Zodiacal Light 2019

In this year of 2019, the best dates and times for observing the zodiacal light are listed below. The sky must be very clear with little or no light pollution. The specific times listed are for Dodgeville, Wisconsin.

2019BeginEndDirection
Tue. Jan. 226:39 p.m.7:03 p.m.West
Wed. Jan. 236:40 p.m.7:40 p.m.West
Thu. Jan. 246:41 p.m.7:41 p.m.West
Fri. Jan. 256:42 p.m.7:42 p.m.West
Sat. Jan. 266:43 p.m.7:43 p.m.West
Sun. Jan. 276:44 p.m.7:44 p.m.West
Mon. Jan. 286:45 p.m.7:45 p.m.West
Tue. Jan. 296:46 p.m.7:46 p.m.West
Wed. Jan. 306:48 p.m.7:48 p.m.West
Thu. Jan. 316:49 p.m.7:49 p.m.West
Fri. Feb. 16:50 p.m.7:50 p.m.West
Sat. Feb. 26:51 p.m.7:51 p.m.West
Sun. Feb. 36:52 p.m.7:52 p.m.West
Mon. Feb. 46:53 p.m.7:53 p.m.West
Tue. Feb. 56:55 p.m.7:55 p.m.West
Wed. Feb. 67:09 p.m.7:56 p.m.West
Thu. Feb. 217:14 p.m.8:14 p.m.West
Fri. Feb. 227:15 p.m.8:15 p.m.West
Sat. Feb. 237:16 p.m.8:16 p.m.West
Sun. Feb. 247:17 p.m.8:17 p.m.West
Mon. Feb. 257:19 p.m.8:19 p.m.West
Tue. Feb. 267:20 p.m.8:20 p.m.West
Wed. Feb. 277:21 p.m.8:21 p.m.West
Thu. Feb. 287:22 p.m.8:22 p.m.West
Fri. Mar. 17:23 p.m.8:23 p.m.West
Sat. Mar. 27:25 p.m.8:25 p.m.West
Sun. Mar. 37:26 p.m.8:26 p.m.West
Mon. Mar. 47:27 p.m.8:27 p.m.West
Tue. Mar. 57:28 p.m.8:28 p.m.West
Wed. Mar. 67:30 p.m.8:30 p.m.West
Thu. Mar. 77:31 p.m.8:31 p.m.West
Fri. Mar. 88:01 p.m.8:32 p.m.West
Fri. Mar. 228:50 p.m.9:24 p.m.West
Sat. Mar. 238:52 p.m.9:52 p.m.West
Sun. Mar. 248:53 p.m.9:53 p.m.West
Mon. Mar. 258:54 p.m.9:54 p.m.West
Tue. Mar. 268:56 p.m.9:56 p.m.West
Wed. Mar. 278:57 p.m.9:57 p.m.West
Thu. Mar. 288:59 p.m.9:59 p.m.West
Fri. Mar. 299:00 p.m.10:00 p.m.West
Sat. Mar. 309:01 p.m.10:01 p.m.West
Sun. Mar. 319:03 p.m.10:03 p.m.West
Mon. Apr. 19:04 p.m.10:04 p.m.West
Tue. Apr. 29:06 p.m.10:06 p.m.West
Wed. Apr. 39:07 p.m.10:07 p.m.West
Thu. Apr. 49:09 p.m.10:09 p.m.West
Fri. Apr. 59:10 p.m.10:10 p.m.West
Sat. Apr. 69:12 p.m.10:12 p.m.West
Sun. Apr. 710:03 p.m.10:13 p.m.West
Thu. Aug. 293:39 a.m.4:39 a.m.East
Fri. Aug. 303:40 a.m.4:40 a.m.East
Sat. Aug. 313:42 a.m.4:42 a.m.East
Sun. Sep. 13:43 a.m.4:43 a.m.East
Mon. Sep. 23:45 a.m.4:45 a.m.East
Tue. Sep. 33:46 a.m.4:46 a.m.East
Wed. Sep. 43:48 a.m.4:48 a.m.East
Thu. Sep. 53:49 a.m.4:49 a.m.East
Fri. Sep. 63:50 a.m.4:50 a.m.East
Sat. Sep. 73:52 a.m.4:52 a.m.East
Sun. Sep. 83:53 a.m.4:53 a.m.East
Mon. Sep. 93:55 a.m.4:55 a.m.East
Tue. Sep. 103:56 a.m.4:56 a.m.East
Wed. Sep. 113:57 a.m.4:57 a.m.East
Thu. Sep. 124:52 a.m.4:59 a.m.East
Fri. Sep. 275:11 a.m.5:18 a.m.East
Sat. Sep. 284:19 a.m.5:19 a.m.East
Sun. Sep. 294:20 a.m.5:20 a.m.East
Mon. Sep. 304:21 a.m.5:21 a.m.East
Tue. Oct. 14:23 a.m.5:23 a.m.East
Wed. Oct. 24:24 a.m.5:24 a.m.East
Thu. Oct. 34:25 a.m.5:25 a.m.East
Fri. Oct. 44:26 a.m.5:26 a.m.East
Sat. Oct. 54:27 a.m.5:27 a.m.East
Sun. Oct. 64:29 a.m.5:29 a.m.East
Mon. Oct. 74:30 a.m.5:30 a.m.East
Tue. Oct. 84:31 a.m.5:31 a.m.East
Wed. Oct. 94:32 a.m.5:32 a.m.East
Thu. Oct. 104:33 a.m.5:33 a.m.East
Fri. Oct. 114:43 a.m.5:34 a.m.East
Sat. Oct. 264:51 a.m.5:19 a.m.East
Sun. Oct. 274:53 a.m.5:53 a.m.East
Mon. Oct. 284:54 a.m.5:54 a.m.East
Tue. Oct. 294:55 a.m.5:55 a.m.East
Wed. Oct. 304:56 a.m.5:56 a.m.East
Thu. Oct. 314:57 a.m.5:57 a.m.East
Fri. Nov. 14:58 a.m.5:58 a.m.East
Sat. Nov. 24:59 a.m.5:59 a.m.East
Sun. Nov. 34:01 a.m.5:01 a.m.East
Mon. Nov. 44:02 a.m.5:02 a.m.East
Tue. Nov. 54:03 a.m.5:03 a.m.East
Wed. Nov. 64:04 a.m.5:04 a.m.East
Thu. Nov. 74:05 a.m.5:05 a.m.East
Fri. Nov. 84:06 a.m.5:06 a.m.East
Sat. Nov. 94:07 a.m.5:07 a.m.East
Sun. Nov. 104:34 a.m.5:08 a.m.East
Sun. Nov. 244:23 a.m.4:27 a.m.East
Mon. Nov. 254:24 a.m.5:24 a.m.East
Tue. Nov. 264:25 a.m.5:25 a.m.East
Wed. Nov. 274:26 a.m.5:26 a.m.East
Thu. Nov. 284:27 a.m.5:27 a.m.East
Fri. Nov. 294:28 a.m.5:28 a.m.East
Sat. Nov. 304:29 a.m.5:29 a.m.East
Sun. Dec. 14:30 a.m.5:30 a.m.East
Mon. Dec. 24:31 a.m.5:31 a.m.East
Tue. Dec. 34:32 a.m.5:32 a.m.East
Wed. Dec. 44:33 a.m.5:33 a.m.East
Thu. Dec. 54:34 a.m.5:34 a.m.East
Fri. Dec. 64:35 a.m.5:35 a.m.East
Sat. Dec. 74:35 a.m.5:35 a.m.East
Sun. Dec. 84:36 a.m.5:36 a.m.East
Mon. Dec. 94:37 a.m.5:37 a.m.East
Tue. Dec. 105:29 a.m.5:38 a.m.East

