The spectral type classification scheme for stars is, among other things, a temperature sequence. A helpful mnemonic for remembering the sequence is Oh, Be A Fine Girl (Guy) Kiss Me Like This, Yes! The O stars have the highest surface temperatures, up to 56,000 K (100,000° F), while the Y infrared dwarfs (brown dwarfs) have surface temperatures as cool as 250 K (-10° F).
Here are the brightest representatives of each of these spectra classes readily visible from the northern hemisphere. Apparent visual magnitude (V-band) is given unless otherwise noted.
George F. R. Ellis writes in Issues in the Philosophy of Cosmology:
A few comments.
1: Random chance. At first, this strikes one as intellectual laziness, but perhaps it is more a reflection of our own intellectual weakness. More on that in a moment.
2: Necessity. Our intellectual journey of discovery and greater understanding must continue, and it may eventually lead us to this conclusion. But not now.
3: High probability. How can we talk about probability when n = 1?
4: Universality. We can hypothesize the existence of other universes, yes, but if we have no way to observe or interact with them, how can we call this endeavor science? Furthermore, explaining the existence of multiple universes seems even more problematic that explaining the existence of a single universe—ours.
5: Cosmological Natural Selection. We do not know that black holes can create other universes, or that universes that contain life are more likely to have laws of physics that allow an abundance of black holes
6. Purpose of Design. The presupposition of design is not evidence of design. It is possible that scientific evidence of a creator or designer might be found in nature—such as an encoded message evincing purposeful intelligence in DNA or the cosmic microwave background—but to date no such evidence has been found. Even if evidence of a creator is forthcoming, how do we explain the existence of the creator?
I would now like to suggest a seventh option (possibly a variant of Ellis’s Option 1 Random Chance or Option 2 Necessity).
7. Indeterminate Due to Insufficient Intelligence. It is at least possible that there are aspects of reality and our origins that may be beyond what humans are currently capable of understanding. For some understanding of how this might be possible, we need look no further than the primates we are most closely related to, and other mammals. Is a chimpanzee self-aware? Can non-humans experience puzzlement? Are animals aware of their own mortality? Even if the answer to all these questions is “yes”1, there are clearly many things humans can do that no other animal is capable of. Why stop at humans? Isn’t it reasonable to assume that there is much that humans are cognitively incapable of?
Why do we humans develop remarkable technologies and yet fail dismally to eradicate poverty, war, and other violence? Why does the world have so many religions if they are not all imperfect and very human attempts to imbue our lives with meaning?
What is consciousness? Will we ever understand it? Can we extrapolate from our current intellectual capabilities to a complete understanding of our origins and the origins of the universe, or is something more needed that we currently cannot even envision?
“Sometimes attaining the deepest familiarity with a question is our best substitute for actually having the answer.” —Brian Greene, The Elegant Universe
“To ask what happens before the Big Bang is a bit like asking what happens on the surface of the earth one mile north of the North Pole. It’s a meaningless question.” —Stephen Hawking, Interview with Timothy Ferris, Pasadena, 1985
1 For more on the topic of the emotional and cognitive similarities between animals and humans, see “Mama’s Last Hug: Animal Emotions and What They Tell Us about Ourselves” by primatologist Frans de Waal, W. W. Norton & Company (2019). https://www.amazon.com/dp/B07DP6MM92 .
G.F.R. Ellis, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
It is time to put an end to right-turn-on-red. It unnecessarily puts pedestrians and bicyclists trying to cross at crosswalks in harm’s way. I’m old enough to remember driving when a red light meant stop—and stay stopped—always. I’ve never liked right-turn-on-red. During my 21 years working at the Iowa Department of Transportation, I learned that doing whatever we can to minimize the potential for driver confusion or uncertainty will always improve safety.
Massachusetts was the last state to adopt right-turn-on-red, on January 1, 1980. New York City still bans right-turn-on-red, unless a sign indicates otherwise. That should be the norm, not the exception.
Short of an outright ban, a good approach would be to put up signs at major intersections with crosswalks, as shown below, but I would add “or bicyclists” as bicyclists often must use pedestrian crosswalks when it is not safe to ride in the street.
The most dangerous situation occurs when a pedestrian (or bicyclist) is waiting for the crosswalk signal to turn from “Don’t Walk” to “Walk”, and a driver who will be crossing the pedestrian’s crosswalk is stopped at a red light. The driver is eager to make a right turn on red and can’t really see when your crosswalk signal turns to walk, so they may turn right in front of you at the same time you are (legally) starting to cross the intersection. This is even more dangerous for bicyclists because they move faster into the intersection than a pedestrian does. This situation is illustrated in the diagram below.
Here in Dodgeville, Wisconsin, a particularly dangerous location for pedestrians and bicyclists is the south-to-north crosswalk at the SW corner of the intersection of Bequette and US 18, where drivers frequently make right turns from US 18 EB to Bequette SB. Right turns should be prohibited here with a sign that says No Turn on Red When Pedestrians or Bicyclists Present.
If you’re an astronomy teacher that likes to put a trick question on an open book quiz or test once in a while to encourage your students to think more deeply, here’s a good one for you:
On average, what planet is closest to the Earth?
The correct answer is C. Mercury.
Huh? Venus comes closest to the Earth, doesn’t it? Yes, but there is a big difference between minimum distance and average distance. Let’s do some quick calculations to help us understand minimum distance first, and then we’ll discuss the more involved determination of average distance.
