Spectroscopic Parallax

For the nearest stars, the change in the position of the Earth in its orbit results in a tiny shift in the position of the nearby star relative to the distant background stars. This shift is called the trigonometric parallax. You can see the effect by holding your thumb up at arms length, closing your left eye, and lining up your thumb with something across the room. Now, alternate back and forth between having your right eye open and your left eye open and you’ll see the position of your thumb shift relative to an object further away. Move your thumb closer, and the shift is larger. That is the essence of trigonometric parallax.

Trigonometric Parallax

The distance to the star in parsecs (1 pc = 3.26 ly) is just

Now, a star’s distance, apparent brightness, and “true” (or intrinsic) brightness are related in the following way:

M = m + 5 (1 – log d)

where M = the absolute magnitude of the star

and m = the apparent magnitude of the star

and d = the distance to the star in parsecs

The absolute magnitude is the apparent magnitude the star would have if it were at a distance of 10 parsecs. Looking at it another way, the absolute magnitude is a proxy for the intrinsic brightness. The apparent magnitude is the star’s apparent brightness (as seen from Earth).

While the above equation is highly useful for general purpose calculations, to get the most accurate values astronomers must take into account atmospheric and interstellar extinction. And, anytime we deal with a star’s luminosity and its apparent brightness at some distance, d , we must specify the photometric system and optical filter that is being used. Or, less commonly (for practical reasons), we specify that the star’s luminosity and apparent brightness is to include all wavelengths of the electromagnetic spectrum, thus bolometric magnitudes are to be used.

Spectroscopic parallax is a bit of a misnomer, but here’s how it works for approximating the distance to main-sequence stars that are too far away to exhibit a measurable, reasonably certain, trigonometric parallax: measure the apparent magnitude of the star, and then using its spectrum to find its position on the H-R diagram, read off its absolute magnitude. Using your measured apparent magnitude and the star’s estimated absolute magnitude, you can solve for d the distance in the above equation.

Hertzsprung–Russell (H-R) diagram

The star’s color (the x-axis on the H-R diagram) is easy to measure, but a deeper analysis of the spectral lines is needed to determine whether the star is a main-sequence, giant, or supergiant star (or something else).

Using the Inverse Hyperbolic Sine

Image processing is both an art and a science, in equal measure, and I never cease to be amazed at the skill of the few people who are able to master it.

One tool in the ever-expanding workshop is the inverse hyperbolic sine, also known as the hyperbolic arcsine. Its use for image processing was described twenty years ago by Robert Lupton et al. (2003) in a paper entitled “Preparing Red-Green-Blue (RGB) Images from CCD Data.” In the abstract, the authors write:

We also introduce the use of an asinh stretch, which allows us to show faint objects while simultaneously preserving the structure of brighter objects in the field, such as the spiral arms of large galaxies.

Before we can know what a hyperbolic arcsine (asinh) is, we need to understand what a hyperbolic sine is. Just as a circle can be drawn out by the set of coordinates (x,y) = (cos θ, sin θ), the right half of an equilateral hyperbola (also known as a rectangular hyperbola) can be drawn using (x,y) = (cosh θ, sinh θ) where cosh is the hyperbolic cosine, and sinh is the hyperbolic sine. Just as the arcsine is the inverse sine function, i.e. if y = sin x, then x = asin y (also written as x = sin-1 y), so, too, the hyperbolic arcsine is the inverse hyperbolic sine function, i.e. if y = sinh x, then x = asinh y (or x = sinh-1 y).

If we consider the light intensity recorded by a pixel (say, a number between 0 and 65,536, where 0 is the darkest value and 65,536 the brightest) to be x, and then x′ to be the value of that pixel after passing through the hyperbolic arcsine function, we can map pixels using the following equation:

x'=sinh^{-1}\left ( \frac{x}{\beta } \right )=ln \left ( \frac{x+\sqrt{x^{2}+\beta ^{2}}}{\beta } \right )

where β is called the “softening parameter”, something you can tweak to bring out desired details.

If you play with this equation a little bit, you’ll quickly see that the smallest values of x (representing the darkest parts of your image) are pretty much left alone, but large values of x (representing the brightest parts of your image) are transformed to much smaller numbers. This then allows you to bring out the fainter details in your image without completely saturating the brighter parts of your image, since whether displayed on a monitor or the printed page, you have a limited dynamic range that can be rendered. Here is an example of an image that has benefited from a hyperbolic arcsine stretch.1

M17 with linear display (left) and after asinh stretching (right)

1IRIS Tutorial: Stretching levels and colors

IDA Information Sheets

I recently received a membership renewal notice from the International Dark-Sky Association (IDA) quoting Christopher Kyba that if light pollution continues to grow at the rate it currently is, “Orion’s belt will disappear at some point.”

This made me remember that I had written an IDA Information Sheet back in March 1997 that also had addressed how light pollution could erase much of the Orion constellation. I wrote,

Orion, arguably the most prominent of the constellations, begins to look more like “Orion, the Hunted” under a magnitude +4.0 sky. Under a magnitude +3.0 sky, Orion is on his deathbed. When light pollution is so bad that we have a magnitude +2.0 sky, only blazing Betelgeuse, regal Rigel, and Bellatrix and Alnilam remain to regale us.

Speaking of the IDA Information Sheets, I was the IDA Information Sheet Editor from 1996-1999, during which time I revised and edited most of the existing information sheets, edited and added many new ones from a number of contributors, as well as contributed many new ones that I authored, though I never credited myself as the author. One of the ones that I wrote was IDA Information Sheet 120, referenced above (and shown below). I have a complete hard copy set of IDA Information Sheets 1 through 175, the last of which was published in June 2000. I also have WordPerfect Macintosh source files for IDA Information Sheets 1 through 158, the last of which was completed on October 27, 1999.

Here’s IDA Information Sheet 120:

It is a shame that these IDA Information Sheets are no longer available anywhere on the Internet. At the very least, they are of historical interest, and I would say that much of the content is still relevant. Presumably, the IDA still has all of these information sheets, but after the Dave Crawford era, they have decided to remove access to them.

Finally, I want to express my disappointment that the International Dark-Sky Association has recently decided to change their name to DarkSky International. They are still in the process of changing everything over, but once that transition is complete, the IDA will be no more. The break with the Dave Crawford era will be complete. I, for one, will never forget how much Dave Crawford was able to accomplish during those early years, and how proud I was to have been a part of it.