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.

Total Lunar Eclipse 2019

We’ll be treated to a front-row seat for the total lunar eclipse this coming Sunday night and Monday morning, January 20/21, 2019! Here are the local circumstances for Dodgeville, Wisconsin.

Time (CST)EventAltitude
8:36:29 p.m.Penumbral Eclipse Begins40°
9:10 p.m.Penumbra first visible?46°
9:33:55 p.m.Partial Eclipse Begins50°
10:41:19 p.m.Total Eclipse Begins60°
11:12:18 p.m.Greatest Eclipse64°
11:43:18 p.m.Total Eclipse Ends66°
12:14:31 a.m.Moon crosses the celestial meridian67°
12:50:42 a.m.Partial Eclipse Ends66°
1:15 a.m.Penumbra last visible?64°
1:48:06 a.m.Penumbral Eclipse Ends60°

This is the first total lunar eclipse visible in its entirety from SW Wisconsin since September 28, 2015; the next such event won’t occur again until May 16, 2022. You’ll note in the table above, the Moon will be 64° above the horizon at mid-totality. The Moon has not been this high in our sky at mid-totality since November, 29, 1993 (66°), and it will not be this high again at mid-totality until January 21, 2048 (67°).

The first hint of shading will occur on the left (eastward-facing) edge of the Moon around 9:10 p.m. The first sliver of the full Moon enters the umbral shadow of the Earth at 9:33 p.m., so you’ll want to be watching by then. The entire Moon will be immersed in the umbral shadow of the Earth 67 minutes later at 10:41 p.m. This means that if you were anywhere on the nearside of the Moon you would see the dark Earth (except for city lights) completely covering the Sun, with a spectacular “ring of fire” all the way round the limb of the Earth refracting orangish-red light through our atmosphere—the combined light of all the world’s sunrises and sunsets at that moment.

