Video Meteors 2020 – I

During the first half of 2020, I serendipitously captured a whopping nine meteors on my telescope’s 17 x 11 arcminute video field of view while observing potential asteroid occultation events. I used the method described in There’s a Meteor in My Image to determine the radiant for each meteor. Here they are.

Antihelion meteor 22 March 2020 UT; Field location UCAC4 575-024067 in Gemini
Each frame is an exposure of 0.53s

The International Meteor Organization (IMO) identifies the antihelion source as “a large, roughly oval area of about 30˚ in right ascension and 15˚ in declination, centered about 12˚ east of the solar opposition point on the ecliptic, hence its name. It is not a true shower at all, but is rather a region of sky in which a number of variably, if weakly, active minor showers have their radiants.”

Sporadic meteor 10 Apr 2020 UT, Field location HD 119307 in Centaurus
Each frame is an exposure of 0.13s

A sporadic meteor is any meteor that does not come from a known radiant.

Sporadic meteor 14 Apr 2020 UT, Field location UCAC4 387-065649 in Libra
Each frame is an exposure of 0.27s (faint meteor in the upper right corner)
Possible Eta Aquariid meteor 28 April 2020 UT; Field location UCAC4 326-064938 in Corvus
Each frame is an exposure of 0.13s
Sporadic meteor or satellite? 8 May 2020 UT; Field location UCAC4 345-084929 in Ophiuchus
Each frame is an exposure of 0.03s

Meteors enter the Earth’s atmosphere at a speed between 10 and 70 km/s, and burn up at an altitude of about 80 km. For a sight line perpendicular to the meteor’s path, the angular velocity should range between 7˚ and 41˚ per second. This means a meteor should cross the 17′ x 11′ field of my video camera in 0.03 seconds or less. Field traversal will take longer than this the closer the meteor is to its radiant or anti-radiant point.

The lowest stable altitude a satellite can orbit is about 200 km, where it will have an orbital velocity on the order of 8 km/s. This is slower than the slowest meteors. For a sight line perpendicular to the satellite’s path, the maximum angular velocity a satellite should have is about 2˚ per second.

Given these admittedly BOTEC calculations, one could reasonably conclude that if the object traverses the field in a single frame, it is probably a meteor. If not (and it is not an airplane), it is a satellite.

The object in the 8 May 2020 video does appear to be moving slow enough to be a satellite, but because it is traveling much faster than satellites usually do it must be orbiting quite low, close to re-entry. I was not able to identify the satellite, which is often the case for the fastest-moving satellites. My camera is sensitive enough to pick up tiny pieces of space debris orbiting at low altitude, and though these objects are no doubt catalogued by military organizations, they do not generally show up in the publicly-available orbital element datasets for satellites.

Antihelion meteor or satellite? 12 May 2020 UT; Field location UCAC4 585-130160 in Pegasus
Each frame is an exposure of 0.27s

This one’s unusual in that there are two distinct “flare-ups” along the path. It is reasonably good match to the antihelion radiant for 12 May 2020, and though I have seen meteors experiencing outbursts along their paths, a more likely explanation for this event is that it is low altitude satellite with two “sun glint” events. What do you think?

Sporadic meteor 13 May 2020 UT; Field location UCAC4 348-150732 in Sagittarius
Each frame is an exposure of 0.53s
Antihelion meteor 17 June 2020 UT; Field location UCAC4 294-088825 in Lupus
Each frame is an exposure of 1.07s
Sporadic meteor 18 June 2020 UT; Field location UCAC4 330-150629 in Sagittarius
Each frame is an exposure of 0.53s

I was surprised to record so many meteors during the first half of 2020, as there is generally much less meteor activity between January and June than there is between July and December.

References

International Meteor Organization, 2o2o Meteor Shower Calendar, Jürgen Rendtel, ed. https://www.imo.net/files/meteor-shower/cal2020.pdf.

Mirador Astronomy Village

Photo by John Rummel, Madison WI

Since the beginning of February, I have been able dedicate 10+ hours each week towards creating an astronomy-friendly community called Mirador Astronomy Village. Will you join me in that effort?

Here’s the “placeholder” website:

https://miradorastrovillage.org/

And here are some recent posts I’ve made to Dark-Sky-Communities on groups.io (https://dark-sky-communities.groups.io/g/main) to give you an idea where we’re currently at with this exciting project.