The IDA/DSI is still a great organization, and I strongly encourage you to generously support it, as I do. It remains the most effective organization in the world addressing light pollution and the loss of our night sky and the natural nighttime environment.

Hidden Wonders of the Southern Sky

Here in southern Arizona, we can theoretically see 92.4% of the celestial sphere. I say “theoretically” because atmospheric extinction, light pollution, local topography, and obstructions limit the amount of the celestial sphere that we can see well. Also, far southern objects (down to δ = -58° at φ = 32° N) spend very little time above our horizon each day.

Practically speaking, then, we see somewhat less than 92% of all that there is to see from spaceship Earth.

Percent of the Celestial Sphere Visible

\% = 50\left [ 1-sin\left ( \left|\varphi \right| -90^{\circ}\right ) \right ]

where |φ| is the absolute value of your latitude in degrees

What are the most prominent objects we are missing, and what objects that we can see are they closest to?

Alpha Centauri

Never visible north of latitude 27° N, the nearest star system beyond our solar system is Alpha Centauri. Alpha Centauri A & B are bright stars, having a visual magnitude of 0.0 and +1.3, respectively, and in 2023 they are separated by just 8 arcseconds, about 1/4 of the angular separation between Albireo A & B. While Alpha Centauri A & B—which orbit each other once every 79.8 years—lie just 4.36 ly away, a faint red dwarf companion, Proxima Centauri (shining at magnitude +11.1), is even closer at 4.24 light years. It is not yet known whether Proxima Centauri, discovered in 1915, is gravitationally bound to Alpha Centauri A & B, or just presently passing through the neighborhood. Proxima is a full 2.2° away (over four moon-widths) from Alpha Centauri A & B.

When Arcturus (α Boo) and Zubenelgenubi (α Lib) are crossing our celestial meridian, so are Alpha & Proxima Centauri below the southern horizon.

Large Magellanic Cloud

The Large Magellanic Cloud (LMC), the largest satellite galaxy of our Milky Way galaxy and easily visible to the unaided eye, lies directly below our southern horizon when Rigel has crossed the meridian and Bellatrix is preparing to do so.

Small Magellanic Cloud

The Small Magellanic Cloud (SMC), the second-largest satellite galaxy of the mighty Milky Way lies underneath our southern horizon when M31, the Great Andromeda Galaxy, crosses the meridian near the zenith.

47 Tucanae

The 2nd brightest globular cluster in the sky (after Omega Centauri) is impressive 47 Tucanae. It is just 2.3° west and a little north of the Small Magellanic Cloud, so crosses the meridian below our horizon just as M31 is nearing the meridian.

Eta Carinae Nebula

Four times larger and brighter than the Orion Nebula, NGC 3372, the Eta Carinae Nebula, is a spectacular star-forming region containing a supermassive (130 – 180 M) binary star (Eta Carinae) that may go supernova at any time. When Leo the Lion is straddling the meridian, the Eta Carinae Nebula sneaks across as well.


Any other spectacular objects I should be including that are south of declination -58°? If so, please post a comment here.

Infinity

George F. R. Ellis weighs in on the concept of infinity in his excellent paper, Issues in the Philosophy of Cosmology, available on astro-ph at https://arxiv.org/abs/astro-ph/0602280. He writes:

9.3.2 Existence of Infinities

The nature of existence is significantly different if there is a finite amount of matter or objects in the universe, as opposed to there being an infinite quantity in existence. Some proposals claim there may be an infinite number of universes in a multiverse and many cosmological models have spatial sections that are infinite, implying an infinite number of particles, stars, and galaxies. However, infinity is quite different from a very large number! Following David Hilbert, one can suggest these unverifiable proposals cannot be true: the word “infinity” denotes a quantity or number that can never be attained, and so will never occur in physical reality.38 He states:

Our principal result is that the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought . . . The role that remains for the infinite to play is solely that of an idea . . . which transcends all experience and which completes the concrete as a totality . . .

This suggests “infinity” cannot be arrived at, or realized, in a concrete physical setting; on the contrary, the concept itself implies its inability to be realized!

Thesis I2: The often claimed physical existence of infinities is questionable. The claimed existence of physically realized infinities in cosmology or multiverses raises problematic issues. One can suggest they are unphysical; in any case such claims are certainly unverifiable.

This applies in principle to both small and large scales in any single universe:

The existence of a physically existing spacetime continuum represented by a real (number) manifold at the micro-level contrasts with quantum gravity claims of a discrete spacetime structure at the Planck scale, which one might suppose was a generic aspect of fully non-linear quantum gravity theories. In terms of physical reality, this promises to get rid of the uncountable infinities the real line continuum engenders in all physical variables and fields40. There is no experiment that can prove there is a physical continuum in time or space; all we can do is test space-time structure on smaller and smaller scales, but we cannot approach the Planck scale.

Infinitely large space-sections at the macro-level raise problems as indicated by Hilbert, and leads to the infinite duplication of life and all events. We may assume space extends forever in Euclidean geometry and in many cosmological models, but we can never prove that any realised 3-space in the real universe continues in this way—it is an untestable concept, and the real spatial geometry of the universe is almost certainly not Euclidean. Thus Euclidean space is an abstraction that is probably not physically real. The infinities supposed in chaotic inflationary models derive from the presumption of pre-existing infinite Euclidean space sections, and there is no reason why those should necessarily exist. In the physical universe spatial infinities can be avoided by compact spatial sections, resulting either from positive spatial curvature, or from a choice of compact topologies in universes that have zero or negative spatial curvature. Machian considerations to do with the boundary conditions for physics suggest this is highly preferable; and if one invokes string theory as a fundamental basis for physics, the “dimensional democracy” suggests the three large spatial dimensions should also be compact, since the small (“compactified”) dimensions are all taken to be so. The best current data from CBR and other observations indeed suggest k = +1, implying closed space sections for the best-fit FL model.

