Understanding Space and Time

Have you ever noticed how it is almost impossible to find documentaries made more than a few years ago?  I was doing some reading on the Casimir effect this evening and came across the name of Julian Schwinger (1918-1994), the American theoretical physicist who shared the 1965 Nobel Prize in Physics with Richard Feynman (1918-1988) and Shin’ichirō Tomonaga (1906-1979).  I remember, after all these years, that I had enjoyed watching a BBC documentary series that featured Schwinger (as well as George Abell) called Understanding Space and Time.  It was broadcast in 1979 or 1980 and featured thirteen 28-minute episodes.

  1. Ground control to Mr. Galileo
  2. As Surely as Columbus Saw America
  3. Pushed to the Limit
  4. Conflict Brought to Light
  5. Marking Time
  6. E = mc2
  7. An Isolated Fact
  8. The Royal Road
  9. At the Frontier
  10. Shades of Black
  11. Measuring Shadows: The Universe Today
  12. A Note of Uncertainty: The Universe Tomorrow
  13. Vanished Brilliance: The Universe Yesterday

Granted, some of this material is now dated, but much of it is still relevant and certainly of historical interest.  Why is it (and a host of other documentaries) not available on DVD or for downloading?

We really need a company to fill a different niche alongside The Great Courses, Curiosity Stream, and Netflix.  That niche would be to uncover and rerelease past documentaries of merit1, often hosted or presented by historically important individuals.  Documentaries such as Understanding Space and Time would be nice to own and watch again.

1One must certainly include many PBS documentaries and older episodes of documentary series—NOVA, for example—that are no longer available.

Dateline 2024: Total Solar Eclipse

In little more than six years, another total solar eclipse across the continental U.S. will pass as close as Southern Illinois and Indiana.  Like our recent eclipse of August 21, 2017, the next total solar eclipse will also take place on a Monday and, remarkably, just a few minutes earlier in the day.  Save the date: April 8, 2024.   Actually, not long to wait.  Think about what you were doing around December 7, 2011.  Can you remember?  No question about it, the next six years will go faster than the previous six did.  Seems that as we age our sense of time changes, and time seems to go faster and faster.

The point of maximum length of totality for the 2017 eclipse was 12 miles NW of the center of Hopkinsville, Kentucky, where totality lasted 2m40s and the path of totality was 71 miles wide.

The point of maximum length of totality for the 2024 eclipse will be near Nazas, Mexico (in the state of Durango), where totality will last 4m28s and the path of totality will be 123 miles wide.  Yes, this will be a longer eclipse!

Remarkably, there is a location in southern Illinois that is on the centerline of both the 2017 and 2024 eclipses!  That location is 37°38’32” N, 89°15’55” W, SW of Carbondale, Illinois, near Cedar Lake and the Midland Hills Country Club.

When did a total solar eclipse last grace Dodgeville, Wisconsin?  Nearly 639 years ago, on May 16, 1379.  The duration of totality was 3m48s.  Perhaps the Oneota people then living in this area witnessed the event.

The next total solar eclipse visible from Dodgeville won’t happen for another 654 years.  There’ll be annular eclipses in 2048, 2213, 2410, 2421, and 2614.  Then, finally, on June 17, 2672, the totally-eclipsed Sun will once again grace the skies of Dodgeville—weather permitting, of course.  The duration of the eclipse at Dodgeville will be 2m47s.  There will be another annular eclipse in 2678, followed by another total eclipse (duration 3m01s) on June 8, 2681.  Then, just two years later there’ll be another total eclipse at Dodgeville: on November 10, 2683 (0m49s).  That’s three total eclipses and one annular eclipse visible at Dodgeville in just 11 years!

Faintest Constellations

There are a dozen constellations with no star brighter than +4.0 magnitude.  Many of them are deep in the southern sky.  They are:

ANTLIA, the Air Pump
Brightest Star: Alpha Antliae, apparent visual magnitude +4.25

ANT-lee-uh

CAELUM, the Engraving Tool
Brightest Star: Alpha Caeli, apparent visual magnitude +4.45

SEE-lum

CAMELOPARDALIS, the Giraffe
Brightest Star: Beta Camelopardalis, apparent visual magnitude +4.02

cuh-MEL-oh- PAR-duh-liss

CHAMAELEON, the Chameleon
Brightest Star: Alpha Chamaeleontis, apparent visual magnitude +4.047

cuh-MEAL-yun, or cuh-MEAL-ee-un

COMA BERENICES, Berenice’s Hair
Brightest Star: Beta Comae Berenices, apparent visual magnitude +4.25

