## Satellites and More – 2020 #1

Edmund Weiss (1837-1917) and many astronomers since have called asteroids “vermin of the sky”, but on October 4, 1957 another “species” of sky vermin made its debut: artificial satellites.  In the process of video recording stars for possible asteroid occultations, I frequently see satellites passing through my 17 × 11 arcminute field of view.

I’ve put together a video montage of satellites I serendipitously recorded during the first half of 2020.  Many of the satellites move across the field as “dashes” because of the longer integration times I need to use for some of my asteroid occultation work. A table of these events is shown below the video. The range is the distance between observer and satellite at the time of observation. North is up and east is to the left.

Interestingly, three of the above satellites (7,9,18) are in retrograde orbits, that is their orbital inclination is > 90˚ and their east-west component of motion is towards the west instead of the east. However, I was surprised to find that two of the prograde orbiting satellites (5,6) appear to be orbiting retrograde! Both have orbital inclinations close to 90˚ (82.6˚ and 87.5˚, respectively), and both were in the western sky at northern declinations at the time of observation. But another satellite (8) with an orbital inclination of 82.5˚ at a southern declination in the southern sky at the time of observation exhibited the expected “barely” prograde motion. I suspect the ~0.5 km/s rotation of the Earth towards the east might have something to do with this “apparent retrograde” motion, but I was unable to find any reference that describes this situation.

Satellite #12 has an interesting story. It is the Inertial Upper Stage (IUS) used to launch USA-48 (Magnum), a classified DoD payload, from the Space Shuttle Discovery (STS-33).

In addition to these 18 satellites, I observed 7 geosynchronous satellites, shown below.

This non-operational Soviet communications satellite is a “tumbler”, meaning its changing orientation causes variation in its brightness, as shown below.

This non-operational communications satellite is also a tumbler, as seen in this light curve from a portion of the video.

There were four satellites I was unable to identify, shown in the video below. They were either classified satellites or, more likely, small pieces of space debris that only government agencies or contractors are keeping track of.

Occasionally, I record other phenomena of interest. Meteors during this period are described here, and you will find a couple of other curiosities below.

References
Hughes, D. W. & Marsden, B. G. 2007, J. Astron. Hist. Heritage, 10, 21

## Luna 16: First Robotic Lunar Sample Return Mission

Fifty years ago this day, the Soviet Union’s Luna 16 robotic probe made a night landing in the Sea of Fertility. It drilled nearly 14 inches into the lunar regolith, collected 3.6 ounces of soil, and delivered its precious cargo to Earth four days later.

The astronauts on Apollo 11, 12, 14, 15, 16, and 17 between 1969 and 1972 brought back a total of 840 lbs of moon rocks and soil. Each successive Apollo mission brought back a larger amount of lunar material.

The Soviets brought back a total of 0.7 lbs of lunar soil through their robotic sample return missions Luna 16 (1970), Luna 20 (1972), and Luna 24 (1976).

So, excluding lunar meteorites that have befallen the Earth, a total of 840.7 lbs of lunar material has been brought to research laboratories here on Earth.

After a hiatus of over 44 years, China plans to launch two lunar sample return missions, Chang’e 5 in November 2020 and Chang’e 6 in 2023 or 2024. Chang’e 5 is expected to return at least 4.4 lbs of lunar material from nearly 7 ft. below the surface at its landing site in the Mons Rümker region of Oceanus Procellarum.

Chang’e is the Chinese goddess of the Moon, and is pronounced chong-EE.

## Video Meteors 2020 – I

During the first half of 2020, I serendipitously captured a whopping nine meteors on my telescope’s 17 x 11 arcminute video field of view while observing potential asteroid occultation events. I used the method described in There’s a Meteor in My Image to determine the radiant for each meteor. Here they are.

The International Meteor Organization (IMO) identifies the antihelion source as “a large, roughly oval area of about 30˚ in right ascension and 15˚ in declination, centered about 12˚ east of the solar opposition point on the ecliptic, hence its name. It is not a true shower at all, but is rather a region of sky in which a number of variably, if weakly, active minor showers have their radiants.”