Acquiring Land for Mirador Astronomy Village

The Mirador specifications document located in our Files section and here gives a lot of detail about our vision for an astronomy-friendly residential community and astronomy resort & learning center. But before any of this can be developed, we need to have land.

The next step for Mirador is to create a legal entity that can raise money for a land purchase.

Some challenges we face:

  • Mirador could be located in Arizona, New Mexico, or West Texas. We don’t want to limit our land search to one state, but incorporating in the state where land will be purchased is less complicated.
  • We need an attorney who is familiar with Arizona, New Mexico, and West Texas law, but especially with real estate law and corporate law.
  • Does anyone know an attorney who is interested in astronomy, might want to become involved with this project, and might be willing to do some pro bono work?
  • Does anyone know a fundraising professional who is interested in astronomy and might want to become involved with this project?

Our most immediate need is to find an attorney to help us create the legal entity that will be necessary to raise money for a land purchase. This legal entity will exist for one and only one purpose: to purchase land for Mirador Astronomy Village.

Here is what we currently envision for the land-purchase legal entity. Would appreciate your thoughts before we submit this to a prospective attorney.


Land Purchase

Issuance of Shares

  • 1 share = $1000
  • No limit on the number of shares that can be purchased
  • Initial shares and additional shares can be purchased at any time
  • Hold the money in an FDIC-insured interest-bearing account
  • Value of shares remains unchanged except for interest accrued
  • Shareholders can return shares and remove their investment (plus interest) at any time up through the point of the shareholders voting in favor of making an offer on a property but before an offer is actually made
  • 1 share = 1 vote
  • Funds can only be used to purchase a property for Mirador Astronomy Village; any leftover funds will be returned to the shareholders proportional to the number of shares they own.
  • If there are insufficient funds to purchase the property without financing, the shareholders will not be a party to that financing arrangement.
  • It is possible we may acquire land that is “partially donated”, that is the land owner may agree to sell us the land for the amount of funds we have raised to date.
  • Shareholders will be known as Community Founders.
  • After the property is purchased, the monetary value of the shares goes to $0.
  • Benefits for shareholders after the property is purchased will include free RV, camping, and astronomy access to the property as soon as it is acquired; after development, no-additional-cost benefits such as free access to astronomy programs will be offered.
  • Benefits will be proportional to the number of shares owned.
  • If Mirador Astronomy Village isn’t established on the property within five years, the property will be sold and the proceeds returned to the shareholders in proportion to the number of shares they own.

Some Reasons Why I Want to Live in a Dark-Sky Community

Posted 13 July 2020

I drove 20 miles round-trip early Saturday morning to view Comet NEOWISE (C/2020 F3) for the first time. It is beautiful! Easily visible to the unaided eye and spectacular in binoculars. And now, in the more convenient evening sky!

I had to trespass onto private land (as I often do) because we are not allowed to be in any of our state parks here in Wisconsin during the hours of 11:00 p.m. to 6:00 a.m. (unless you are a paid camper at a campsite).

One of my motivations for living in a dark-sky community is having a great view of a comet like C/2020 F3 literally right outside my door night after night. The same goes for watching meteors. The visibility of comets and meteors are severely impacted by light pollution—both the general urban skyglow but also nearby lights. Along with just about every other aspect of observational astronomy.

All my adult life I have spent significant time and energy educating (and becoming educated myself) about light pollution, environmentally-friendly lighting, and, of course, astronomy. There have been small victories, yes, but overall I feel my contributions have been a drop in the proverbial bucket.

Living in a “regular community” (as I have all my life), there is always the trepidation with every new neighbor or lighting technology change that your view of the night sky will be degraded even further than it already has, and there is not a darned thing you can do about it if the perpetrator (be it a neighbor or the city) chooses to marginalize you and your kindly-presented concerns. Heck, this can even be a problem living in a rural area. When I had my Outdoor Lighting Associates, Inc. business in Iowa from 1994-2005, I can’t count the many times I got a call from a distressed rural resident that had a new neighbor who decided to light up their place like Las Vegas.

Sure, a lighting ordinance would help a lot, but in most cities and towns these days they’ll look at you like you’re from Mars if you try to make enacting one a priority.