The existence of an eternal universe implies that an infinite time actually exists, which has its own problems: if an event happens at any time t0, one needs an explanation as to why it did not occur before that time (as there was an infinite previous time available for it to occur); and Poincaré eternal return will be possible if the universe is truly cyclic. In any case it is not possible to prove that the universe as a whole, or even the part of the universe in which we live, is past infinite; observations cannot do so, and the physics required to guarantee this would happen (if initial conditions were right) is untestable. Even attempting to prove it is future infinite is problematic (we cannot for example guarantee the properties of the vacuum into the infinite future—it might decay into a state corresponding to a negative effective cosmological constant).

It applies to the possible nature of a multiverse. Specifying the geometry of a generic universe requires an infinite amount of information because the quantities necessary to do so are fields on spacetime, in general requiring specification at each point (or equivalently, an infinite number of Fourier coefficients): they will almost always not be algorithmically compressible. All possible values of all these components in all possible combinations will have to occur in a multiverse in which “all that can happen, does happen”. There are also an infinite number of topological possibilities. This greatly aggravates all the problems regarding infinity and the ensemble. Only in highly symmetric cases, like the FL solutions, does this data reduce to a finite number of parameters, each of which would have to occur in all possible values (which themselves are usually taken to span an infinite set, namely the entire real line). Many universes in the ensemble may themselves have infinite spatial extent and contain an infinite amount of matter, with all the problems that entails. To conceive of physical creation of an infinite set of universes (most requiring an infinite amount of information for their prescription, and many of which will themselves be spatially infinite) is at least an order of magnitude more difficult than specifying an existent infinitude of finitely specifiable objects.

One should note here particularly that problems arise in the multiverse context from the continuum of values assigned by classical theories to physical quantities. Suppose for example that we identify corresponding times in the models in an ensemble and then assume that all values of the density parameter and the cosmological constant occur at each spatial point at that time. Because these values lie in the real number continuum, this is a doubly uncountably infinite set of models. Assuming genuine physical existence of such an uncountable infinitude of universes is the antithesis of Occam’s razor. But on the other hand, if the set of realised models is either finite or countably infinite, then almost all possible models are not realised. And in any case this assumption is absurdly unprovable. We can’t observationally demonstrate a single other universe exists, let alone an infinitude. The concept of infinity is used with gay abandon in some multiverse discussions, without any concern either for the philosophical problems associated with this statement, or for its completely unverifiable character. It is an extravagant claim that should be treated with extreme caution.

38An intriguing further issue is the dual question: Does the quantity zero occur in physical reality? This is related to the idea of physical existence of nothingness, as contrasted with a vacuum. A vacuum is not nothing!

40To avoid infinities entirely would require that nothing whatever is a continuum in physical reality (since any continuum interval contains an infinite number of points). Doing without that, conceptually, would mean a complete rewrite of many things. Considering how to do so in a way compatible with observation is in my view a worthwhile project.


So, given this discussion of infinities, the answer to the doubly hypothetical question, “Can God make a rock so big he can’t pick it up?” is likely a “Yes”! – D.O.

Nearest Stars & Planets

Here’s a table of all known star systems within 15 light years (ly) of our Solar System. I will endeavor to keep this list up to date, so please post a comment here if anything needs to be corrected or added.

There are 41 star systems1 within a volume of

V = \frac{4}{3}\pi r^{3} = \frac{4}{3}\pi (15\;ly)^{3} = 14,137\;ly^{3}

Assuming that these 41 star systems are uniformly distributed within a sphere of radius 15 ly, the average distance from any star to its nearest neighbor is given by

\bar{d} = r\left [ \frac{\pi }{3n\;\sqrt[]{2}} \right ]^{\frac{1}{3}} = (15\; ly)\left [ \frac{\pi }{3(41)\;\sqrt[]{2}} \right ]^{\frac{1}{3}} = 3.94\;ly

So, even though it seems that 41 star systems within a distance of 15 ly from our Solar System is a lot, the volume of 14,137 cubic light years is not that small, and the average distance between any star and its nearest neighbor is about 3.94 ly. Our nearest neighbor is Proxima Centauri, which at a distance of 4.24 ly is quite close to the 3.94 ly average distance derived above.

Nearest Stars (within 15 light years)

Star Distance (ly) Spectral Type Constellation Planets?
Sun 0.00 G2V zodiacal Yes
Proxima Centauri 4.24 M5.0V Centaurus Yes
Alpha Centauri A & B 4.36 G2V & K0.0V Centaurus Unknown
Barnard's Star 5.97 M3.5V Ophiuchus Unknown
Luhman 16 A & B 6.59 L8 & T1 Vela Unknown
WISE 0855-0714 7.26 Y2 Hydra Unknown
Wolf 359 7.87 M5.5V Leo Yes
Lalande 21185 8.29 M2.0V Ursa Major Yes
Sirius A & B 8.65 A1V & DA2 Canis Major Unknown
Luyten 726-8 A & B 8.79 M5.5V & M6.0V Cetus Unknown
Ross 154 9.70 M3.5V Sagittarius Unknown
Ross 248 10.29 M5.5V Andromeda Unknown
Epsilon Eridani 10.48 K2.0V Eridanus Yes
Lacaille 9352 10.72 M1.0V Piscis Austrinus Yes
Ross 128 11.01 M4.0V Virgo Yes
EZ Aquarii A, B, & C 11.27 M5.0VJ Aquarius Unknown
61 Cygni A & B 11.40 K5.0V & K7.0V Cygnus Unknown
Procyon A & B 11.44 F5IV-V & DQZ Canis Minor Unknown
Struve 2398 A & B 11.49 M3.0V & M3.5V Draco Yes
Groombridge 34 A & B 11.62 M1.5V & M3.5V Andromeda Yes
DX Cancri 11.68 M6.0V Cancer Unknown
Epsilon Indi A, B, & C 11.81 K4.0V, T1, & T6 Indus Yes
Tau Ceti 11.89 G8.5V Cetus Yes
Gliese 1061 11.98 M5.0V Horologium Yes
YZ Ceti 12.11 M4.0V Cetus Yes
Luyten's Star 12.25 M3.5V Canis Minor Yes
Teegarden's Star 12.50 M6.5V Aries Yes
Kapteyn's Star 12.83 M2.0VI Pictor Unknown
Lacaille 8760 12.95 K9.0V Microscopium Unknown
SCR 1845-6357 A & B 13.05 M8.5 & T6 Pavo Unknown
Kruger 60 A & B 13.08 M3.0V & M4.0V Cepheus Unknown
DENIS J1048-3956 13.19 M8.5V Antlia Unknown
UGPS 0722-05 13.43 T9 Monoceros Unknown
Ross 614 A & B 13.49 M4.0V & M5.5V Monoceros Unknown
Wolf 424 A & B 13.98 M5.0VJ Virgo Unknown
Wolf 1061 14.05 M3.5V Ophiuchus Yes
van Maanen 2 14.07 DZ7 Pisces Unknown
Gliese 1 14.17 M1.5V Sculptor Unknown
TZ Arietis 14.59 M4.0V Aries Yes
Gliese 674 14.84 M2.5V Ara Yes
Gliese 687 14.84 M3.0V Draco Yes
LHS 292 14.90 M6.5V Sextans Unknown