A sporadic meteor is any meteor that does not come from a known radiant.

Meteors enter the Earth’s atmosphere at a speed between 10 and 70 km/s, and burn up at an altitude of about 80 km. For a sight line perpendicular to the meteor’s path, the angular velocity should range between 7˚ and 41˚ per second. This means a meteor should cross the 17′ x 11′ field of my video camera in 0.03 seconds or less. Field traversal will take longer than this the closer the meteor is to its radiant or anti-radiant point.

The lowest stable altitude a satellite can orbit is about 200 km, where it will have an orbital velocity on the order of 8 km/s. This is slower than the slowest meteors. For a sight line perpendicular to the satellite’s path, the maximum angular velocity a satellite should have is about 2˚ per second.

Given these admittedly BOTEC calculations, one could reasonably conclude that if the object traverses the field in a single frame, it is probably a meteor. If not (and it is not an airplane), it is a satellite.

The object in the 8 May 2020 video does appear to be moving slow enough to be a satellite, but because it is traveling much faster than satellites usually do it must be orbiting quite low, close to re-entry. I was not able to identify the satellite, which is often the case for the fastest-moving satellites. My camera is sensitive enough to pick up tiny pieces of space debris orbiting at low altitude, and though these objects are no doubt catalogued by military organizations, they do not generally show up in the publicly-available orbital element datasets for satellites.

This one’s unusual in that there are two distinct “flare-ups” along the path. It is reasonably good match to the antihelion radiant for 12 May 2020, and though I have seen meteors experiencing outbursts along their paths, a more likely explanation for this event is that it is low altitude satellite with two “sun glint” events. What do you think?

I was surprised to record so many meteors during the first half of 2020, as there is generally much less meteor activity between January and June than there is between July and December.

References

International Meteor Organization, 2o2o Meteor Shower Calendar, Jürgen Rendtel, ed. https://www.imo.net/files/meteor-shower/cal2020.pdf.

## Apollo 11

On Sunday, July 20, 1969, astronauts Neil Armstrong and Buzz Aldrin landed the Apollo 11 lunar module, Eagle, on the surface of the Moon at 3:17 p.m. CDT. Later that day, Armstrong, age 38, and Aldrin, age 39, became the first human beings to walk on another world, 51 years ago this day. Fifty-one years before that, World War I was nearing its end while the 1918 flu pandemic was ramping up in its fifth month of a twenty-six month ordeal.

Armstrong and Aldrin landed at lunar latitude 0.7° N and longitude 23.5° E, in Mare Tranquillitatis (The Sea of Tranquillity). Back here on Earth, the lunar phase was waxing crescent (35% illuminated), and the Moon set that night in Dodgeville at 11:23 p.m.—just a few minutes before Armstrong and Aldrin returned to the lunar module after spending over two hours on the surface of the Moon.

Neil Armstrong stepped down onto the lunar surface at 9:56 p.m. CDT, followed by Buzz Aldrin at 10:15 p.m. After exploring the lunar surface and setting up several scientific instruments, Buzz Aldrin returned to the lunar module at 12:01 a.m., followed by Neil Armstrong at 12:09 a.m. Monday morning.

After five hours of work stowing samples and other housekeeping tasks, Armstrong and Aldrin tried to get some sleep during a scheduled seven hour rest period. However, there were no beds in the lunar module—not even any chairs! Armstrong tried to sleep on the ascent engine cover in the rear of the cabin and Aldrin tried to sleep curled up on the floor. Adding to their discomfort, both astronauts had to keep their spacesuits on. And the lunar module was noisy, bright light leaked into the cabin, and they were too excited to sleep. Aldrin got about two hours of restless sleep. Armstrong got none.

The lunar module took off at 12:54 p.m. Monday afternoon, docked with the command module piloted by Michael Collins at 4:35 p.m., and then the astronauts began their journey home.

One of the little known facts of the Apollo missions is all the high-tech “garbage” that was left behind on the lunar surface to allow the astronauts to bring back more moon rocks. All in all, over 800 lbs. of moon rocks and lunar soil were brought back to Earth during the six lunar landing missions, the last of which returned to Earth on December 19, 1972.