COE-muh BER-uh-NICE-eez

CORONA AUSTRALIS, the Southern Crown
Brightest Star: Meridiana, apparent visual magnitude +4.087

cuh-ROE-nuh aw-STRAL-iss

MENSA, the Table Mountain
Brightest Star: Alpha Mensae, apparent visual magnitude +5.09

MEN-suh

MICROSCOPIUM, the Microscope
Brightest Star: Gamma Microscopii, apparent visual magnitude +4.654

my-cruh-SCOPE-ee-um

NORMA, the Carpenter’s Square
Brightest Star: Gamma2 Normae, apparent visual magnitude +4.02

NOR-muh

SCULPTOR, the Sculptor
Brightest Star: Alpha Sculptoris, apparent visual magnitude +4.27

SCULP-ter

SEXTANS, the Sextant
Brightest Star: Alpha Sextantis, apparent visual magnitude +4.49

SEX-tunz

VULPECULA, the Fox
Brightest Star: Anser, apparent visual magnitude +4.45

vul-PECK-yuh-luh

Planets Without Satellites

It may be rare for terrestrial planets to be accompanied by satellites, especially large ones.  It is far too early for us to draw any conclusions about terrestrial exoplanets (as no terrestrial exoplanet exomoons have yet been detectable), but in our own solar system, only two planets have no satellites, and they are both terrestrial planets: Mercury and Venus.  Mars has two small satellites that are almost certainly captured asteroids from the adjacent asteroid belt rather than primordial moons, and that leaves only the Earth among the terrestrial planets to host a large satellite, though it, too, is almost certainly not primordial.  Only the giant planets (Jupiter, Saturn, Uranus, and Neptune) have large systems of satellites, at least some of which may have formed while the planet itself was forming.

Though neither Mercury nor Venus has any natural satellites, Venus is known to have at least four transient quasi-satellites, more generally referred to as co-orbitals.  They are:

322756 (2001 CK32)
Comes close to both Earth and Mercury in its eccentric orbit (e=0.38).
Wiki  JPL  Orrery

2002 VE68
Comes close to both Earth and Mercury in its eccentric orbit (e=0.41).
Wiki  JPL  Orrery

2012 XE133
Comes close to both Earth and Mercury in its eccentric orbit (e=0.43).
Wiki JPL Orrery

2013 ND15
Comes close to both Earth and Mercury in its very eccentric orbit (e=0.61), and is the only known trojan of Venus, currently residing near its L4 Lagrangian point.
Wiki JPL Orrery

2015 WZ12 is a possible fifth Venus co-orbital candidate.  Observations during the next favorable observing opportunity in November of this year will hopefully better determine its orbit and nature.

2015 WZ12
Possible Venus co-orbital.
Wiki JPL Orrery

There is concern that there may be many more Venus co-orbitals, as yet undiscovered (and challenging to discover) that pose risks as potentially hazardous asteroids (PHAs) to our planet.

There are no known Mercury co-orbitals.  If any do exist, they will be exceedingly difficult to detect since they will always be in the glare of the Sun as seen from Earth.

Asteroids orbiting interior to Mercury’s orbit (a < 0.387 AU) would be called vulcanoids.  I say “would be” because none have been discovered yet, though in all fairness, they will be extremely difficult to detect.

A spacecraft orbiting interior to Mercury’s orbit looking outward would be an ideal platform for detecting, inventorying, and characterizing all potentially hazardous asteroids (PHAs) that exist in the inner solar system. A surveillance telescope in a circular orbit 0.30 AU from the Sun would orbit the Sun every 60 days.

The Parker Solar Probe, scheduled to launch later this year, will orbit the Sun between 0.73 AU and an extraordinarily close 0.04 AU, though it will be looking towards the Sun, not away from it.  The Near-Earth Object Camera (NEOCam) is a proposed mission to look specifically for PHAs using an infrared telescope from a vantage point at the Sun-Earth L1 Lagrangian point.

References
de la Fuente Marcos, C., & de la Fuente Marcos, R. 2014, MNRAS, 439, 2970
de la Fuente Marcos, C., & de la Fuente Marcos, R. 2017, RNAAS, 1, 3
Sheppard, S., & Trujillo, C. 2009, Icarus, 202, 12

Spirit and Opportunity

The Mars Exploration Rovers Spirit and Opportunity landed on Mars on January 4, 2004 and January 25, 2004, respectively.  Spirit continued operating until contact was lost on March 22, 2010, a total of 2,269 Earth days, which is 2,208 days on Mars (sols)1Spirit operated on the Martian surface 24.5 times as long as its design life of 90 sols.

Even more amazing: Opportunity has been operating on the Martian surface (as of this publication date) for 5,108 Earth days, which is 4,971 sols.   That’s 55.2 times its design life of 90 sols!