Here’s some easily-found data on the terrestrial planets:
I’ve intentionally left the last two columns of the table empty. We’ll come back to those in a moment. a is the semi-major axis of each planet’s orbit around the Sun, in astronomical units (AU). It is often taken that this is the planet’s average distance from the Sun, but that is strictly true only for a circular orbit.1 e is the orbital eccentricity, which is a unitless number. The closer the value is to 0.0, the more circular the orbit. The closer the value is to 1.0, the more elliptical the orbit, with 1.0 being a parabola.
The two empty columns are for q the perihelion distance, and Q the aphelion distance. Perihelion occurs when the planet is closest to the Sun. Aphelion occurs when the planet is farthest from the Sun. How do we calculate the perihelion and aphelion distance? It’s easy.
Perihelion: q = a (1 – e)
Aphelion: q = a (1 + e)
Now, let’s fill in the rest of our table.
|Planet||a (AU)||e||q (AU)||Q (AU)|
Ignoring, for a moment, each planet’s orbital eccentricity, we can calculate the “average” closest approach distance between any two planets by simply taking the difference in their semi-major axes. For Venus, it is 1.000 – 0.723 = 0.277 AU, and for Mars, it is 1.524 – 1.000 = 0.524 AU. We see that Venus comes closest to the Earth.
But, sometimes, Venus and Mars come even closer to the Earth than 0.277 AU and 0.524 AU, respectively. The minimum minimum distance between Venus and the Earth in conjunction should occur when Venus is at aphelion at the same time as Earth is at perihelion: 0.983 – 0.728 = 0.255 AU. The minimum minimum distance between Earth and Mars at opposition should occur when Mars is at perihelion and Earth is at aphelion: 1.382 – 1.017 = 0.365 AU. Mars does not ever come as close to the Earth as Venus does at every close approach.
The above assumes that all the terrestrial planets orbit in the same plane, which they do not. Mercury has an orbital inclination relative to the ecliptic of 7.004˚, Venus 3.395˚, Earth 0.000˚ (by definition), and Mars 1.848˚. Calculating the distances in 3D will change the values a little, but not by much.
Now let’s switch gears and find the average distance over time between Earth and the other terrestrial planets—a very different question. But we want to pick a time period to average over that is sufficiently long enough that each planet spends as much time on the opposite side of the Sun from us as it does on our side of the Sun. The time interval between successive conjunctions (in the case of Mercury and Venus) or oppositions (Mars) is called the synodic period and is calculated as follows:
P1 = 87.9691d = orbital period of Mercury
P2 = 224.701d = orbital period of Venus
P3 = 365.256d = orbital period of Earth
P4 = 686.971d = orbital period of Mars
S1 = (P1-1 – P3-1)-1 = synodic period of Mercury = 115.877d
S2 = (P2-1 – P3-1)-1 = synodic period of Venus = 583.924d
S4 = (P3-1 – P4-1)-1 = synodic period of Mars = 779.946d
I wrote a quick little SAS program to numerically determine that an interval of 9,387 days (25.7 years) would be a good choice, because
9387 / 115.877 = 81.0083, for Mercury
9387 / 583.924 = 16.0757, for Venus
9387 / 779.946 = 12.0354, for Mars
The U.S Naval Observatory provides a free computer program called the Multiyear Interactive Computer Almanac (MICA), so I was able to quickly generate a file for each planet, Mercury, Venus, and Mars, giving the Earth-to-planet distance for 9,387 days beginning 0h UT 1 May 2019 through 0h UT 10 Jan 2045. Here are the results:
|Planet||Mean (AU)||Median (AU)||Min (AU)||Max (AU)|
As you can see, averaged over time, Mercury is the nearest planet to the Earth!
For a more mathematical treatment, see the article in the 12 Mar 2019 issue of Physics Today.
1 See my article Average Orbital Distance for details.
American composer George Gershwin left us much too soon at the young age of 38. He died of a brain tumor in 1937, and eight years after his death a somewhat fictionalized movie about his life was released in 1945, Rhapsody in Blue.
One remarkable aspect of this movie is a number of people who knew Gershwin were in the movie as themselves: Oscar Levant, Paul Whiteman (who premiered Rhapsody in Blue), Hazel Scott, Anne Brown, Al Jolson, George White, and Elsa Maxwell. It is a love letter to this remarkable composer and musician.
Robert Alda (father of Alan Alda) turns in a great performance as George Gershwin, as does Joan Leslie as his fictionalized love interest Julie Adams.
Strong performances were also turned in by Morris Carnovsky as George Gershwin’s father, Albert Bassermann as his fictionalized teacher Professor Franck (perhaps patterned in part after both Charles Hambitzer and Rubin Goldmark), and Herbert Rudley as Ira Gershwin.
And then there’s the wonderful music of George Gershwin throughout the film, including much of An American in Paris, a personal favorite of mine. I’ll bet you’ll hear familiar songs that you didn’t even know were written by Gershwin!
I loved this movie. Unfortunately, it is not available through either Netflix or Amazon streaming, but you can purchase a high-quality DVD for $12.99 from Warner Brothers.
If you don’t know much about George Gershwin, this movie is a good starting point. After you watch it, I guarantee you’ll want to learn more about the real George Gershwin and his music. Enjoy!