There are many advantages to living in a small community, but where I live now (population 4,700) there is no community will nor interest in reigning in bad lighting or in protecting the night sky. However, in 1999 I was deeply involved with writing a lighting ordinance and getting it approved in Ames, Iowa, a university town of 50,000 (at the time). Being a well-educated university town had a lot to do with our success there. Those were kinder, gentler times then, too.


Lighting at Mirador

I’d like to take this opportunity to explain more about the outdoor lighting aspects of an “astronomy-friendly” community. Indoor lighting would have no restrictions except the amount of light shining outdoors at night would need to be controlled with some sort of window covering.

Ideally, an astronomy-friendly community would not allow any dusk-to-dawn lighting. Why have a light shining all night long when most of the night no one will be making use of its illumination? Modern light sources such as LEDs, occupancy sensors, and control electronics have advanced to the point (both in terms of technology and affordability) that dusk-to-dawn lighting is no longer needed, at least not in the kind of small community we are talking about here. I would like Mirador Astronomy Village to be an ongoing demonstration project for the wider world showing a better way to do outdoor lighting. By “better” I mean lighting that provides needed illumination where and when it is needed without adversely affecting the nighttime environment, including our view of the night sky. By “better” I also mean using passive reflective or light-colored materials where possible to reduce the need for—or brightness of—outdoor lighting.

There’s a lot to be said in favor of using “personal lighting devices”, also known as flashlights, when walking about at night.

The permanent outdoor lighting that is installed should be properly shielded and directed so that only what needs to be illuminated is illuminated, thus eliminating glare, light trespass, and direct uplight. The right amount of light for the intended task should be used, never more than is needed.

We certainly will need to be mindful of anyone visiting or living in our community with vision limitations. This is most likely going to be an issue in the areas open to the public at night. Observational astronomers, as a general rule, have learned to see better at low illumination levels through familiarity and experience, but the same is not true for the general public. Accommodations will need to be made with this in mind, and I would expect the public areas to have more illumination.


Getting this project off the ground has been challenging in the midst of a pandemic. There is at least one of several things you can do right now to help this project along.

  1. Post a comment here!
  2. Join the Dark-Sky-Communities discussion group at https://dark-sky-communities.groups.io/g/main. There are several subscription options for your convenience, and even if you subscribe to receive individual emails, the traffic on this moderated group is light and focused specifically on astronomy-friendly residential communities.
  3. Visit the Mirador Astronomy Village website.
  4. Take the time to read through the detailed Mirador Astronomy Village specifications document.
  5. Send me an email at DaveDarkSky@mac.com or call me at 608-930-2120 to discuss.
  6. Spread the word! There may be only a half a dozen people in the United States who can help me to make Mirador Astronomy Village a reality. How do I reach them?

Thank you!

Photo by John Rummel, Madison WI

Comet NEOWISE (C/2020 F3)

Finally, a bright comet! Comet C/2020 F3 NEOWISE was discovered on March 27, 2020 by the NEOWISE space telescope. NEOWISE (Near-Earth Object Wide-field Infrared Survey Explorer) is the current extended “warm” mission of WISE after its hydrogen coolant became depleted.

Currently visible in the morning twilight sky, Comet NEOWISE is already a naked-eye object and is spectacular in binoculars, low in the NE, below and a little to the left of the bright star Capella. Soon it will be moving into the evening sky, though it is expected to diminish in brightness somewhat as it gets further from the Sun. Here’s an ephemeris for Comet NEOWISE for July and August showing when it will be at least 10˚ above the horizon in a sky that is not brightened by either twilight or moonlight. Avoiding light pollution, however, is up to you. Enjoy!

Comet naming these days is a mess! For one, some of the acronyms used for the automated surveys that discover them are unattractive. Thank heavens neither of the two comets named ASASSN (C/2017 O1 and C/2018 N2) ever became as bright as our current comet!

There were three comets NEOWISE in 2014, three in 2015, three in 2016, one in 2017, two in 2018, two in 2019, and one (so far) in 2020.

Comet NEOWISE

C/2014 C3
P/2014 L2
C/2014 N3
P/2015 J3
C/2015 X8
C/2015 YG1
C/2016 B1
C/2016 C2
C/2016 U1
C/2017 C1
C/2018 EN4
C/2018 N1
C/2019 H1
C/2019 L2
C/2020 F3

Might I suggest that we give this year’s first NEOWISE comet the following name?