Spirit and Opportunity faced their greatest challenge up to that point during the global Martian dust storm of July 2007.  Here is what I wrote about it back then.

Spirit and Opportunity‘s Greatest Challenge (7-26-07)

The intrepid Mars Exploration Rovers Spirit and Opportunity—which have been operating on the surface of Mars over 14 times longer than planned—each carry two 8 amp-hour lithium batteries, and these batteries are charged by solar panels.  Before dust storms began significantly reducing the amount of sunlight reaching the rovers’ solar panels, they were generating about 700 watt-hours of electricity each day—enough to power a 100-watt light bulb for seven hours.  Not much, it may seem, but plenty enough to operate each rover’s internal heaters, motors, scientific instruments, and communication equipment.

In recent weeks, both rovers have seriously been affected by the dust storms, particularly Opportunity which last week was able to generate only 128 watt-hours of electricity on the worst day.  With precious little energy to replenish the internal batteries, controllers have hunkered down the rovers to conserve energy for the most critical need—internal heaters to keep the core electronics warm enough to operate.  Remember, the average surface temperature on Mars is -85° F!

At press time, weather conditions appear to be improving for both rovers, but there are still worries that the rovers could have been damaged by all that dust blowing at them for days on end.


As it turns out, after the global dust storm of 2007 subsided, the rovers benefited from subsequent “cleaning events” where the winds of Mars blew most of the dust off of the solar panels.

There have been no global dust storms on Mars since 2007; however, another one is anticipated later this year.  Hopefully, our intrepid Opportunity will weather the storm and continue to generate enough life-giving power from its precious solar panels .

1A Martian day is called a sol and is slightly longer than an Earth day.  A mean solar day on Earth is 24h00m00s, by definition, but a mean solar day on Mars is 24h39m35.244s Earth time.  To convert Earth days to Martian sols, divide the number of Earth days by 1.0275.

Welcome to the Zooniverse!

We live in a society where science is little more than a “spectator sport” for most of us who have an interest in it.  Data collection and original research often require substantial investments of time and money, as well as a long-term commitment.  Those of us who are already working full time and, in spite of that, have little discretionary income, often find “participatory science” out of reach, no matter how great our enthusiasm or aptitude.

As today’s scientific instruments increasingly generate enormous quantities of data, the people who “do science” for a living are too few in number to analyze all that data.  Fortunately, this is one area where “citizen scientists” can help.

There are a number of interesting scientific projects that lend themselves well to “crowd sourcing”, and Zooniverse is a portal to many of them.

Here are the currently active Zooniverse projects in the disciplines of astronomy and physics.

Backyard Worlds: Planet 9
Discover new brown dwarfs and possibly a new solar system planet by scrutinizing images from the Wide-field Infrared Survey Telescope (WISE).

Comet Hunters
Discover new comets previously misidentified as asteroids by analyzing deep images taken by the Subaru 8.2-meter telescope in Hawaii.

Disk Detective
Help search for stars with undiscovered disks of dust around them.  These stars show us where to look for planetary systems and how they form.

Exoplanet Explorers
Discover transiting exoplanet candidates in Kepler’s K2 data.

Galaxy Zoo   Galaxy Zoo: 3D
Classify galaxies, many of which have never been studied before, and look for unusual features.

Gravity Spy
Identify and characterize “glitches” in LIGO data to make it easier to identify gravitational wave events.

Higgs Hunters
Help search for unknown exotic particles in data from the Large Hadron Collider (LHC), the world’s largest and most powerful particle collider.

Milky Way Project
Classify images from two infrared space telescopes: the Spitzer Space Telescope (SST) and the Wide-field Infrared Survey Telescope (WISE).

Planet Four
Identify and measure features on the surface of Mars.

Planet Hunters
Discover transiting exoplanet candidates in data from the Kepler spacecraft.

Radio Galaxy Zoo
Search radio images of galaxies for evidence of jets caused by matter falling into supermassive black holes.

Radio Meteor Zoo
Identify meteors through the reflection of radio waves from their ionization trails.

Solar Stormwatch II
Characterize solar storms and their interaction with the solar wind through the analysis of images from NASA’s twin Solar Terrestrial Relations Observatory (STEREO) spacecraft.

Supernova Hunters
Scrutinize the most recent images collected by the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) in Hawaii in comparison to reference images to discover new supernovae that can then be immediately followed by ground-based and space-based telescopes.