1 Here we are considering Proxima Centauri and Alpha Centauri A & B to be one star system.

References
Henry, T.J. 2020, The Nearest Stars in The Observer’s Handbook 2023, ed. J. Edgar, The Royal Astronomical Society of Canada, p. 284-288.

Zodiacal Light 2023

In 2023, the best dates and times for observing the zodiacal light are listed in the calendar below. The sky must be very clear with little or no light pollution. The specific times listed are for Tucson, Arizona (32° 16′ N, 111° 03′ W).

Here’s a nicely-formatted printable PDF file of the zodiacal light calendar:

January 2023
SUN MON TUE WED THU FRI SAT
1 2 3 4 5 6 7
8
Zodiacal Light 7:02 – 7:14 p.m. West
9
Zodiacal Light 7:03 – 8:03 p.m. West
10
Zodiacal Light 7:04 – 8:04 p.m. West
11
Zodiacal Light 7:04 – 8:04 p.m. West
12
Zodiacal Light 7:05 – 8:05 p.m. West
13
Zodiacal Light 7:06 – 8:06 p.m. West
14
Zodiacal Light 7:07 – 8:07 p.m. West
15
Zodiacal Light 7:07 – 8:07 p.m. West
16
Zodiacal Light 7:08 – 8:08 p.m. West
17
Zodiacal Light 7:09 – 8:09 p.m. West
18
Zodiacal Light 7:10 – 8:10 p.m. West
19
Zodiacal Light 7:11 – 8:11 p.m. West
20
Zodiacal Light 7:11 – 8:11 p.m. West
21
Zodiacal Light 7:12 – 8:12 p.m. West
22
Zodiacal Light 7:13 – 8:13 p.m. West
23 24 25 26 27 28
29 30 31        

February 2023
SUN MON TUE WED THU FRI SAT
      1 2 3 4
5 6 7
Zodiacal Light 7:26 – 7:58 p.m. West
8
Zodiacal Light 7:27 – 8:27 p.m. West
9
Zodiacal Light 7:27 – 8:27 p.m. West
10
Zodiacal Light 7:28 – 8:28 p.m. West
11
Zodiacal Light 7:29 – 8:29 p.m. West
12
Zodiacal Light 7:30 – 8:30 p.m. West
13
Zodiacal Light 7:31 – 8:31 p.m. West
14
Zodiacal Light 7:31 – 8:31 p.m. West
15
Zodiacal Light 7:32 – 8:32 p.m. West
16
Zodiacal Light 7:33 – 8:33 p.m. West
17
Zodiacal Light 7:34 – 8:34 p.m. West
18
Zodiacal Light 7:34 – 8:34 p.m. West
19
Zodiacal Light 7:35 – 8:35 p.m. West
20
Zodiacal Light 7:36 – 8:36 p.m. West
21 22 23 24 25
26 27 28        

March 2023
SUN MON TUE WED THU FRI SAT
      1 2 3 4
5 6 7 8 9
Zodiacal Light 7:49 – 8:43 p.m. West
10
Zodiacal Light 7:49 – 8:49 p.m. West
11
Zodiacal Light 7:50 – 8:50 p.m. West
12
Zodiacal Light 7:51 – 8:51 p.m. West
13
Zodiacal Light 7:52 – 8:52 p.m. West
14
Zodiacal Light 7:52 – 8:52 p.m. West
15
Zodiacal Light 7:53 – 8:53 p.m. West
16
Zodiacal Light 7:54 – 8:54 p.m. West
17
Zodiacal Light 7:55 – 8:55 p.m. West
18
Zodiacal Light 7:55 – 8:55 p.m. West
19
Zodiacal Light 7:56 – 8:56 p.m. West
20
Zodiacal Light 7:57 – 8:57 p.m. West
21
Zodiacal Light 7:58 – 8:58 p.m. West
22 23 24 25
26 27 28 29 30 31  

April 2023
SUN MON TUE WED THU FRI SAT
            1
2 3 4 5 6 7
Zodiacal Light 8:12 – 8:37 p.m. West
8
Zodiacal Light 8:13 – 9:13 p.m. West
9
Zodiacal Light 8:14 – 9:14 p.m. West
10
Zodiacal Light 8:14 – 9:14 p.m. West
11
Zodiacal Light 8:15 – 9:15 p.m. West
12
Zodiacal Light 8:16 – 9:16 p.m. West
13
Zodiacal Light 8:17 – 9:17 p.m. West
14
Zodiacal Light 8:18 – 9:18 p.m. West
15
Zodiacal Light 8:19 – 9:19 p.m. West
16
Zodiacal Light 8:20 – 9:20 p.m. West
17
Zodiacal Light 8:21 – 9:21 p.m. West
18
Zodiacal Light 8:22 – 9:22 p.m. West
19
Zodiacal Light 8:23 – 9:23 p.m. West
20
Zodiacal Light 8:24 – 9:24 p.m. West
21 22
23 24 25 26 27 28 29
30            