Comet NEOWISE 15 (C/2020 F3)

Comet NEOWISE (C/2020 F3) 19 July 2020 3:21:59 UT 30s 55 mm f/4 ISO 1600 Canon EOS 100D
Photo by David Oesper
Comet NEOWISE (C/2020 F3) 20 July 2020 3:38:57 UT 3m 55 mm f/4.5 ISO 1600 Canon EOS 100D
Photo by David Oesper
Comet NEOWISE (C/2020 F3) 23 July 2020 3:22:17 UT 2m 55 mm f/4 ISO 1600 Canon EOS 100D
Photo by David Oesper

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 this weekend, is one such shower. The expected worldwide peak this year is Saturday, June 27 around 5 p.m. CDT. Though the radiant is above the horizon all night, the best two hours to watch will be from around 1:00 to 3:00 a.m. Sunday morning. (Moonset is at 1:11 a.m. and morning twilight begins at 3:06 a.m. at Dodgeville, CDT.)

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. Enjoy the process, even if you don’t see any meteors. The weather is pleasant at night this time of year, so get out there and observe!

Geostationary Satellite Declinations

A few years ago, I was doing some telescope sweeping of the meridian sky around declination -6˚ when, to my surprise and delight, a 10th- or 11th-magnitude slow-moving object entered my field of view. As it slowly traversed eastward through the field, I remembered the declination I was pointed to and realized that it must be a geostationary, or at least a geosynchronous, satellite. Centering the moving object and then turning off the telescope’s clock drive confirmed my suspicions. The object was a geosynchronous satellite because it appeared to lay motionless while all the stars in the field drifted toward the west. Serendipity is the spice of life!

Satellites stationed in orbits that are always directly above the Earth’s equator and that have an orbital period of 23h 56m 04.0905s (one sidereal day) have the interesting property of remaining stationary as seen from any point on the surface of the Earth. This property of geostationary satellites, as they are called, is used to great advantage by many communications and weather satellites. There are currently at least 554 satellites in geosynchronous orbits. They are stationed all around the Earth at various longitudes.

At what altitude do geostationary satellites orbit the Earth? It is well above human-occupied spacecraft like the International Space Station which currently orbits 260 miles above the Earth’s surface. Geosynchronous orbit lies some 22,236 miles above the Earth’s equator. This is quite a ways out, as the entire Earth subtends an angle of only 17° 12′ at this distance—about the same as the angular distance between Capella (α Aur) and Elnath (β Tau).

Looking at it another way, geostationary satellites orbit at an altitude that is 2.8 Earth diameters above the equator. Since the Moon orbits at a distance that ranges between 27.4 and 31.4 Earth diameters above the Earth’s surface, geosynchronous orbit is about 1/10 of the way to the Moon.

If you have a telescope, know where to point it, and turn tracking off, you can see a geostationary satellite as a stationary point of light while the stars drift by due to the Earth’s rotation. At our latitude here in southern Wisconsin (43° N), the area where you want to search for geostationary satellites (near the meridian) is around declination -6° 37′. Remember, declination tells you how many degrees above or below the celestial equator an object is, and the numbers range from -90° to +90°, the south celestial pole and north celestial pole, respectively. The celestial equator has a declination of 0°.

For any latitude1, the declination you want to search is given by

\delta _{gs}=\textup{tan}^{-1}\left [ 6.611\textup{ csc }\phi - \textup{cot }\phi \right ]-90^{\circ}

where δgs is the declination of the geostationary satellite in degrees
     and ϕ is your latitude in degrees

Since most calculators don’t have the cosecant (csc) or cotangent (cot) functions, this formula can be rewritten in a slightly more complicated form as

\delta _{gs}=\textup{tan}^{-1}\left [ \frac{6.611}{\textup{sin }\phi }-\frac{1}{\textup{tan }\phi } \right ]-90^{\circ}

Why aren’t the satellites right on the celestial equator (δ = 0°)? They would be if they were millions of miles away or if we were located on the Earth’s equator, but at our northern latitude trigonometric parallax causes us to see the satellites somewhat below the celestial equator, relative to the distant stars.