All of these projects utilize “machine learning” computer algorithms such as neural networks and random forests (artificial intelligence, or AI) to some extent, and in fact citizen scientist participants help “train” these algorithms so they do a better job of finding or classifying or whatever.  For a great introduction to this subject, see “Machines Learning Astronomy” by Sky & Telescope news editor Monica Young in the December 2017 issue, pp. 20-27.

As machine learning algorithms get better and better, they may no longer need citizen scientists to train them.

In the meantime, have fun and contribute to science!

Zodiacal Light 2018

In this year of 2018, the best dates and times for observing the zodiacal light are listed below.  The sky must be very clear.  The specific times listed are for Dodgeville, Wisconsin.

2018 Begin End Direction
Fri. Feb. 2 6:52 p.m. 7:52 p.m. West
Sat. Feb. 3 6:53 p.m. 7:53 p.m. West
Sun. Feb. 4 6:54 p.m. 7:54 p.m. West
Mon. Feb. 5 6:55 p.m. 7:55 p.m. West
Tue. Feb. 6 6:57 p.m. 7:57 p.m. West
Wed. Feb. 7 6:58 p.m. 7:58 p.m. West
Thu. Feb. 8 6:59 p.m. 7:59 p.m. West
Fri. Feb. 9 7:00 p.m. 8:00 p.m. West
Sat. Feb. 10 7:01 p.m. 8:01 p.m. West
Sun. Feb. 11 7:02 p.m. 8:02 p.m. West
Mon. Feb. 12 7:04 p.m. 8:04 p.m. West
Tue. Feb. 13 7:05 p.m. 8:05 p.m. West
Wed. Feb. 14 7:06 p.m. 8:06 p.m. West
Thu. Feb. 15 7:07 p.m. 8:07 p.m. West
Fri. Feb. 16 7:08 p.m. 8:08 p.m. West
Sat. Mar. 3 7:27 p.m. 7:59 p.m. West
Sun. Mar. 4 7:28 p.m. 8:28 p.m. West
Mon. Mar. 5 7:29 p.m. 8:29 p.m. West
Tue. Mar. 6 7:30 p.m. 8:30 p.m. West
Wed. Mar. 7 7:32 p.m. 8:32 p.m. West
Thu. Mar. 8 7:33 p.m. 8:33 p.m. West
Fri. Mar. 9 7:34 p.m. 8:34 p.m. West
Sat. Mar. 10 7:35 p.m. 8:35 p.m. West
Sun. Mar. 11 8:37 p.m. 9:37 p.m. West
Mon. Mar. 12 8:38 p.m. 9:38 p.m. West
Tue. Mar. 13 8:39 p.m. 9:39 p.m. West
Wed. Mar. 14 8:41 p.m. 9:41 p.m. West
Thu. Mar. 15 8:42 p.m. 9:42 p.m. West
Fri. Mar. 16 8:43 p.m. 9:43 p.m. West
Sat. Mar. 17 8:44 p.m. 9:44 p.m. West
Sun. Mar. 18 8:46 p.m. 9:46 p.m. West
Mon. Mar. 19 9:38 p.m. 9:47 p.m. West
Mon. Apr. 2 9:06 p.m. 9:56 p.m. West
Tue. Apr. 3 9:08 p.m. 10:08 p.m. West
Wed. Apr. 4 9:09 p.m. 10:09 p.m. West
Thu. Apr. 5 9:11 p.m. 10:11 p.m. West
Fri. Apr. 6 9:12 p.m. 10:12 p.m. West
Sat. Apr. 7 9:14 p.m. 10:14 p.m. West
Sun. Apr. 8 9:15 p.m. 10:15 p.m. West
Mon. Apr. 9 9:17 p.m. 10:17 p.m. West
Tue. Apr. 10 9:18 p.m. 10:18 p.m. West
Wed. Apr. 11 9:20 p.m. 10:20 p.m. West
Thu. Apr. 12 9:21 p.m. 10:21 p.m. West
Fri. Apr. 13 9:23 p.m. 10:23 p.m. West
Sat. Apr. 14 9:25 p.m. 10:25 p.m. West
Sun. Apr. 15 9:26 p.m. 10:26 p.m. West
Mon. Apr. 16 9:28 p.m. 10:28 p.m. West
Tue. Apr. 17 9:43 p.m. 10:29 p.m. West
Thu. Aug. 9 3:08 a.m. 3:44 a.m. East
Fri. Aug. 10 3:09 a.m. 4:09 a.m. East
Sat. Aug. 11 3:11 a.m. 4:11 a.m. East
Sun. Aug. 12 3:13 a.m. 4:13 a.m. East
Mon. Aug. 13 3:14 a.m. 4:14 a.m. East
Tue. Aug. 14 3:16 a.m. 4:16 a.m. East
Wed. Aug. 15 3:18 a.m. 4:18 a.m. East
Thu. Aug. 16 3:19 a.m. 4:19 a.m. East
Fri. Aug. 17 3:21 a.m. 4:21 a.m. East
Sat. Aug. 18 3:22 a.m. 4:22 a.m. East
Sun. Aug. 19 3:24 a.m. 4:24 a.m. East
Mon. Aug. 20 3:26 a.m. 4:26 a.m. East
Tue. Aug. 21 3:27 a.m. 4:27 a.m. East
Wed. Aug. 22 3:29 a.m. 4:29 a.m. East
Thu. Aug. 23 3:30 a.m. 4:30 a.m. East
Fri. Aug. 24 4:20 a.m. 4:32 a.m. East
Sat. Sep. 8 3:54 a.m. 4:54 a.m. East
Sun. Sep. 9 3:55 a.m. 4:55 a.m. East
Mon. Sep. 10 3:57 a.m. 4:57 a.m. East
Tue. Sep. 11 3:58 a.m. 4:58 a.m. East
Wed. Sep. 12 3:59 a.m. 4:59 a.m. East
Thu. Sep. 13 4:01 a.m. 5:01 a.m. East
Fri. Sep. 14 4:02 a.m. 5:02 a.m. East
Sat. Sep. 15 4:03 a.m. 5:03 a.m. East
Sun. Sep. 16 4:05 a.m. 5:05 a.m. East
Mon. Sep. 17 4:06 a.m. 5:06 a.m. East
Tue. Sep. 18 4:07 a.m. 5:07 a.m. East
Wed. Sep. 19 4:09 a.m. 5:09 a.m. East
Thu. Sep. 20 4:10 a.m. 5:10 a.m. East
Fri. Sep. 21 4:11 a.m. 5:11 a.m. East
Sat. Sep. 22 4:12 a.m. 5:12 a.m. East
Sun. Sep. 23 5:07 a.m. 5:14 a.m. East
Sun. Oct. 7 4:30 a.m. 5:04 a.m. East
Mon. Oct. 8 4:32 a.m. 5:32 a.m. East
Tue. Oct. 9 4:33 a.m. 5:33 a.m. East
Wed. Oct. 10 4:34 a.m. 5:34 a.m. East
Thu. Oct. 11 4:35 a.m. 5:35 a.m. East
Fri. Oct. 12 4:36 a.m. 5:36 a.m. East
Sat. Oct. 13 4:37 a.m. 5:37 a.m. East
Sun. Oct. 14 4:39 a.m. 5:39 a.m. East
Mon. Oct. 15 4:40 a.m. 5:40 a.m. East
Tue. Oct. 16 4:41 a.m. 5:41 a.m. East
Wed. Oct. 17 4:42 a.m. 5:42 a.m. East
Thu. Oct. 18 4:43 a.m. 5:43 a.m. East
Fri. Oct. 19 4:44 a.m. 5:44 a.m. East
Sat. Oct. 20 4:45 a.m. 5:45 a.m. East
Sun. Oct. 21 4:47 a.m. 5:47 a.m. East
Mon. Oct. 22 4:57 a.m. 5:48 a.m. East