This, of course, will continue as the Moon penetrates deeper into the umbral shadow of the Earth, reaching its closest to the center of the Earth’s shadow at mid-eclipse at 11:12 p.m.

The best place in the world to view this total lunar eclipse (assuming it is clear) will be Guantánamo Province in Cuba. Just 8 miles north of the municipality of El Salvador, Cuba, the Moon will be directly overhead at mid-eclipse.

There has been an unfortunate tendency of the mainstream media in recent years to use the term “Blood Moon” to describe a total lunar eclipse. Why must we use imagery so often associated with violence, death, and destruction in our discourse? The color of a total lunar eclipse depends upon the condition and transparency of the Earth’s atmosphere during the eclipse, and it can range from orange to coppery to red, and rarely even gray or brownish, so why not say orangish-red and leave it at that?

Direct Imaging of Exoplanets Through Occultations

Planetary orbits are randomly oriented throughout our galaxy. The probability that an exoplanet’s orbit will be fortuitously aligned to allow that exoplanet to transit across the face of its parent star depends upon the radius of the star, the radius of the planet, and the distance of the planet from the star. In general, planets orbiting close-in are more likely to be seen transiting their star then planets orbiting further out.

The equation for the probability of observing a exoplanet transit event is

p_{tra} = \left (\frac{R_{\bigstar}+R_{p}}{a} \right )\left (\frac{1}{1-e^{2}} \right )

where ptra is the transit probability, R* is the radius of the star, Rp is the radius of the planet, a is the semi-major axis of the planetary orbit, and e is the eccentricity of the planetary orbit 

Utilizing the data in the NASA Exoplanet Archive for the 1,463 confirmed exoplanets where the above data is available (and assuming e = 0 when eccentricity is unavailable), we find that the median exoplanet transit probability is 0.0542. This means that, on average, 1 out of every 18 planetary systems will be favorably aligned to allow us to observe transits. However, keep in mind that our present sample of exoplanets is heavily biased towards large exoplanets orbiting close to their parent star. Considering a hypothetical sample of Earth-sized planets orbiting 1 AU from a Sun-sized star, the transit probability drops to 0.00469, which means that we would be able to detect only about 1 out of every 213 Earth-Sun analogs using the transit method.

How might we detect some of the other 99.5%? My admired colleague in England, Abdul Ahad, has written a paper about his intriguing idea: “Detecting Habitable Exoplanets During Asteroidal Occultations”. Abdul’s idea in a nutshell is to image the immediate environment around nearby stars while they are being occulted by asteroids or trans-Neptunian objects (TNOs) in order to detect planets orbiting around them. While there are many challenges (infrequency of observable events, narrow shadow path on the Earth’s surface, necessarily short exposure times, and extremely faint planetary magnitudes), I believe that his idea has merit and will one day soon be used to discover and characterize exoplanets orbiting nearby stars.

Ahad notes that the apparent visual magnitude of any given exoplanet will be directly proportional to the apparent visual magnitude of its parent star, since exoplanets shine by reflected light. Not only that, Earth-sized and Earth-like planets orbiting in the habitable zone of any star would shine by reflected light of the same intrinsic brightness, regardless of the brightness of the parent star. He also notes that the nearer the star is to us, the greater will be a given exoplanet’s angular distance from the occulted star. Thus, given both of these considerations (bright parent star + nearby parent star = increased likelihood of detection), nearby bright stars such as Alpha Centauri A & B, Sirius A, Procyon A, Altair, Vega, and Fomalhaut offer the best chance of exoplanet detection using this technique.

Since an exoplanet will be easiest to detect when it is at its greatest angular distance from its parent star, we will be seeing only about 50% of its total reflected light. An Earth analog orbiting Alpha Centauri A would thus shine at visual magnitude +23.7 at 0.94″ angular distance, and for Alpha Centauri B the values would be +24.9 and 0.55″.

Other considerations include the advantage of an extremely faint occulting solar system object (making it easier to detect faint exoplanets during the occultation event), and the signal boost offered by observing in the infrared, since exoplanets will be brightest at these wavelengths.

A distant (and therefore slow-moving) TNO would be ideal, but the angular size of the TNO needs to be larger than the angular size of the occulted star. However, slow-moving objects mean that occultation events will be rare.