What if the geostationary satellite is situated east or west of your meridian? How do you calculate its declination then? As you might expect, because the range (observer-to-satellite distance) is greater the further from the meridian the satellite is, the less the parallax is, and therefore the closer the declination is to the equator, though not by a lot. The declination is also symmetric about the meridian, east and west: a geostationary satellite one hour east of the meridian will have the same declination as another geostationary satellite one hour west of the meridian.

If you know the longitude of the geostationary satellite (for example, the GOES-16 weather satellite is stationed above 75.2˚ W longitude), you can calculate its declination (and right ascension) using the following two-step process.

\textup{h}=\textup{tan}^{-1}\left [ \frac{\textup{sin }\Delta\lambda  }{\textup{cos }\Delta \lambda-0.15126\textup{ cos }\phi  } \right ]

where h is the hour angle in degrees
     and Δλ = λsat − λobs , the difference between the satellite and observer
          longitudes, in degrees
     and ϕ is the latitude of the observer in degrees

\delta _{gs}=\textup{tan}^{-1}\left [ \frac{-0.15126\textup{ sin }\phi \textup{ sin h}}{\textup{sin }\Delta \lambda } \right ]

To determine the right ascension of the geostationary satellite, add the value of h to your local sidereal time (the right ascension of objects on your meridian). Make sure you convert h to hours before adding it to your LST.

What if you want to calculate the geostationary declination at a particular hour angle? That is a bit trickier. I could not figure out how to manipulate the equation for h above so that Δλ = f (h,φ). Instead, I rewrote the equation as

\sin \Delta \lambda =\tan h\cdot \left ( \cos \Delta \lambda -0.15126\cos \phi  \right )

and using h as a starting value for Δλ, substituted it into the cos Δλ expression, calculated sin Δλ, took the arcsine to get a new value of Δλ, then substituted that back into the cos Δλ expression, and iterated. Fortunately, the value of Δλ converges very fast. Once you have Δλ, you can use the two-step process we used earlier to determine the declination of the geostationary satellite for a particular hour angle.

Please note that the value of the hour angle h we use here is positive east of the meridian and negative west of the meridian. This is opposite from the normal astronomical sense.

Here is a simple SAS program illustrating how to do all these calculations using a computer.

And here is the output from that program.

1 For latitudes south of the equator, add 180° to get your meridian geostationary declination. The equation goes singular at the equator (φ=0°) and at the poles (φ=90° N and 90° S) since we’re dividing by sin φ = 0 at the equator and tan φ is undefined at the poles. However, as you asymptotically get closer and closer to latitude 0° (0.0001° and -0.0001°, for example) you find that the meridian geostationary declination approaches δ = 0°. Likewise, as you asymptotically approach latitude 90° N and 90° S, you’ll find that the meridian geostationary declination approaches -8°36′ and +8°36′, respectively. Of course, in both cases the geostationary satellites always remain below your horizon. How far north or south in latitude would you have to go, then, to find that geostationary satellites on your meridian are on your horizon due south or due north, respectively? Through a little algebraic manipulation of the first equation above and utilizing some simple trigonometric identities, one finds that at latitudes 81°18′ N and 81°18′ S, geostationary satellites on your meridian would be on the horizon. North or south of there, respectively, you would not be able to see them because the Earth would be in the way.

References

Gérard Maral, Michel Bousquet, Zhili Sun. Satellite Communications Systems: Systems, Techniques and Technology, Fifth Edition. Wiley, 2009. See section 8.3.6.3 Polar mounting.

The Lunar Equator

The equator of the Moon is defined by its rotational axis. It is the great circle contained by the plane that is perpendicular to the line connecting the north and south poles of the Moon.

Map of the Moon (nearside) with selenographic coordinate lines (latitude and longitude)

Here is a list of named lunar features through which the Moon’s equator passes, from lunar east to lunar west on the part of the Moon visible from the Earth.

Remember, lunar longitude is opposite the direction in the sky. East longitude is the west/right side of the moon, and west longitude is the east/left side of the moon as viewed from the northern hemisphere of the Earth.

The diameter of each feature is included, followed by the depth of the feature, where available.