## Geostationary Satellite Declinations

A few years ago, I was doing some telescope sweeping of the meridian sky around declination -6˚ when, to my surprise and delight, a 10th- or 11th-magnitude slow-moving object entered my field of view. As it slowly traversed eastward through the field, I remembered the declination I was pointed to and realized that it must be a geostationary, or at least a geosynchronous, satellite. Centering the moving object and then turning off the telescope’s clock drive confirmed my suspicions. The object was a geosynchronous satellite because it appeared to lay motionless while all the stars in the field drifted toward the west. Serendipity is the spice of life!

Satellites stationed in orbits that are always directly above the Earth’s equator and that have an orbital period of 23h 56m 04.0905s (one sidereal day) have the interesting property of remaining stationary as seen from any point on the surface of the Earth. This property of geostationary satellites, as they are called, is used to great advantage by many communications and weather satellites. There are currently at least 554 satellites in geosynchronous orbits. They are stationed all around the Earth at various longitudes.

At what altitude do geostationary satellites orbit the Earth? It is well above human-occupied spacecraft like the International Space Station which currently orbits 260 miles above the Earth’s surface. Geosynchronous orbit lies some 22,236 miles above the Earth’s equator. This is quite a ways out, as the entire Earth subtends an angle of only 17° 12′ at this distance—about the same as the angular distance between Capella (α Aur) and Elnath (β Tau).

Looking at it another way, geostationary satellites orbit at an altitude that is 2.8 Earth diameters above the equator. Since the Moon orbits at a distance that ranges between 27.4 and 31.4 Earth diameters above the Earth’s surface, geosynchronous orbit is about 1/10 of the way to the Moon.

If you have a telescope, know where to point it, and turn tracking off, you can see a geostationary satellite as a stationary point of light while the stars drift by due to the Earth’s rotation. At our latitude here in southern Wisconsin (43° N), the area where you want to search for geostationary satellites (near the meridian) is around declination -6° 37′. Remember, declination tells you how many degrees above or below the celestial equator an object is, and the numbers range from -90° to +90°, the south celestial pole and north celestial pole, respectively. The celestial equator has a declination of 0°.

For any latitude1, the declination you want to search is given by

$\delta _{gs}=\textup{tan}^{-1}\left [ 6.611\textup{ csc }\phi - \textup{cot }\phi \right ]-90^{\circ}$

where δgs is the declination of the geostationary satellite in degrees
and ϕ is your latitude in degrees

Since most calculators don’t have the cosecant (csc) or cotangent (cot) functions, this formula can be rewritten in a slightly more complicated form as

$\delta _{gs}=\textup{tan}^{-1}\left [ \frac{6.611}{\textup{sin }\phi }-\frac{1}{\textup{tan }\phi } \right ]-90^{\circ}$

Why aren’t the satellites right on the celestial equator (δ = 0°)? They would be if they were millions of miles away or if we were located on the Earth’s equator, but at our northern latitude trigonometric parallax causes us to see the satellites somewhat below the celestial equator, relative to the distant stars.

What if the geostationary satellite is situated east or west of your meridian? How do you calculate its declination then? As you might expect, because the range (observer-to-satellite distance) is greater the further from the meridian the satellite is, the less the parallax is, and therefore the closer the declination is to the equator, though not by a lot. The declination is also symmetric about the meridian, east and west: a geostationary satellite one hour east of the meridian will have the same declination as another geostationary satellite one hour west of the meridian.

If you know the longitude of the geostationary satellite (for example, the GOES-16 weather satellite is stationed above 75.2˚ W longitude), you can calculate its declination (and right ascension) using the following two-step process.

$\textup{h}=\textup{tan}^{-1}\left [ \frac{\textup{sin }\Delta\lambda }{\textup{cos }\Delta \lambda-0.15126\textup{ cos }\phi } \right ]$

where h is the hour angle in degrees
and Δλ = λsat − λobs , the difference between the satellite and observer
longitudes, in degrees
and ϕ is the latitude of the observer in degrees

$\delta _{gs}=\textup{tan}^{-1}\left [ \frac{-0.15126\textup{ sin }\phi \textup{ sin h}}{\textup{sin }\Delta \lambda } \right ]$

To determine the right ascension of the geostationary satellite, add the value of h to your local sidereal time (the right ascension of objects on your meridian). Make sure you convert h to hours before adding it to your LST.

