The LED Lighting Revolution

Solid state lighting, namely light-emitting diodes (LEDs), are completely revolutionizing indoor and outdoor lighting.  Here’s why:

  1. White LEDs on the market today have a system luminous efficacy ranging from 50 (least efficient) to 80 (average) to 140 (most efficient) lumens per watt.  This far exceeds the luminous efficacy of incandescent (5-35 lumens/watt), and generally exceeds compact fluorescents (45-60 lumens/watt).  Prototypes of the next generation of white LEDs have luminous efficacies up to 150 lumens/watt, and theoretically 200-250 lumens per watt may someday be achievable.  Since the traditional white light source of choice for outdoor lighting has been metal halide with a luminous efficacy of 65-115 lumens/watt, white LEDs are well on the way towards replacing metal halide.  Even the more efficient orange high pressure sodium (HPS) lights, with an efficacy of 150 lumens/watt, are nearly matched by the best white LEDs.  Only monochromatic low-pressure sodium (LPS) with an efficacy of 183-200 lumens/watt will give more lumens per watt than the best white LEDs.
  2. White LEDs last much longer than other light sources: 50,000 to 100,000 hours (between 12 and 24 years, operating dusk-to-dawn 365 days a year).  In comparison, high pressure sodium typically lasts about 5 years, and metal halide a little less at 4 years.
  3. Unlike high-intensity discharge (HID) sources such as metal halide, HPS, LPS, and mercury vapor, white LEDs are “instant on / instant off” with no warmup time to full brightness, so they can be switched on and off as often as you like with no shortening of bulb life; and they are easily dimmable. LEDs will render dusk-to-dawn lighting a questionable option rather than an operational necessity.

My only concern is that we finally “get it right” with LEDs instead of blindly following the “more is better” philosophy as we have with every lighting efficiency improvement in the past.  Low levels of white light (fully shielded to minimize direct source glare) is the most effective and efficient way to provide adequate illumination.  This shouldn’t come as a surprise, however.  Think of the light provided by a full moon as we have this week.

Unfortunately, most places that is not what is happening.  Light levels are increasing, as is the amount of lighting.  We seem well on the way towards eliminating anything resembling a natural nighttime environment for most people.  I don’t know about you, but that is not a world I want to live in.

DIAL (15 June 2016). Efficiency of LEDs: The highest luminous efficacy of a white LED.  Retrieved from

Kyba, C., Kuester, T., et al. 2017, Science Advances, 3, 11, e1701528

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.

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

It Came from Outer Space

Just watched a sci-fi movie this past weekend I had never seen before, thanks to Netflix.  In fact, this movie was released three years before I was born—in 1953.  I probably passed this one by before now because of its cheesy, B-movie title: It Came from Outer Space.

Actually, this movie was far better than I had expected.  Definitely a sci-fi classic, a must see for anyone interested in the science fiction genre.  It is rated “G” so is suitable for all ages (so rare nowadays for any dramatic movie, sadly), and is 1h21m in length, so not a huge time commitment.  The story is by noted author Ray Bradbury (1920-2012).

And, hey, the lead characters are an amateur astronomer and his gorgeous schoolteacher girlfriend, living in Arizona.

Without giving away too much of the plot, let me just say that aliens crash land in Arizona, and are simply trying to repair their damaged spacecraft so they can return to outer space.  How do we humans react?  All too predictably, sad to say.  The unknown frightens us, and  “What we don’t understand we want to destroy.”

As you’d expect from Bradbury, it is a good story.  Enjoy.  And think about the implications for the survival of the human race.

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.

A Better Lotion Bottle

For many of us, winter in the Upper Midwest means dry, cracked hands and nasty splits at the ends of our thumbs and fingers.  The only way to avoid or at least mitigate this is to apply lotion to your hands after every hand washing, because soap removes too much of your skin’s natural moisturizing oils (lipids).

I’m not a big fan of pump dispensers when it comes to lotion.  When the pump has pumped all the lotion it can, there is still a lot of lotion left behind in the bottle.  And most of us don’t want to go through the extra effort needed to get to the remaining lotion, so we throw the bottle out rather than utilizing the remaining lotion and then recycling the bottle.

Wasteful lotion container on the left – Better lotion container on the right

Recently, just to see how much lotion was left in a Gold Bond® pump dispenser (excellent lotion, by the way), we used a razor blade to cut all the way around the midsection of the lotion bottle, separating it into roughly two halves.  Then we used a spoon to scoop out all the remaining lotion in the two halves and put it into a clean plastic tub—formerly a sour cream container.  The amount of leftover lotion is substantial, as you can see in the photograph below.  A many-days supply, to be sure!

Leftover lotion from a seemingly empty pump dispenser

We consumers need to put pressure on pump-dispenser lotion manufacturers to package their lotions in containers that make it easy to extract all the lotion.  Some lotion manufacturers are already doing this, and we should purchase their products.  O’Keeffe’s® Working Hands® is one good example.

You can get all of the lotion out of a container like this

Sometimes, lotion manufacturers package their product in both types of containers—pump dispensers and tub containers—but your local grocery store, pharmacy, or big-box store only carries the less environmentally-friendly pump-dispenser type of container.  Do your research, and meet with the store manager to ask them to carry the tub container alternative instead of—or in addition to—the pump dispenser.

Each and every day we can make choices that are better for our environment.  This is yet another example: use all the product and make it easy to recycle the container.

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.


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