household, for Readers of All Classes (1869)
Aaron David Bernstein (1812-1884)

Half-hours with the Telescope: Being a Popular Guide to the Use of the Telescope as a Means of Amusement and Instruction (1873)
Richard Anthony Proctor (1837-1888)

Astronomical Myths: Based on Flammarions’s “History of the Heavens” (1877)
John Frederick Blake (1839-1906)
Camille Flammarion (1842-1925)

New and Original Theories of the Great Physical Forces (1878)
Henry Raymond Rogers (1822-1901)

Recreations in Astronomy: With Directions for Practical Experiments and Telescopic Work (1879)
Henry White Warren (1831-1912)

The Sidereal Messenger of Galileo Galilei and a Part of the Preface to Kepler’s Dioptrics Containing the Original Account of Galileo’s Astronomical Discoveries (1880)
Galileo Galilei (1564-1642)
Johannes Kepler (1571-1630)
Edward Stafford Carlos ((1842–1927), translator

Sir William Herschel: His Life and Works (1880)
Edward Singleton Holden (1846-1914)

Popular Scientific Recreations in Natural Philosophy, Astronomy, Geology, Chemistry, etc., etc., etc. (1881)
Gaston Tissandier (1843-1899)

Publications of the Astronomical Society of the Pacific, Volume 1 (1889)
Astronomical Society of the Pacific (1889-)

A Textbook of General Astronomy for Colleges and Scientific Schools (1889)
Charles Augustus Young (1834-1908)

Time and Tide: A Romance of the Moon (1889)
Robert Stawell Ball (1840-1913)

Astronomy with an Opera-glass: A Popular Introduction to the Study of the Starry Heavens with the Simplest of Optical Instruments (1890)
Garrett Putman Serviss (1851-1929)

Pioneers of Science (1893)
Sir Oliver Joseph Lodge (1851-1940)

Great Astronomers (1895)
Robert Stawell Ball (1840-1913)

The Astronomy of Milton’s ‘Paradise Lost’ (1896)
Thomas Nathaniel Orchard, M.D.

Myths and Marvels of Astronomy (1896)
Richard Anthony Proctor (1837-1888)

The Story of Eclipses (1899)
George Frederick Chambers (1841-1915)

The Tides and Kindred Phenomena in the Solar System: The Substance of Lectures Delivered in 1897 at the Lowell Institute, Boston, Massachusetts (1899)
Sir George Howard Darwin (1845-1912)

The Royal Observatory, Greenwich: A Glance at Its History and Work (1900)
Edward Walter Maunder (1851-1928)

The Story of the Heavens (1900)
Robert Stawell Ball (1840-1913)

Other Worlds: Their Nature, Possibilities and Habitability in the Light of the Latest Discoveries (1901)
Garrett Putman Serviss (1851-1929)

Pleasures of the telescope: An Illustrated Guide for Amateur Astronomers and a Popular Description of the Chief Wonders of the Heavens for General Readers (1901)
Garrett Putman Serviss (1851-1929)

A Text-Book of Astronomy (1903)
George Cary Comstock (1855-1934)

Astronomical Discovery (1904)
Herbert Hall Turner (1861-1930)

A New Astronomy (1906)
David Peck Todd (1855-1939)

New Theories in Astronomy (1906)
William Stirling (1822-1900)

Side-Lights on Astronomy and Kindred Fields of Popular Science (1906)
Simon Newcomb (1835-1909)

The Children’s Book of Stars (1907)
Geraldine Edith Mitton (1868-1955)

Mathematical Geography (1907)
Willis Ernest Johnson (1869-1951)

Astronomical Instruments and Accessories (1908)
William Gaertner and Company (1896-)
now Gaertner Scientific Corporation

The Astronomy of the Bible: An Elementary Commentary on the Astronomical References of Holy Scripture (1908)
Edward Walter Maunder (1851-1928)

A Popular History of Astronomy During the Nineteenth Century, Fourth Edition (1908)
Agnes Mary Clerke (1842-1907)