On the February, March, and April evenings listed above, you will see a broad, faint band of light extending upwards from the western horizon, sloping a little to the left, and reaching nearly halfway to the top of the sky.

On the August, September, and October mornings listed above, you will see a broad, faint band of light extending upwards from the eastern horizon, sloping a little to the right, and reaching nearly halfway to the top of the sky.

It is essential that your view is not spoiled by nearby streetlights, parking lot lights, or dusk-to-damn insecurity lights, nor any city to the west (Feb-Apr) or east (Aug-Oct).  Give your eyes a few minutes to adjust to the darkness.  Slowly sweeping your eyes back and forth from southwest to northwest (Feb-Apr) or northeast to southeast (Aug-Oct) will help you spot the zodiacal light band.  Once spotted, you should be able to see it without moving your head.

On the February, March, and April evenings listed above, the zodiacal light is best seen right at the end of evening twilight, and remains visible for an hour or so after that.

On the August, September, and October mornings listed above, the zodiacal light is best seen about an hour or so before the beginning of morning twilight, right up to the beginning of morning twilight.

Enjoy!

Mid-Winter Mid-Night Satellite

While video recording the star Tycho 1311-1818-1 in Taurus on a very cold Thursday evening last week (-4° F) in the hope that asteroid 126561 (2002 CF105) would pass in front of it (it didn’t), I was surprised and delighted to serendipitously record a very slow moving Earth-orbiting satellite crossing the field.  Now, in order to see a satellite, it must be illuminated by sunlight.  But to see any satellite during the first week of January only 10 minutes before local midnight, it must be very far from the Earth indeed (more on that later).