Crater Wyld
Wyld
Center: 98.101˚ E, 1.416˚ S
Range: 96.395˚ - 99.806˚ E, 3.121˚ S - 0.289˚N
Crater; libration zone
58 mi
James Hart Wyld (1913-1953), American rocket engineer
Wrinkle ridge Dorsum Cloos
Dorsum Cloos
Center: 90.410˚ E, 1.149˚ N
Range: 90.387˚ - 91.144˚ E, 0.268˚ S - 2.576˚ N
Wrinkle ridge; libration zone
64 mi
Hans Cloos (1885-1951), German geologist
Mare Smythii, “Smyth’s Sea”
Mare Smythii
Center: 87.049˚ E, 1.709˚ S
Range: 80.941˚ - 92.719˚ E, 7.456˚ S - 4.496˚ N
Mare; libration zone; Smyth's Sea
232 mi, 3.1 mi
William Henry Smyth (1788-1865), English naval officer and astronomer
Craters Schubert J, Jenkins, Schubert X, and Nobili
Schubert J
Center: 78.935˚ E, 0.012˚ S
Range: 78.579˚ - 79.292˚ E, 0.344˚ S - 0.320˚ N
Crater
12 mi
Friedrich Theodor von Schubert (1758-1825), German astronomer & geographer 
Jenkins
Center: 78.041˚ E, 0.372˚ N
Range: 77.418˚ - 78.663˚ E, 0.251˚ S - 0.994˚ N
Crater
24 mi, 1.9 mi
Louise Freeland Jenkins (1888-1970), American astronomer
Schubert X
Center: 76.750˚ E, 0.310˚ N
Range: 75.940˚ - 77.561˚ E, 0.501˚ S - 1.121˚ N
Crater
32 mi
Friedrich Theodor von Schubert (1758-1825), German astronomer & geographer
Nobili
Center: 75.949˚ E, 0.166˚ N
Range: 75.260˚ - 76.638˚ E, 0.523˚ S - 0.855˚ N
Crater
26 mi, 2.4 mi
Leopoldo Nobili (1784-1835), Italian physicist
Craters Maclaurin X and Maclaurin O
Maclaurin X
Center: 68.708˚ E, 0.091˚ N
Range: 68.403˚ - 69.014˚ E, 0.214˚ S - 0.397˚ N
Crater
15 mi
Colin Maclaurin (1698-1746), Scottish mathematician
Maclaurin O
Center: 67.557˚ E, 0.135˚ S
Range: 66.873˚ - 68.241˚ E, 0.819˚ S - 0.548˚ N
Crater
23 mi
Colin Maclaurin (1698-1746), Scottish mathematician
Mare Spumans, “The Foaming Sea”
Mare Spumans
Center: 65.303˚ E, 1.302˚ N
Range: 63.613˚ - 66.733˚ E, 1.062˚ S - 3.722˚ N
Mare
87 mi
The Foaming Sea
Crater Webb C
Webb C
Center: 63.833˚ E, 0.149˚ N
Range: 63.267˚ - 64.398˚ E, 0.247˚ S - 0.544˚ N
Crater
21 mi
Thomas William Webb (1807-1885), English astronomer
Sinus Successus, “Bay of Success”
Sinus Successus
Center: 58.520˚ E, 1.124˚ N
Range: 56.519˚ - 60.188˚ E, 0.861˚ S - 2.872˚ N
Bay
82 mi
Bay of Success
Mare Fecunditatis, “Sea of Fertility”
Mare Fecunditatis
Center: 53.669˚ E, 7.835˚ S
Range: 40.771˚ - 63.340˚ E, 21.695˚ S - 6.112˚ N
Mare
429 mi, 1.1 mi
Sea of Fertility
Craterlet Taruntius P is on the left (Taruntius K is at right)
Taruntius P
Center: 51.585˚ E, 0.060˚ N
Range: 51.473˚ - 51.696˚ E, 0.051˚ S - 0.172˚ N
Craterlet
5 mi, 0.9 mi
Lucius Tarutius Firmanus (fl. 86 B.C.), Roman philosopher, mathematician, and astrologer
Wrinkle ridge Dorsum Cayeux, with craterlets Taruntius P (left) and Taruntius K (right) in the lower left
Dorsum Cayeux
Center: 51.220˚ E, 0.763˚ N
Range: 50.922˚ - 52.000˚ E, 0.598˚ S - 2.113˚ N
Wrinkle ridge
59 mi
Lucien Cayeux (1864-1944), French sedimentary petrographer
Wrinkle ridges Dorsa Cato (north is to the right in this Apollo 11 view)
Dorsa Cato
Center: 47.701˚ E, 0.213˚ N
Range: 46.605˚ - 49.599˚ E, 1.165˚ S - 2.233˚ N
Wrinkle ridges
87 mi
Marcus Porcius Cato (234-149 B.C.), Roman soldier, senator, and historian
Rille Rima Messier
Rima Messier
Center: 44.545˚ E, 0.756˚ S
Range: 43.357˚ - 45.581˚ E, 1.561˚ S - 0.015˚ N
Rille
62 mi
Charles Messier (1730-1817), French astronomer
Crater Lubbock R
Lubbock R
Center: 40.453˚ E, 0.167˚ S
Range: 40.060˚ - 40.845˚ E, 0.559˚ S - 0.225˚ N
Crater
15 mi
Sir John William Lubbock (1803-1865), English banker, barrister, mathematician, and astronomer
Maskelyne T & Maskelyne A (click on image for higher resolution view)
Maskelyne T
Center: 36.593˚ E, 0.040˚ S
Range: 36.507˚ - 36.678˚ E, 0.125˚ S - 0.046˚ N
Craterlet
3 mi
Nevil Maskelyne (1732-1811), English astronomer