Astronomical Curiosities: Facts and Fallacies (1909)
John Ellard Gore (1845-1910)

The Future of Astronomy (1909)
Edward Charles Pickering (1846-1919)

History of Astronomy (1909)
George Forbes (1849-1936)

Astronomy for Amateurs (1910)
Camille Flammarion (1842-1925)

Astronomy of To-day: A Popular Introduction in Non-Technical Language (1910)
Cecil Goodrich Julius Dolmage (1870-1908)

The World’s Greatest Books — Volume 15 — Science (1910)
Arthur Mee (1875-1943), editor
Sir John Alexander Hammerton (1871-1949), editor

The Science of the Stars (1912)
Edward Walter Maunder (1851-1928)

Are the Planets Inhabited? (1913)
Edward Walter Maunder (1851-1928)

Woman in Science: With an Introductory Chapter on Woman’s Long Struggle for Things of the Mind (1913)
John Augustine Zahm (1851-1921), writing under the name H. J. Mozans

A Field Book of the Stars (1914)
William Tyler Olcott (1873-1936)

An Introduction to Astronomy (1916)
Forest Ray Moulton (1872-1952)

Scientific Papers by Sir George Howard Darwin. Volume V. Supplementary Volume (1916)
Sir George Howard Darwin (1845-1912)
Ernest William Brown (1866-1938), contributor
Sir Francis Darwin (1848-1925), contributor

The gradual acceptance of the Copernican theory of the universe (1917)
Dorothy Stimson (1890-1988)

Astronomical Lore in Chaucer (1919)
Florence Marie Grimm

Lectures on Stellar Statistics (1921)
Carl Vilhelm Ludwig Charlier (1862-1934)

The Star People (1921)
Gaylord Johnson

Terrestrial and Celestial Globes Volume 1: Their History and Construction Including a Consideration of their Value as Aids in the Study of Geography and Astronomy (1921)
Edward Luther Stevenson (1858-1944)

Terrestrial and Celestial Globes Volume 2: Their History and Construction Including a Consideration of their Value as Aids in the Study of Geography and Astronomy (1921)
Edward Luther Stevenson (1858-1944)

Astronomy for Young Folks (1922)
Isabel Martin Lewis (1881-1966)

Astronomy: The Science of the Heavenly Bodies (1922)
David Peck Todd (1855-1939)

The New Heavens (1922)
George Ellery Hale (1868-1938)

Watchers of the Sky (1922)
Alfred Noyes (1880-1958)

Biography of Percival Lowell (1935)
Abbott Lawrence Lowell (1856-1943)

## Like Sun, Like Moon

The Earth orbits the Sun once every 365.256363 (mean solar) days relative to the distant stars.  The Earth’s orbital speed ranges from 18.2 miles per second at aphelion, around July 4th, to 18.8 miles per second at perihelion, around January 3rd.  In units we’re perhaps more familiar with, that’s 65,518 mph at aphelion and 67,741 mph at perihelion. That’s a difference of 2,223 miles per hour!

As we are on a spinning globe, the direction towards which the Earth is orbiting is different at different times of the day.  When the Sun crosses the celestial meridian, due south, at its highest point in the sky around noon (1:00 p.m. daylight time), the Earth is orbiting towards your right (west) as you are facing south. Since the Earth is orbiting towards the west, the Sun appears to move towards the east, relative to the background stars—if we could see them during the day.  Since there are 360° in a circle and the Earth orbits the Sun in 365.256363 days (therefore the Sun appears to go around the Earth once every 365.256363 days relative to the background stars), the Sun’s average angular velocity eastward relative to the background stars is 360°/365.256363 days = 0.9856° per day.

The constellations through which the Sun moves are called the zodiacal constellations, and historically the zodiac contained 12 constellations, the same number as the number of months in a year.  But Belgian astronomer Eugène Delporte (1882-1955) drew up the 88 constellation boundaries we use today, approved by the IAU in 1930, so now the Sun spends a few days each year in the non-zodiacal constellation Ophiuchus, the Serpent Bearer. Furthermore, because the Earth’s axis is precessing, the calendar dates during which the Sun is in a particular zodiacal constellation is gradually getting later.