May 2023
SUN MON TUE WED THU FRI SAT
  1 2 3 4 5 6
7
Zodiacal Light 8:41 – 9:41 p.m. West
8
Zodiacal Light 8:42 – 9:42 p.m. West
9
Zodiacal Light 8:43 – 9:43 p.m. West
10
Zodiacal Light 8:44 – 9:44 p.m. West
11
Zodiacal Light 8:45 – 9:45 p.m. West
12
Zodiacal Light 8:46 – 9:46 p.m. West
13
Zodiacal Light 8:47 – 9:47 p.m. West
14
Zodiacal Light 8:48 – 9:48 p.m. West
15
Zodiacal Light 8:49 – 9:49 p.m. West
16
Zodiacal Light 8:50 – 9:50 p.m. West
17
Zodiacal Light 8:51 – 9:51 p.m. West
18
Zodiacal Light 8:52 – 9:52 p.m. West
19
Zodiacal Light 8:53 – 9:53 p.m. West
20
Zodiacal Light 8:54 – 9:54 p.m. West
21 22 23 24 25 26 27
28 29 30 31      

June 2023
SUN MON TUE WED THU FRI SAT
        1 2 3
4 5 6 7 8 9 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30  

July 2023
SUN MON TUE WED THU FRI SAT
            1
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31          

August 2023
SUN MON TUE WED THU FRI SAT
    1 2 3 4 5
6 7 8 9 10 11 12
13 14
Zodiacal Light 3:59 – 4:18 a.m. East
15
Zodiacal Light 3:19 – 4:19 a.m. East
16
Zodiacal Light 3:20 – 4:20 a.m. East
17
Zodiacal Light 3:21 – 4:21 a.m. East
18
Zodiacal Light 3:22 – 4:22 a.m. East
19
Zodiacal Light 3:23 – 4:23 a.m. East
20
Zodiacal Light 3:24 – 4:24 a.m. East
21
Zodiacal Light 3:24 – 4:24 a.m. East
22
Zodiacal Light 3:25 – 4:25 a.m. East
23
Zodiacal Light 3:26 – 4:26 a.m. East
24
Zodiacal Light 3:27 – 4:27 a.m. East
25
Zodiacal Light 3:28 – 4:28 a.m. East
26
Zodiacal Light 3:29 – 4:29 a.m. East
27
Zodiacal Light 3:30 – 4:30 a.m. East
28
Zodiacal Light 3:31 – 4:31 a.m. East
29
Zodiacal Light 4:03 – 4:31 a.m. East
30 31    

September 2023
SUN MON TUE WED THU FRI SAT
          1 2
3 4 5 6 7 8 9
10 11 12 13
Zodiacal Light 3:43 – 4:43 a.m. East
14
Zodiacal Light 3:44 – 4:44 a.m. East
15
Zodiacal Light 3:45 – 4:45 a.m. East
16
Zodiacal Light 3:46 – 4:46 a.m. East
17
Zodiacal Light 3:46 – 4:46 a.m. East
18
Zodiacal Light 3:47 – 4:47 a.m. East
19
Zodiacal Light 3:48 – 4:48 a.m. East
20
Zodiacal Light 3:49 – 4:49 a.m. East
21
Zodiacal Light 3:49 – 4:49 a.m. East
22
Zodiacal Light 3:50 – 4:50 a.m. East
23
Zodiacal Light 3:51 – 4:51 a.m. East
24
Zodiacal Light 3:51 – 4:51 a.m. East
25
Zodiacal Light 3:52 – 4:52 a.m. East
26
Zodiacal Light 3:53 – 4:53 a.m. East
27
Zodiacal Light 4:06 – 4:53 a.m. East
28 29 30

October 2023
SUN MON TUE WED THU FRI SAT
1 2 3 4 5 6 7
8 9 10 11 12 13
Zodiacal Light 4:04 – 5:04 a.m. East
14
Zodiacal Light 4:05 – 5:05 a.m. East
15
Zodiacal Light 4:06 – 5:06 a.m. East
16
Zodiacal Light 4:06 – 5:06 a.m. East
17
Zodiacal Light 4:07 – 5:07 a.m. East
18
Zodiacal Light 4:08 – 5:08 a.m. East
19
Zodiacal Light 4:08 – 5:08 a.m. East
20
Zodiacal Light 4:09 – 5:09 a.m. East
21
Zodiacal Light 4:10 – 5:10 a.m. East
22
Zodiacal Light 4:11 – 5:11 a.m. East
23
Zodiacal Light 4:11 – 5:11 a.m. East
24
Zodiacal Light 4:12 – 5:12 a.m. East
25
Zodiacal Light 4:13 – 5:13 a.m. East
26
Zodiacal Light 4:13 – 5:13 a.m. East
27 28
29 30 31        

November 2023
SUN MON TUE WED THU FRI SAT
      1 2 3 4
5 6 7 8 9 10 11
12
Zodiacal Light 4:26 – 5:26 a.m. East
13
Zodiacal Light 4:27 – 5:27 a.m. East
14
Zodiacal Light 4:27 – 5:27 a.m. East
15
Zodiacal Light 4:28 – 5:28 a.m. East
16
Zodiacal Light 4:29 – 5:29 a.m. East
17
Zodiacal Light 4:30 – 5:30 a.m. East
18
Zodiacal Light 4:30 – 5:30 a.m. East
19
Zodiacal Light 4:31 – 5:31 a.m. East
20
Zodiacal Light 4:32 – 5:32 a.m. East
21
Zodiacal Light 4:33 – 5:33 a.m. East
22
Zodiacal Light 4:33 – 5:33 a.m. East
23
Zodiacal Light 4:34 – 5:34 a.m. East
24
Zodiacal Light 4:35 – 5:35 a.m. East
25
Zodiacal Light 5:13 – 5:36 a.m. East
26 27 28 29 30    

December 2023
SUN MON TUE WED THU FRI SAT
          1 2
3 4 5 6 7 8 9
10 11
Zodiacal Light 4:47 – 5:47 a.m. East
12
Zodiacal Light 4:48 – 5:48 a.m. East
13
Zodiacal Light 4:48 – 5:48 a.m. East
14
Zodiacal Light 4:49 – 5:49 a.m. East
15
Zodiacal Light 4:50 – 5:50 a.m. East
16
Zodiacal Light 4:50 – 5:50 a.m. East
17
Zodiacal Light 4:51 – 5:51 a.m. East
18
Zodiacal Light 4:51 – 5:51 a.m. East
19
Zodiacal Light 4:52 – 5:52 a.m. East
20
Zodiacal Light 4:53 – 5:53 a.m. East
21
Zodiacal Light 4:53 – 5:53 a.m. East
22
Zodiacal Light 4:54 – 5:54 a.m. East
23
Zodiacal Light 4:54 – 5:54 a.m. East
24
Zodiacal Light 5:14 – 5:54 a.m. East
25 26 27 28 29 30
31            

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

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

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

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

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

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

Meteor Shower Calendar 2023

Here’s our meteor shower calendar for 2023.  It is sourced from the IMO’s Working List of Visual Meteor Showers (https://www.imo.net/files/meteor-shower/cal2023.pdf, Table 5, p. 25).