The best chance of making this a usable technique for exoplanet discovery would be a space-based observatory that could be positioned at the center of the predicted shadow and would be able to move along with the shadow to increase exposure times (Ahad, personal communication). It would be an interesting challenge in orbital mechanics to design the optimal base orbit for such a spacecraft. The spacecraft orbit would be adjusted to match the position and velocity of the occultation shadow for each event using an ion drive or some other electric propulsion system.

One final thought on the imaging necessary to detect exoplanets using this technique. With a traditional CCD you would need to begin and end the exoplanet imaging exposure(s) only while the parent star is being occulted. This would not be easy to do, and would require two telescopes – one for the occultation event detection and one for the exoplanet imaging. A better approach would be to use a Geiger-mode avalanche photodiode (APD). Here’s a description of the device captured in 2016 on the MIT Lincoln Labs Advanced Imager Technology website:

A Geiger-mode avalanche photodiode (APD), on the other hand, can be used to build an all-digital pixel in which the arrival of each photon triggers a discrete electrical pulse. The photons are counted digitally within the pixel circuit, and the readout process is therefore noise-free. At low light levels, there is still noise in the image because photons arrive at random times so that the number of photon detection events during an exposure time has statistical variation. This noise is known as shot noise. One advantage of a pixel that can digitally count photons is that if shot noise is the only noise source, the image quality will be the best allowed by the laws of physics. Another advantage of an array of photon counting pixels is that, because of its noiseless readout, there is no penalty associated with reading the imager out frequently. If one reads out a thousand 1-ms exposures of a static scene and digitally adds them, one gets the same image quality as a single 1-s exposure. This would not be the case with a conventional imager that adds noise each time it is read out.

References
Ahad, A., “Detecting Habitable Exoplanets During Asteroidal Occultations”, International Journal of Scientific and Innovative Mathematical Research, Vol. 6(9), 25-30 (2018).
MIT Lincoln Labs, Advanced Imager Technology, https://www.ll.mit.edu/mission/electronics/ait/single-photon-sensitive-imagers/passive-photon-counting.html. Retrieved March 17, 2016.
NASA Exoplanet Archive https://exoplanetarchive.ipac.caltech.edu.
Winn, J.N., “Exoplanet Transits and Occultations,” in Exoplanets, ed. Seager, S., University of Arizona Press, Tucson (2011).

My Music Recorded in 1976

Leaving Behind the Tears

All songs written, performed, and recorded by David Oesper

Recorded January – August 1976

Remixed August 20, 1976

Special thanks to Bob Gebhardt for loaning me his open reel tape deck in 1976.

Special thanks also to Jake Ewalt for his skillful analog to digital transfer in July 2002.

VOLUME 1VOLUME 2
1. Hope1. Here With You
2. Leaving Behind the Tears2. Memories
3. Misled Again3. So Long
4. Reaching Out For Love4. Did I Tell You
5. Rock Star5. The Day You Left Me
6. Time Out6. Far Away Somewhere
7. You Should Have Seen7. Moments With You
8. I’m Thinking About You8. Hometown Boogie
9. Destiny9. He’s Gone
10. Picking Up the Pieces10. Hold On
11. Life11. If That Is All
12. For All Time12. In the End
13. Idol13. I’ll Come Back
14. Rock of the Country14. You’re the One
15. Pathless Roads15. No Other Person
16. You Get In Your Own Way

Probing the Proton

We have known since 1968 that protons are not elementary particles and are comprised of three persistent quarks: two up quarks with charge +⅔e, and one down quark with charge -⅓e, where e is the charge of the electron (which is an elementary particle).

But in a brilliant illustration of E = mc2, we now know that very little of the proton’s 938 MeV rest mass comes from the rest mass of its component up and down quarks.

The mass composition of a proton is:

½% up quark rest mass (¼% × 2)

½% down quark rest mass

8% sea quarks (virtual quark-antiquark pairs created  by the strong nuclear force)

23% quark-gluon interaction energy (the trace anomaly)

32% kinetic energy of the up and down quarks

36% momentum energy of the massless gluons that hold the up and down quarks together within the proton

We thus see that just 1% of the rest mass of a proton is provided by the rest mass of its three component valence quarks (2 up + 1 down), and the other 99% is interaction energy!

Even though protons are in the nucleus of every atom of matter in the universe, we still do not fully understand them.  For example, there is the proton radius puzzle, the proton spin puzzle, and the significant question of proton decay.

References
E. Conover. How the proton’s mass adds up. Science News. Vol. 194, December 22, 2018, p. 8.
E. Conover. There’s still a lot we don’t know about the proton. Science News. Vol. 191, April 29, 2017, p. 22.
Y.B. Yang et al. Proton mass decomposition from the QCD energy momentum tensor. Physical Review Letters. Vol. 121, November 23, 2018, p. 212001. doi: 10.1103/PhysRevLett.121.212001.