Here’s a video of the event showing its complete traversal of the field of view:

Slow-Moving Satellite

I’m hoping that one of the good people that frequent the satellite observers’ forum SeeSat-L will be able to identify this unusual object.  Requisite to that, of course, are two precise positions at two precise times and the observer’s location.

A very useful online tool provided by the Department of Physics at Virginia Tech allows one to input the right ascension, declination, and x-y coordinates of between 4 and 10 known objects, and it does an astrometric solution across the field so you can determine the right ascension and declination of an unknown object.

Using Guide 9.1, Limovie, and this tool, I determined the following:

At 5 Jan 2018 5:42:58.122 UT, the satellite was located at:
5h45m48.14s +21°45’17.5″ (apparent coordinates, epoch of date).

At 5 Jan 2018 5:50:22.931 UT, the satellite was located at:
5h46m53.98s +21°48’06.3″ (apparent coordinates, epoch of date).

Observer Location: 42°57’36.9″N, 90°08’31.1″ W, 390 m.

Using the satellite coordinates above, and the angular separation calculator kindly provided by the Indian Institute of Astrophysics, we find that the satellite traversed just 0.2590° in 0.1236 hours.  That’s 2.095° per hour, or only about four moon diameters in an hour!

Surely, this satellite must be way out there.  How far?  To determine that, I did a couple of what we used to call during my college physics days “back-of-the-envelope” (BOTEC) calculations.  These are rough approximations—using simplifying assumptions—that should get you to an answer that is at least the right order of magnitude.

If we can estimate the orbital angular velocity of the satellite, we can determine its orbital period, and if we could determine that, we can calculate it orbital distance.  Now, we don’t know yet if this satellite is in a near-circular or highly-elliptical orbit.  If the satellite is an a highly-elliptical orbit and we observe it near apogee, its angular velocity will be somewhat slower than the angular velocity of a circular orbit at that same distance.  If we observe it near perigee, then its angular velocity will be somewhat faster that the angular velocity of a circular orbit at that same distance.  First simplifying assumption: let’s assume a circular orbit.

The next simplifying assumptions are that (1) the satellite passes through the observer’s zenith, and (2) the distance to the satellite is large in comparison to the radius of the Earth.  At the time of observation, the satellite was at an altitude between 65° and 66° above the horizon.  Not quite the zenith, but maybe close enough.

First, we need to compensate for the fact that the observer’s location on the surface of the Earth is moving in the same direction (along right ascension) as the satellite is orbiting (eastward) as the Earth rotates.  We need to add the Earth’s rotational velocity to the right ascension component of the satellite’s velocity to get its true angular velocity relative to the center of the Earth.  This of course assumes that the radius of the Earth is small compared to the distance to the satellite.

During the 0.1236 hours we observed the satellite, it moved 0.2743° eastward in right ascension and 0.0469° northward in declination.  We now need to add a portion of the Earth’s angular velocity to the right ascension component of the satellite’s angular velocity.  If the satellite were at the north celestial pole, the amount we would add would be zero.  If, on the other hand, the satellite were on the celestial equator, we would add the full amount.  Since cos 90° is 0 and cos 0° is 1, let’s add the Earth’s rotational angular velocity times the cosine of the satellite’s declination to the right ascension component of the satellite’s angular velocity.

The Earth turns through 360° in one mean sidereal day (23h 56m 04s = 86,164s).  That’s 1.8591° during the 0.1236 hours we observed the satellite.  Taking that times the average declination of the satellite during the observation time, we get 1.8591° cos 21.7783° =1.7264°.  Adding this to the 0.2743° the satellite moved in right ascension, we get new components for the satellite’s angular displacement of 0.2743° + 1.7264° = 2.0007° in right ascension and 0.0469° in declination.  This gives us the “true” angular displacement for the satellite of

This is a motion of about 16.19° per hour, giving us a rough orbital period of 22.235 hours or 80,045 seconds.

Using Newton’s form of Kepler’s Third Law to calculate the orbital semi-major axis, we get (as a very rough estimate):

where G is the gravitational constant, M is the mass of the Earth in kg, and P is the satellite’s orbital period in seconds.

Geosynchronous satellites have an orbital radius of 42,164 km, so our mystery satellite is almost as far out as the geosynchronous satellites.  If it were further, the satellite would have been moving westward across our field of view, not eastward.

Admittedly, this is a lot of hand waving and is almost certainly wrong, but perhaps it gets us reasonably close to the right answer.

Now, let’s consider the shadow of the Earth to give us another estimate of the satellite’s distance.