Each meteor shower is identified using its three-character IAU meteor shower code.  Codes are bold on the date of maximum, and one day either side of maximum.

Some additional events have been added to the calendar from Sources of Possible or Additional Activity, Table 6a, p. 27). I used the following abbreviations for the Table 6a events that do not have a standard three-character meteor code:

BA* = 2016 BA14
46P = 46P/Wirtanen

Here’s a printable PDF file of the meteor shower calendar shown below:

Happy meteor watching!

January 2023
SUN MON TUE WED THU FRI SAT
1
QUA COM
2
QUA COM
3
QUA COM
4
QUA COM
5
QUA COM
6
QUA COM
7
QUA COM
8
QUA COM
9
QUA COM KCA
10
QUA COM GUM KCA
11
QUA COM GUM KCA
12
QUA COM GUM
13
COM GUM
14
COM GUM
15
COM GUM
16
COM GUM
17
COM GUM
18
COM GUM
19
COM GUM
20
COM GUM
21
COM GUM
22
COM GUM
23
COM
24
COM
25
COM
26
COM
27
COM
28
COM
29
COM
30
COM
31
COM ACE
       
February 2023
SUN MON TUE WED THU FRI SAT
      1
COM ACE
2
COM ACE
3
COM ACE
4
COM ACE
5
ACE
6
ACE
7
ACE
8
ACE
9
ACE
10
ACE
11
ACE
12
ACE
13
ACE
14
ACE
15
ACE
16
ACE
17
ACE
18
ACE
19
ACE
20
ACE
21 22 23 24 25
GNO
26
GNO
27
GNO
28
GNO
       
March 2023
SUN MON TUE WED THU FRI SAT
      1
GNO
2
GNO
3
GNO
4
GNO
5
GNO
6
GNO
7
GNO
8
GNO
9
GNO
10
GNO
11
GNO
12
GNO
13
GNO
14
GNO
15
GNO
16
GNO
17
GNO
18
GNO
19
GNO
20
BA* GNO
21
BA* GNO
22
BA* GNO
23
GNO
24
GNO
25
GNO
26
GNO
27
GNO
28
GNO
29 30 31  
April 2023
SUN MON TUE WED THU FRI SAT
            1
2 3 4 5 6 7 8
9 10 11 12 13 14
LYR
15
PPU LYR
16
PPU LYR
17
PPU LYR
18
PPU LYR
19
ETA PPU LYR
20
ETA PPU LYR
21
ETA PPU LYR
22
ETA PPU LYR
23
ETA PPU LYR
24
ETA PPU LYR
25
ETA PPU LYR
26
ETA PPU LYR
27
ETA PPU LYR
28
ETA PPU LYR
29
ETA LYR
30
ETA LYR
           
May 2023
SUN MON TUE WED THU FRI SAT
  1
ETA
2
ETA
3
ELY ETA
4
ELY ETA
5
ELY ETA
6
ELY ETA
7
ELY ETA
8
ELY ETA
9
ELY ETA
10
ELY ETA
11
ELY ETA
12
ELY ETA
13
ELY ETA
14
ARI ELY ETA
15
ARI ETA
16
ARI ETA
17
ARI ETA
18
ARI ETA
19
ARI ETA
20
ARI ETA
21
ARI ETA
22
ARI ETA
23
ARI ETA
24
ARI ETA
25
ARI ETA
26
ARI ETA
27
ARI ETA
28
ARI CAM ETA
29
ARI CAM
30
ARI CAM
31
ARI
     
June 2023
SUN MON TUE WED THU FRI SAT
        1
ARI
2
ARI
3
ARI
4
ARI
5
ARI
6
ARI
7
ARI
8
ARI
9
ARI
10
ARI
11
ARI
12
ARI
13
ARI
14
ARI
15
ARI
16
ARI
17
ARI
18
ARI
19
ARI
20
ARI
21
ARI
22
JBO ARI
23
JBO ARI
24
JBO ARI
25
JBO
26
JBO
27
JBO
28
JBO
29
JBO
30
JBO
 
July 2023
SUN MON TUE WED THU FRI SAT
            1
JBO
2
JBO
3
CAP
4
CAP JPE
5
CAP JPE
6
CAP JPE
7
CAP JPE
8
CAP JPE
9
CAP JPE
10
CAP JPE
11
CAP JPE
12
CAP SDA JPE
13
CAP SDA JPE
14
CAP SDA JPE
15
CAP SDA PAU
16
CAP SDA PAU
17
PER CAP SDA PAU
18
PER CAP SDA PAU
19
PER CAP SDA PAU
20
PER CAP SDA PAU
21
PER CAP SDA PAU
22
PER CAP SDA PAU
23
PER CAP SDA PAU
24
PER CAP SDA PAU
25
PER CAP SDA GDR PAU
26
PER CAP SDA GDR PAU
27
PER CAP SDA GDR PAU
28
PER CAP SDA GDR PAU
29
PER CAP SDA GDR
30
PER CAP SDA GDR PAU
31
PER ERI CAP SDA GDR PAU
         
August 2023
SUN MON TUE WED THU FRI SAT
    1
PER ERI CAP SDA PAU
2
PER ERI CAP SDA PAU
3
KCG PER ERI CAP SDA PAU
4
KCG PER ERI CAP SDA PAU
5
KCG PER ERI CAP SDA PAU
6
KCG PER ERI CAP SDA PAU
7
KCG PER ERI CAP SDA PAU
8
KCG PER ERI CAP SDA PAU
9
KCG PER ERI CAP SDA PAU
10
KCG PER ERI CAP SDA PAU
11
KCG PER ERI CAP SDA
12
KCG PER ERI CAP SDA
13
KCG PER ERI CAP SDA
14
KCG PER ERI CAP SDA
15
KCG PER ERI CAP SDA
16
KCG PER ERI SDA
17
KCG PER ERI SDA
18
KCG PER ERI SDA
19
KCG PER ERI SDA
20
KCG PER SDA
21
KCG PER SDA
22
KCG PER SDA
23
KCG PER SDA
24
KCG PER
25
KCG
26
KCG
27
KCG
28
AUR KCG
29
AUR
30
AUR
31
AUR
   