Maskelyne A
Center: 34.089˚ E, 0.032˚ N
Range: 33.603˚ - 34.574˚ E, 0.453˚ S - 0.517˚ N
Crater
18 mi
Nevil Maskelyne (1732-1811), English astronomer
Mare Tranquillitatis, “Sea of Tranquility”
Mare Tranquillitatis
Center: 30.835˚ E, 8.349˚ N
Range: 16.924˚ - 45.490˚ E, 4.051˚ S - 19.375˚ N
Mare
544 mi
Sea of Tranquility
Rimae Hypatia (two rilles)
Rimae Hypatia
Center: 22.777˚ E, 0.340˚ S
Range: 19.690˚ - 25.975˚ E, 1.406˚ S - 0.672˚ N
Rilles
128 mi
Hypatia (c.370-415), Alexandrian philosopher, mathematician, and astronomer
Craters Lade A and Lade B
Lade A
Center: 12.726˚ E, 0.161˚ S
Range: 11.773˚ - 13.680˚ E, 1.114˚ S - 0.793˚ N
Crater
35 mi
Heinrich Eduard von Lade (1817-1904), German banker and amateur astronomer
Lade B
Center: 9.796˚ E, 0.016˚ N
Range: 9.412˚ - 10.180˚ E, 0.368˚ S - 0.399˚ N
Crater
15 mi
Heinrich Eduard von Lade (1817-1904), German banker and amateur astronomer
Craters Rhaeticus F, Rhaeticus, and Rhaeticus L
Rhaeticus F
Center: 6.438˚ E, 0.060˚ S
Range: 6.134˚ - 6.742˚ E, 0.364˚ S - 0.244˚ N
Crater
11 mi
Georg Joachim Rheticus (1514-1574), Austria-born astronomer & mathematician
Rhaeticus
Center: 4.924˚ E, 0.032˚ N
Range: 4.192˚ - 5.657˚ E, 0.701˚ S - 0.764˚ N
Crater
30 x 27 mi, 1.0 mi
Georg Joachim Rheticus (1514-1574), Austria-born astronomer & mathematician
Rhaeticus L
Center: 3.484˚ E, 0.205˚ N
Range: 3.257˚ - 3.711˚ E, 0.022˚ S - 0.432˚ N
Crater
9 mi
Georg Joachim Rheticus (1514-1574), Austria-born astronomer & mathematician
Sinus Medii, “Bay of the Center”; this feature is closest to the center of the Moon as seen from Earth
Sinus Medii
Center: 1.027˚ E, 1.634˚ N
Range: 3.371˚ W - 5.551˚ E, 2.048˚ S - 4.641˚ N
Bay
178 mi
Bay of the Center
Crater Mösting E
Mösting E
Center: 4.591˚ W, 0.178˚ N
Range: 5.189˚ - 3.992˚ W, 0.421˚ S - 0.777˚ N
Crater
27 mi
Johan Sigismund von Møsting (1759-1843), Danish banker, finance minister, and astronomy enthusiast
Crater Sömmering
Sömmering
Center: 7.526˚ W, 0.193˚ N
Range: 7.987˚ - 7.065˚ W, 0.268˚ S - 0.654˚ N
Crater
17 mi, 0.8 mi
Samuel Thomas von Sömmering (1755–1830),German physician and anatomist
Crater Lansberg
Lansberg
Center: 26.627˚ W, 0.312˚ S
Range: 27.266˚ - 25.988˚ W, 0.951˚ S - 0.327˚ N
Crater
24 mi, 1.9 mi
Philippe van Lansbergen (1561-1632), Dutch astronomer and mathematician
Mare Insularum, “Sea of Islands”
Mare Insularum
Center: 30.640˚ W, 7.792˚ N
Range: 39.195˚ - 22.153˚ W, 0.596˚ S - 16.345˚ N
Mare
318 mi
Sea of Islands
Oceanus Procellarum, “Ocean of Storms”
Oceanus Procellarum
Center: 56.677˚ W, 20.671˚ N
Range: 81.084˚ - 26.850˚ W, 16.266˚ S - 57.433˚ N
Mare
1611 x 353 mi
Ocean of Storms
Crater Lohrmann D cut through by one of the rilles of Rimae Hevelius (arrow points to another part of Rimae Hevelius)
Lohrmann D
Center: 65.273˚ W, 0.141˚ S
Range: 65.442˚ - 65.104˚ W, 0.310˚ S - 0.028˚ N
Crater
7 mi
Wilhelm Gotthelf Lohrmann (1796-1840), German selenographer
Rimae Hevelius
Center: 66.377˚ W, 0.809˚ N
Range: 67.849˚ - 63.582˚ W, 1.284˚ S - 2.956˚ N
Rilles
113 mi
Johannes Hevelius (1611-1687), Polish astronomer
Crater Lohrmann
Lohrmann
Center: 67.383˚ W, 0.440˚ S
Range: 67.898˚ - 66.867˚ W, 0.955˚ S - 0.075˚ N
Crater
19 mi, 1.0 mi
Wilhelm Gotthelf Lohrmann (1796-1840), German selenographer
The lunar equator crosses the rilles of Rimae Riccioli just south of craters Riccioli C and Riccioli H.
Rimae Riccioli
Center: 73.071˚ W, 1.515˚ S
Range: 76.809˚ - 68.566˚ W, 4.754˚ S - 1.247˚ N
Rilles
249 mi
Giovanni Battista Riccioli (1598-1671), Italian astronomer
Crater Schlüter P
Schlüter P
Center: 85.208˚ W, 0.054˚ N
Range: 85.550˚ - 84.865˚ W, 0.289˚ S - 0.397˚ N
Crater; libration zone
12 mi
Heinrich Schlüter (1815-1844), German astronomer