Astrologically, each zodiacal constellation has a width of 30° (360° / 12 constellations = 30° per constellation).  But, of course, the constellations are different sizes and shapes, so astronomically the number of days the Sun spends in each constellation varies. Here is the situation at present.

Constellation
Description
Sun Travel Dates
Capricornus
Sea Goat
Jan 19 through Feb 16
Aquarius
Water Bearer
Feb 16 through Mar 12
Pisces
The Fish
Mar 12 through Apr 18
Aries
The Ram
Apr 18 through May 14
Taurus
The Bull
May 14 through Jun 21
Gemini
The Twins
Jun 21 through Jul 20
Cancer
The Crab
Jul 20 through Aug 10
Leo
The Lion
Aug 10 through Sep 16
Virgo
The Virgin
Sep 16 through Oct 31
Libra
The Scales
Oct 31 through Nov 23
Scorpius
The Scorpion
Nov 23 through Nov 29
Ophiuchus
Serpent Bearer
Nov 29 through Dec 18
Sagittarius
The Archer
Dec 18 through Jan 19

The apparent path the Sun takes across the sky relative to the background stars through these 13 constellations is called the ecliptic.  A little contemplation, aided perhaps by a drawing, will convince you that the ecliptic is also the plane of the Earth’s orbit around the Sun.  The Moon never strays very far from the ecliptic in our sky, since its orbital plane around the Earth is inclined at a modest angle of 5.16° relative to the Earth’s orbital plane around the Sun.  But, relative to the Earth’s equatorial plane, the inclination of the Moon’s orbit varies between 18.28° and 28.60° over 18.6 years as the line of intersection between the Moon’s orbital plane and the ecliptic plane precesses westward along the ecliptic due to the gravitational tug of war the Earth and the Sun exert on the Moon as it moves through space.  This steep inclination to the equatorial plane is very unusual for such a large moon.  In fact, all four satellites in our solar system that are larger than our Moon (Ganymede, Titan, Callisto, and Io) and the one that is slightly smaller (Europa) all orbit in a plane that is inclined less than 1/2° from the equatorial plane of their host planet (Jupiter and Saturn).

Since the Moon is never farther than 5.16° from the ecliptic, its apparent motion through our sky as it orbits the Earth mimics that of the Sun, only the Moon’s angular speed is over 13 times faster, completing its circuit of the sky every 27.321662 days, relative to the distant stars.  Thus the Moon moves a little over 13° eastward every day, or about 1/2° per hour.  Since the angular diameter of the Moon is also about 1/2°, we can easily remember that the Moon moves its own diameter eastward relative to the stars every hour.  Of course, superimposed on this motion is the 27-times-faster-yet motion of the Moon and stars westward as the Earth rotates towards the east.

Now, take a look at the following table and see how the Moon’s motion mimics that of the Sun throughout the month, and throughout the year.

——— Moon’s Phase and Path ———
Date
Sun’s Path
New
FQ
Full
LQ
Mar 20
EQ
EQ
High
EQ
Low
Jun 21
High
High
EQ
Low
EQ
Sep 22
EQ
EQ
Low
EQ
High
Dec 21
Low
Low
EQ
High
EQ

New = New Moon
near the Sun
FQ = First Quarter
90° east of the Sun
Full = Full Moon
180°, opposite the Sun
LQ = Last Quarter
90° west of the Sun

EQ
= crosses the celestial equator heading north
High
= rides high (north) across the sky
EQ
= crosses the celestial equator heading south
Low
= rides low (south) across the sky

So, if you aren’t already doing so, take note of how the Moon moves across the sky at different phases and times of the year.  For example, notice how the full moon (nearest the summer solstice) on June 27/28 rides low in the south across the sky.  You’ll note the entry for the “Jun 21” row and “Full” column is “Low”.  And, the Sun entry for that date is “High”.  See, it works!