September 2023
SUN MON TUE WED THU FRI SAT
          1
AUR
2
AUR
3
AUR
4
AUR
5
SPE AUR
6
SPE
7
SPE
8
SPE
9
DSX SPE
10
DSX SPE
11
DSX SPE
12
DSX SPE
13
DSX SPE
14
DSX SPE
15
DSX SPE
16
DSX SPE
17
DSX SPE
18
DSX SPE
19
DSX SPE
20
STA DSX SPE
21
STA DSX SPE
22
STA DSX
23
STA DSX
24
STA DSX
25
STA DSX
26
STA DSX
27
STA DSX
28
STA DSX
29
STA DSX
30
STA DSX
October 2023
SUN MON TUE WED THU FRI SAT
1
STA DSX
2
STA ORI DSX
3
STA ORI DSX
4
STA ORI DSX
5
STA ORI OCT DSX
6
STA ORI DRA OCT DSX
7
STA ORI DRA OCT DSX
8
STA ORI DRA DSX
9
STA ORI DRA DSX
10
STA ORI DAU DRA
11
STA ORI DAU
12
STA ORI DAU
13
STA ORI DAU
14
STA ORI EGE DAU
15
STA ORI EGE DAU
16
STA ORI EGE DAU
17
STA ORI EGE DAU
18
STA ORI EGE DAU
19
STA LMI ORI EGE
20
NTA STA LMI ORI EGE
21
NTA STA LMI ORI EGE
22
NTA STA LMI ORI EGE
23
NTA STA LMI ORI EGE
24
NTA STA LMI ORI EGE
25
NTA STA LMI ORI EGE
26
NTA STA LMI ORI EGE
27
NTA STA LMI ORI EGE
28
NTA STA ORI
29
NTA STA ORI
30
NTA STA ORI
31
NTA STA ORI
       
November 2023
SUN MON TUE WED THU FRI SAT
      1
NTA STA ORI
2
NTA STA ORI
3
NTA STA ORI
4
NTA STA ORI
5
NTA STA ORI
6
LEO NTA STA ORI
7
LEO NTA STA ORI
8
LEO NTA STA
9
LEO NTA STA
10
LEO NTA STA
11
LEO NTA STA
12
LEO NTA STA
13
NOO LEO NTA STA
14
NOO LEO NTA STA
15
NOO AMO LEO NTA STA
16
NOO AMO LEO NTA STA
17
NOO AMO LEO NTA STA
18
NOO AMO LEO NTA STA
19
NOO AMO LEO NTA STA
20
NOO AMO LEO NTA STA
21
NOO AMO LEO NTA
22
NOO AMO LEO NTA
23
NOO AMO LEO NTA
24
NOO AMO LEO NTA
25
NOO AMO LEO NTA
26
NOO LEO NTA
27
NOO LEO NTA
28
PHO NOO LEO NTA
29
PHO NOO LEO NTA
30
PHO NOO LEO NTA
   
December 2023
SUN MON TUE WED THU FRI SAT
          1
PUP AND PHO NOO NTA
2
PUP AND PHO NOO NTA
3
HYD PUP AND PHO NOO NTA
4
GEM HYD PUP PHO NOO NTA
5
COM GEM HYD MON PUP PHO NOO NTA
6
COM GEM HYD MON PUP PHO NOO NTA
7
COM GEM HYD MON PUP PHO NTA
8
COM GEM HYD MON PUP PHO NTA
9
COM GEM HYD MON PUP PHO NTA
10
COM GEM HYD MON PUP NTA
11
COM GEM 46P HYD MON PUP
12
COM GEM 46P HYD MON PUP
13
COM GEM 46P HYD MON PUP
14
COM GEM HYD MON PUP
15
COM GEM HYD MON PUP
16
COM GEM HYD MON
17
COM URS GEM HYD MON
18
COM URS GEM HYD MON
19
COM URS GEM HYD MON
20
COM URS GEM HYD MON
21
COM URS
22
COM URS
23
COM URS
24
COM URS
25
COM URS
26
COM URS
27
COM
28
QUA COM
29
QUA COM
30
QUA COM
31
QUA COM
           

Eris: Plutoid, Dwarf Planet, or 10th Planet?

Eris was discovered on January 5, 2005 by Michael E. Brown, Chad Trujillo, and David A. Rabinowitz. Its orbit is more eccentric and more highly inclined than Pluto’s, and it is almost as large as Pluto, having a diameter that is 97.9% that of Pluto. Eris last came to perihelion on July 23, 1699 when it was in the constellation Virgo shining at a magnitude of 14.8, well beyond the reach of any telescopes existing at the time.

Pluto, Eris, and Satellites – Sizes and Orbital Distances to Scale

Eris has an orbit that is so eccentric (e = 0.44) that it actually spends some time each orbit closer to the Sun than Pluto is during the outer reaches of its orbit. Pluto’s aphelion distance is 49.31 AU, and Eris will be closer to the Sun than that for 99 years, from 2208 to 2307.

Eris is closer to the Sun than Pluto’s average distance of 40.70 AU for 43 years, between 2236 and 2279. Eris again reaches perihelion in 2257, when it will be 38.09 AU from the Sun.

Eris has an orbit that is tilted at nearly a 45° angle with respect to the ecliptic. This takes it through some interesting constellations during its 559-year orbital period. Here is its upcoming travel itinerary.

Upcoming Travel Plans for Eris (not subject to change1)

2022   Cetus
2036   Pisces
2059   Cetus
2064   Aries
2126   Perseus
2174   Camelopardalis
2197   Lynx
2208   Ursa Major
2237   Canes Venatici
2245   Coma Berenices
2256   Virgo
2274   Libra
2281   Hydra
2285   Centaurus
2286   Lupus
2298   Norma
2308   Ara
2320   Pavo
2357   Indus
2367   Tucana
2376   Grus
2399   Phoenix
2434   Sculptor
2487   Cetus

1 Unless the constellation boundaries are redrawn due to precession or other considerations

In Greek & Roman mythology, Eris is the goddess of strife and discord. 500 years hence, in 2522, Eris will once again be in Cetus, as it is today. But where will we be? What kind of life will our great-great-great-great great-great-great-great-great-great-great-great-great great-great grandchildren have in 2522? Here are some of my hopes for 2522.