At the time of observation, the Sun was located at 19h04m23s -22°36’40”.  The anti-solar point, which is the center of the Earth’s shadow cone, was then located at 7h04m23s +22°36’40”.   That is only 18.1° from the satellite.  The Sun’s angular diameter at that time was 32.5 arcminutes.  In order for the satellite to not be shadowed by the Earth, the angular diameter of the Earth as seen from the satellite must be less thanThe distance from the center of the Earth at which the Earth subtends an angle of 18.6° is given bySo, using this method, the satellite must be at an orbital radius of at least 38,905 km to be outside the Earth’s umbral shadow cone.

Now, on to something less speculative: the varying brightness of the satellite.  I used Limovie to track the satellite across most of the field and got the following light curve.

At first blush, it appears the satellite is tumbling with a period of around 51.2s.  But a closer inspection reveals that a larger amplitude is followed by a smaller amplitude is followed by a larger amplitude, and so on.  So the tumbling period looks to me to be more like 102.4s.  The mean (unfiltered) magnitude of the satellite looks to be around 11.8m, but ranging between 10.7m and 13.0m.  Thus the amplitude is around 2.3 magnitudes.  You will find the raw data here.

Update January 10, 2018

Alain Figer, French astronomer and satellite enthusiast, was kind enough to identify this object for me.  Alain writes, “At first glance I noticed, using Calsky, that Falcon 9 rocket, 2017-025B, #42699, might be your satellite…From the MMT data (astroguard russian site) 2017-025B rotation period was measured at 89.55s on 13 OCT 2017.  That figure seems to me in rather good agreement with yours at 102.4s, since the rotation period of this rocket might be quickly lengthening, a rather classical behaviour for such newly launched rockets.”  Alain goes on to say, “For estimating the satellite altitude from your own observations you have to consider its highly eccentric elliptical orbit.”  Thank you, Alain!

After I got home from work this evening, I began thinking, “Hmm, Guide is such an amazing program, maybe it can show me accurate satellite positions as well.”  Turns out, it can!  After downloading the current orbital elements for all satellites and turning on the satellite display, I was able to confirm Alain’s determination that this object is indeed Falcon 9 rocket body 2017-025B.

SpaceX launched the Inmarsat-5 F4 commercial communications satellite from historic Launch Complex 39A at NASA’s Kennedy Space Center in Florida using a Falcon 9 rocket on May 15, 2017.  Here are some pictures and a video of that launch.

The Falcon 9 rocket body currently orbits the Earth once every 23h21m19s in a highly-elliptical orbit (e=0.8358) that ranges from a perigee height of 432.4 km to an apogee height of 69,783 km.  During the time of observation, its range (i.e. distance from me, the observer) went from 64,388 km to 64,028 km.  The semi-major axis of its orbit is 41,481 km which is 3.3% higher than my (lucky) estimate above.  The shadow criterion of > 38,905 km is met as well.

Orbital inclination 25.6 degrees

Meteor Shower Calendar 2018

Here’s our meteor shower calendar for 2018.  It is sourced from the IMO’s Working List of Visual Meteor Showers (https://www.imo.net/files/meteor-shower/cal2018.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.

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

Meteor Shower Calendar 2018

Happy meteor watching!