What if you want to calculate the geostationary declination at a particular hour angle? That is a bit trickier. I could not figure out how to manipulate the equation for h above so that Δλ = f (h,φ). Instead, I rewrote the equation as

$\sin \Delta \lambda =\tan h\cdot \left ( \cos \Delta \lambda -0.15126\cos \phi \right )$

and using h as a starting value for Δλ, substituted it into the cos Δλ expression, calculated sin Δλ, took the arcsine to get a new value of Δλ, then substituted that back into the cos Δλ expression, and iterated. Fortunately, the value of Δλ converges very fast. Once you have Δλ, you can use the two-step process we used earlier to determine the declination of the geostationary satellite for a particular hour angle.

Please note that the value of the hour angle h we use here is positive east of the meridian and negative west of the meridian. This is opposite from the normal astronomical sense.

Here is a simple SAS program illustrating how to do all these calculations using a computer.

And here is the output from that program.

1 For latitudes south of the equator, add 180° to get your meridian geostationary declination. The equation goes singular at the equator (φ=0°) and at the poles (φ=90° N and 90° S) since we’re dividing by sin φ = 0 at the equator and tan φ is undefined at the poles. However, as you asymptotically get closer and closer to latitude 0° (0.0001° and -0.0001°, for example) you find that the meridian geostationary declination approaches δ = 0°. Likewise, as you asymptotically approach latitude 90° N and 90° S, you’ll find that the meridian geostationary declination approaches -8°36′ and +8°36′, respectively. Of course, in both cases the geostationary satellites always remain below your horizon. How far north or south in latitude would you have to go, then, to find that geostationary satellites on your meridian are on your horizon due south or due north, respectively? Through a little algebraic manipulation of the first equation above and utilizing some simple trigonometric identities, one finds that at latitudes 81°18′ N and 81°18′ S, geostationary satellites on your meridian would be on the horizon. North or south of there, respectively, you would not be able to see them because the Earth would be in the way.

References

Gérard Maral, Michel Bousquet, Zhili Sun. Satellite Communications Systems: Systems, Techniques and Technology, Fifth Edition. Wiley, 2009. See section 8.3.6.3 Polar mounting.

## BepiColombo Passes Earth

The BepiColombo spacecraft flew by the Earth last night, the first of nine gravity-assist maneuvers it will make to slow it down so that it can go into orbit around the planet Mercury on 5 December 2025. This was the only Earth gravity assist. There will be a Venus flyby later this year and next year, and six Mercury flybys from 2021-2025.

BepiColombo passed 7,877 miles over the South Atlantic Ocean at 0425 UT on 10 April 2020 at its closest approach to Earth, and I was able to image it from my backyard observatory in Dodgeville, Wisconsin at 0600 UT at a distance (range) of 21,760 miles.

North is up and East to the left in the video frame, so BepiColombo is moving in a northwesterly direction. The two stars in the field are 3UC 145-134561 (12.2m, north) and 3UC 144-138354 (12.7m, south). The predicted equatorial coordinates (epoch of date) at 0600 UT from JPL Horizons were α = 11h 38m 03.90s, δ = -18° 08′ 25.4″. Please note when using JPL Horizons to generate ephemerides for spacecraft and minor planets passing close to the Earth that you should use the ICRF coordinates (astrometric) and not the apparent coordinates. They can be significantly different!

The integration time in the video above is 7.5 frames per second, or 0.13 second per frame. The field size is 17 x 11 arcminutes.

Here’s the video light curve of BepiColombo as it passed through the field. It was fairly constant in brightness with no obvious variability amidst the noisy measurements.

## Satellite and Meteor Crossings 2019 #2

Edmund Weiss (1837-1917) and many astronomers since have called asteroids “vermin of the sky”, but on October 4, 1957 another “species” of sky vermin made its debut: artificial satellites.  In the process of video recording stars for possible asteroid occultations, I frequently see satellites passing through my 17 × 11 arcminute field of view.