Now that we’ve taken a tour of nearside features along the equator, let us turn to the lunar north and south celestial poles. As you know, the Earth’s north celestial pole (NCP) is currently located quite close to Polaris. However, on the Moon, the NCP is located in Draco near the Cat’s Eye Nebula (NGC 6543), about two-thirds of the way between Polaris and the center of the Head of Draco.

The Moon’s NCP is located near the Cat’s Eye Nebula (NGC 6543), a fine planetary nebula in Draco.

The Moon’s south celestial pole (SCP) is located in the constellation Dorado inside of the Large Magellanic Cloud (LMC). If you were stationed at the south pole of the Moon, you would see the Large Magellanic Cloud directly overhead at all times!

The Moon’s SCP is located in the constellation Dorado within the Large Magellanic Cloud.

The Moon has many fascinating places, tempting us to explore. Some of them have quite interesting names. One of my favorites is Lacus Perseverantiae, Lake of Persistence. Its location is 62.0˚ E and 8.0˚ N. See if you can find it here. (Hint: under Layers : Overlays select Nomenclature, and under Settings select Show Graticule.) Have fun exploring!

References

Cocks, Elijah E.; Cocks, Josiah C. (1995). Who’s Who on the Moon: A Biographical Dictionary of Lunar Nomenclature. Tudor Publishers. ISBN978-0-936389-27-1.

1:1 Million-Scale Maps of the Moon, IAU/USGS/NASA. https://planetarynames.wr.usgs.gov/Page/Moon1to1MAtlas.

Virtual Moon Atlas 6.0 Pro. Computer software. https://ap-i.net/avl/en/start.

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.

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

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.