January 2018
SUN MON TUE WED THU FRI SAT
1
DLM QUA
2
DLM QUA
3
DLM QUA
4
DLM QUA
5
DLM QUA
6
DLM QUA
7
DLM QUA
8
DLM QUA
9
DLM QUA
10
DLM QUA GUM
11
DLM QUA GUM
12
DLM QUA GUM
13
DLM GUM
14
DLM GUM
15
DLM GUM
16
DLM GUM
17
DLM GUM
18
DLM GUM
19
DLM GUM
20
DLM GUM
21
DLM GUM
22
DLM GUM
23
DLM
24
DLM
25
DLM
26
DLM
27
DLM
28
DLM
29
DLM
30
DLM
31
DLM ACE
February 2018
SUN MON TUE WED THU FRI SAT
1
DLM ACE
2
DLM ACE
3
DLM ACE
4
DLM 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 2018
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
GNO
21
GNO
22
GNO
23
GNO
24
GNO
25
GNO
26
GNO
27
GNO
28
GNO
29 30 31
April 2018
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 2018
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 ETA
29
ARI
30
ARI
31
ARI
June 2018
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 2018
SUN MON TUE WED THU FRI SAT
1
JBO
2
JBO
3
CAP
4
CAP
5
CAP
6
CAP
7
CAP
8
CAP
9
CAP
10
CAP
11
CAP
12
CAP SDA
13
CAP SDA
14
CAP SDA
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 PAU
26
PER CAP SDA PAU
27
PER CAP SDA PAU
28
PER CAP SDA PAU
29
PER CAP SDA PAU
30
PER CAP SDA PAU
31
PER CAP SDA PAU
August 2018
SUN MON TUE WED THU FRI SAT
1
PER CAP SDA PAU
2
PER CAP SDA PAU
3
KCG PER CAP SDA PAU
4
KCG PER CAP SDA PAU
5
KCG PER CAP SDA PAU
6
KCG PER CAP SDA PAU
7
KCG PER CAP SDA PAU
8
KCG PER CAP SDA PAU
9
KCG PER CAP SDA PAU
10
KCG PER CAP SDA PAU
11
KCG PER CAP SDA
12
KCG PER CAP SDA
13
KCG PER CAP SDA
14
KCG PER CAP SDA
15
KCG PER CAP SDA
16
KCG PER SDA
17
KCG PER SDA
18
KCG PER SDA
19
KCG PER SDA
20
KCG PER SDA
21
KCG PER SDA
22
KCG PER SDA
23
KCG PER SDA
24
KCG PER
25
KCG
26 27 28
AUR
29
AUR
30
AUR
31
AUR
September 2018
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
STA DSX SPE
11
STA DSX SPE
12
STA DSX SPE
13
STA DSX SPE
14
STA DSX SPE
15
STA DSX SPE
16
STA DSX SPE
17
STA DSX SPE
18
STA DSX SPE
19
STA 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 2018
SUN MON TUE WED THU FRI SAT
1
STA DSX
2
ORI STA DSX
3
ORI STA DSX
4
ORI STA DSX
5
ORI STA OCT DSX
6
ORI STA DRA OCT DSX
7
ORI STA DRA OCT DSX
8
ORI STA DRA DSX
9
ORI STA DRA DSX
10
ORI DAU STA DRA
11
ORI DAU STA
12
ORI DAU STA
13
ORI DAU STA
14
ORI EGE DAU STA
15
ORI EGE DAU STA
16
ORI EGE DAU STA
17
ORI EGE DAU STA
18
ORI EGE DAU STA
19
LMI ORI EGE STA
20
NTA LMI ORI EGE STA
21
NTA LMI ORI EGE STA
22
NTA LMI ORI EGE STA
23
NTA LMI ORI EGE STA
24
NTA LMI ORI EGE STA
25
NTA LMI ORI EGE STA
26
NTA LMI ORI EGE STA
27
NTA LMI ORI EGE STA
28
NTA ORI STA
29
NTA ORI STA
30
NTA ORI STA
31
NTA ORI STA
November 2018
SUN MON TUE WED THU FRI SAT
1
NTA ORI STA
2
NTA ORI STA
3
NTA ORI STA
4
NTA ORI STA
5
NTA ORI STA
6
LEO NTA ORI STA
7
LEO NTA ORI STA
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 2018
SUN MON TUE WED THU FRI SAT
1
PUP PHO NOO NTA
2
PUP PHO NOO NTA
3
HYD PUP PHO NOO NTA
4
GEM HYD PUP PHO NOO NTA
5
DLM GEM HYD MON PUP PHO NOO NTA
6
DLM GEM HYD MON PUP PHO NOO NTA
7
DLM GEM HYD MON PUP PHO NTA
8
DLM GEM HYD MON PUP PHO NTA
9
DLM GEM HYD MON PUP PHO NTA
10
DLM GEM HYD MON PUP NTA
11
DLM GEM HYD MON PUP
12
DLM COM GEM HYD MON PUP
13
DLM COM GEM HYD MON PUP
14
DLM COM GEM HYD MON PUP
15
DLM COM GEM HYD MON PUP
16
DLM COM GEM MON
17
DLM URS COM GEM MON
18
DLM URS COM MON
19
DLM URS COM MON
20
DLM URS COM MON
21
DLM URS COM
22
DLM URS COM
23
DLM URS COM
24
DLM URS
25
DLM URS
26
DLM URS
27
DLM
28
DLM QUA
29
DLM QUA
30
DLM QUA
31
DLM QUA

The Good Old Days of Astronomy…

Those of you who grew up in the 1950s and 1960s as I did will especially delight in reading the July 7, 2007 entry of Uncle Rod’s Astro Blog, courtesy of Alabama astronomer Rod Mollise.  What a hoot!

And here’s a note from Phil Harrington’s website about Celestron’s ads in the 1990s: “It must be good to be an amateur astronomer in California, judging by the ads run by Celestron over the years…Yup, just another typical club star party, right?”  Photo montage by Rod Mollise.