I’ve put together a video montage of satellites I serendipitously recorded between August 9, 2019 and December 22, 2019.  Many of the satellite crossings are moving across the fields as “dashes” because of the longer integration times I need to use for some of my asteroid occultation work. A table of these events is shown below the video. The range is the distance between observer and satellite at the time of observation. North is up and east is to the left.

Satellites in higher orbits take longer to cross the field. In the next video, the originally geosynchronous satellite OPS 1570 (IMEWS-3, “Integrated Missile Early Warning System”) is barely visible until it exhibits an amazing sunglint around 3:41:22 UT.

I caught one meteor on October 6, 2019 at 9:57:43 UT. Field location was UCAC4 515-043597. The meteor was a Daytime Sextantid, as determined using the method I described previously in There’s a Meteor in My Image. The meteor even left a brief afterglow—a meteor train!

References
Hughes, D. W. & Marsden, B. G. 2007, J. Astron. Hist. Heritage, 10, 21

## Radio Telescope in a Carpet

The lunar farside would be a splendid place to do radio astronomy. First, the cacophony of the Earth would be silenced by up to 2,160 miles of rock. Second, lacking an atmosphere, a radio telescope located on the lunar surface would be able to detect radio waves at frequencies that are absorbed or reflected back into space by the Earth’s ionosphere.

Radio waves below a frequency of 10 MHz (λ ≥ 30 m) cannot pass through the ionosphere to reach the Earth’s surface. The Earth’s atmosphere is variably opaque to radio waves in the frequency range of 10 MHz to 30 MHz (λ = 10 to 30 m), depending upon conditions. The Earth’s atmosphere is mostly transparent to frequencies between 30 MHz (10 m) and 22 GHz (1.4 cm).

Not surprisingly, electromagnetic radiation of a non-terrestrial origin having wavelengths longer than 10 meters has been little studied. If we look, we might discover new types of objects and phenomena.

The best part is the lunar radio telescope wouldn’t have to be a steerable parabolic dish, but instead could be a series of dipole antennas (simple metal rods or wires) imbedded into a plastic carpet that could easily be rolled out onto the lunar surface. This type of radio telescope is “steered” (pointed) electronically through phasing of the dipole elements.

Even though the ever-increasing number of lunar satellites should be communicating at wavelengths far shorter than 10 meters, care must be taken to minimize their impact (both communication and noise emissions) upon all lunar farside radio astronomy.

## Space Travel Under Constant 1g Acceleration

The basic principle behind every high-thrust interplanetary space probe is to accelerate briefly and then coast, following an elliptical, parabolic, or mildly hyperbolic solar trajectory to your destination, using gravity assists whenever possible. But this is very slow.

Imagine, for a moment, that we have a spacecraft that is capable of a constant 1g (“one gee” = 9.8 m/s2) acceleration. Your spacecraft accelerates for the first half of the journey, and then decelerates for the second half of the journey to allow an extended visit at your destination. A constant 1g acceleration would afford human occupants the comfort of an earthlike gravitational environment where you would not be weightless except during very brief periods during the mission. Granted such a rocket ship would require a tremendous source of power, far beyond what today’s chemical rockets can deliver, but the day will come—perhaps even in our lifetimes—when probes and people will routinely travel the solar system in just a few days. Journeys to the stars, however, will be much more difficult.

The key to tomorrow’s space propulsion systems will be fusion and, later, matter-antimatter annihilation. The fusion of hydrogen into helium provides energy E = 0.008 mc2. This may not seem like much energy, but when today’s technological hurdles are overcome, fusion reactors will produce far more energy in a manner far safer than today’s fission reactors. Matter-antimatter annihilation, on the other hand, completely converts mass into energy in the amount given by Einstein’s famous equation E = mc2. You cannot get any more energy than this out of any conceivable on-board power or propulsion system. Of course, no system is perfect, so there will be some losses that will reduce the efficiency of even the best fusion or matter-antimatter propulsion system by a few percent.