  • Humanism will have replaced religion.
  • There will be no poverty in the world.
  • Everyone will have adequate health care, and it will be free.
  • Zero population growth will have been achieved by the only humane way possible: having fewer children.
  • There will be no more wars, no weapons of mass destruction.
  • There will be no need for guns, and no one will have them.
  • Violence will not be tolerated, nor will society glorify it or dwell on it in any way.
  • Individuals who “cross the line” and violate others through the use of physical violence will be psychologically re-engineered so they will live productive and fulfilling lives without being a threat to others. This neutralization of violent tendencies must be accomplished humanely and in a way that does not violate the individual’s essential humanity.
  • The Earth will be treated as the oasis it is.
  • Money will no longer exist, nor will it be needed.

Though no one alive today is likely to ever see any of these things, that in no way excuses us from working substantially towards these goals. To do anything less is a dereliction of moral duty.

A Case for Ten Planets

Clyde Tombaugh (1906-1997) spent the first fifteen years of his life on a farm near Streator, Illinois, and then his family moved to a farm near Burdett, Kansas (no wonder he got interested in astronomy!), and he went to high school there. Then, on February 18, 1930, Tombaugh, a self-taught amateur astronomer and telescope maker, discovered the ninth planet in our solar system, Pluto. It had been nearly 84 years since the eighth planet, Neptune, had been discovered, in 1846. And it would be another 62 years before another trans-Neptunian object (TNO) would be discovered.

Clyde Tombaugh made his discovery using a 13-inch f/5.3 photographic refractor at the Lowell Observatory in Flagstaff, Arizona.

Clyde Tombaugh was 24 years old when he discovered Pluto. He died in 1997 at the age of 90 (almost 91). I was very fortunate to meet Prof. Tombaugh at a lecture he gave at Iowa State University in 1990. At that lecture, he told a fascinating story about the discovery of Pluto, and I remember well his comment that he felt certain that no “tenth planet” larger than Pluto exists in our solar system, because of the thorough searches he and others had done since his discovery of Pluto. But, those searches were done before the CCD revolution, and just two years later, the first TNO outside the Pluto-Charon system, 15760 Albion (1992 QB1), would be discovered by David Jewitt (1958-) and Jane Luu (1963-), although only 1/9th the size of Pluto.

Pluto is, by far, the smallest of the nine planets. At only 2,377 km across, Pluto is only 2/3 the size of our Moon! Pluto has a large moon called Charon (pronounced SHAR-on) that is 1,212 km across (over half the size of Pluto), discovered in 1978 by James Christy (1938-). Two additional moons were discovered using the Hubble Space Telescope (HST) in 2005: Hydra (50.9 × 36.1 × 30.9 km) and Nix (49.8 × 33.2 × 31.1 km). A fourth moon was discovered using HST in 2011: Kerberos (10 × 9 × 9 km). And a fifth moon, again using HST, in 2012: Styx (16 × 9 × 8 km).

Pluto has been visited by a single spacecraft. New Horizons passed 12,472 km from Pluto and 28,858 km from Charon on July 14, 2015. Then, about 3½ years later, New Horizons passed 3,538 km from 486958 Arrokoth, on January 1, 2019.

Only one other TNO comparable in size to Pluto (or larger) is known to exist. 136199 Eris and its moon Dysnomia were discovered in 2005 by Mike Brown (1965-), Chad Trujillo (1973-), and David Rabinowitz (1960-). It is currently estimated that Eris is 97.9% the size of Pluto. Not surprisingly, in 2006 Pluto was “demoted” by the IAU from planethood to dwarf planet status. (Is not a “dwarf planet” a planet? Confusing…)

My take on this is that Pluto should be considered a planet along with Eris, of course. The definition of “planet” is really rather arbitrary, so given that Pluto was discovered 75 years before Eris, and 62 years before TNO #2, I think we should (in deference to the memory of Mr. Tombaugh, mostly) define a planet as any non-satellite object orbiting the Sun that is around the size of Pluto or larger. So, by my definition, there are currently ten known planets in our solar system. Is that really too many to keep track of?

There is precedent for including history in scientific naming decisions. William Herschel (1738-1822) is thought to have coined the term “planetary nebula” in the 1780s, and though we now know they have nothing to do with planets (unless their morphology is affected by orbiting planets), we still use the term “planetary nebula” to describe them today.

In the table below, you will find the eight “classical” planets, plus the five largest TNOs, all listed in order of descending size. (The largest asteroid, Ceres, is 939 km across, and is thus smaller than the smallest of these TNOs.)

You’ll see that the next largest TNO after Eris is Haumea, and that its diameter is only 67% that of Eris.

I’ve also listed the largest satellite for each of these objects. Venus and Mercury do not have a satellite—at least not at the present time.

It is amazing to note that both Ganymede and Titan are larger than the planet Mercury! And Ganymede, Titan, the Moon, and Triton are all larger than Pluto.

Largest Objects in the Solar System

Object Diameter (km) Largest Satellite Diameter (km) Size Ratio
Jupiter 139,822 Ganymede 5,268 3.8%
Saturn 116,464 Titan 5,149 4.4%
Uranus 50,724 Titania 1,577 3.1%
Neptune 49,244 Triton 2,707 5.5%
Earth 12,742 Moon 3,475 27.3%
Venus 12,104 N/A N/A N/A
Mars 6,779 Phobos 23 0.3%
Mercury 4,879 N/A N/A N/A
Pluto 2,377 Charon 1,212 51.0%
Eris 2,326 Dysnomia 700 30.1%
Haumea 1,560 Hiʻiaka 320 20.5%
Makemake 1,430 S/2015 (136472) 175 12.2%
Gonggong 1,230 Xiangliu 200 16.3%

Should any other non-satellite objects with a diameter of at least 2,000 km be discovered in our solar system, I think we should call them planets, too.