How long would it take to travel from Earth to the Moon or any of the planets in our solar system under constant 1g acceleration for the first half of the journey and constant 1g deceleration during the second half of the journey? Using the equations below, you can calculate this easily.

Keep in mind that under a constant 1g acceleration, your velocity quickly becomes so great that you can assume a straight-line trajectory from point a to point b anywhere in our solar system.

Maximum velocity is reached at the halfway point (when you stop accelerating and begin decelerating) and is given by

The energy per unit mass needed for the trip (one way) is then given by

How much fuel will you need for the journey?

hydrogen fusion into helium gives: Efusion = 0.008 mfuel c2

matter-antimatter annihilation gives: Eanti = mfuel c2

This assumes 100% of the fuel goes into propelling the spacecraft, but of course there will be energy losses and operational energy requirements which will require a greater amount of fuel than this. Moreover, we are here calculating the amount of fuel you’ll need for each kg of payload. We would need to use calculus to determine how much additional energy will be needed to accelerate the ever changing amount of fuel as well. The journey may well be analogous to the traveler not being able to carry enough water to survive crossing the desert on foot.

Now, let’s use the equations above for a journey to the nearest stars. There are currently 58 known stars within 15 light years. The nearest is the triple star system Alpha Centauri A & B and Proxima Centauri (4.3 ly), and the farthest is LHS 292 (14.9 ly).

I predict that interstellar travel will remain impractical until we figure out a way to harness the vacuum energy of spacetime itself. If we could extract energy from the medium through which we travel, we wouldn’t need to carry fuel onboard the spacecraft.

We already do something analogous to this when we perform a gravity assist maneuver. As the illustration below shows, the spacecraft “borrows” energy by infinitesimally slowing down the much more massive Jupiter in its orbit around the Sun and transferring that energy to the tiny spacecraft so that it speeds up and changes direction. When the spacecraft leaves the gravitational sphere of influence of Jupiter, it is traveling just as fast as it did when it entered it, but now the spacecraft is farther from the Sun and moving faster than it would have otherwise.

Of course, our spacecraft will be “in the middle of nowhere” traveling through interstellar space, but what if space itself has energy we can borrow?

## Satellite, Meteor, and Aircraft Crossings 2019

Edmund Weiss (1837-1917) and many astronomers since have called asteroids “vermin of the sky”, but on October 4, 1957 another “species” of sky vermin made its debut: artificial satellites.  In the process of video recording stars for possible asteroid occultations, I frequently see satellites passing through my ~¼° field of view.

I’ve put together a video montage of satellites I serendipitously recorded between March 31, 2019 and July 12, 2019.  Many of the satellite crossings are moving across the fields as “dashes” because of the longer integration times I need to use for some of my asteroid occultation work. A table of these events is shown below the video. The range is the distance between observer and satellite at the time of observation.

Satellites in higher orbits take longer to cross the field. When possible, I’ve included graphs of brightness as a function of time for these slower-moving satellites after each individual video and corresponding table. When you watch the videos of geostationary satellites, you are actually seeing the rotation of the Earth as the line between you and the satellite sweeps across the stars as the Earth rotates!

I caught one meteor on 4 Jan 2019 between 5:32:57 and 5:32:59 UT. Field location was UCAC4 419-017279. I’m pretty sure the meteor was a Quadrantid!

And two aircraft crossed my field: on 7 Dec 2018 1:40:05 – 1:40:13 UT (UCAC4 563-026131) and 26 Jun 2019 5:02:07 – 5:02:10 UT (UCAC4 291-144196).

And high energy particles (natural radioactivity or cosmic rays) “zing” my CCD/CMOS detector every once in a while. Here are a few examples: 5 Jan 2019 3:46:00 – 3:46:02 UT (UCAC4 473-001074); 20 Apr 2019 3:41:46 – 3:41:47 UT (UCAC4 501-062663); 30 Jun 2019 7:37:31 – 7:37:33 (UCAC4 354-179484) and 7:47:41 – 7:46:44 (TYC 6243-00130-1).

References
Hughes, D. W. & Marsden, B. G. 2007, J. Astron. Hist. Heritage, 10, 21