A Use For Robert Forward’s Statite Concept: Artificial Pole Stars

A guest post by Joseph Friedlander

The recent striking close conjunction

of Jupiter (around -1.8 or -2 magnitude) and Venus (-4.5 magnitude) in the late June and early July sky after sunset has given an easy visual comparison for bright starlike objects.
At closest Venus and Jupiter were  less than one Moon diameter apart.

 Are even  brighter starlight objects possible? Of course. You could have an object with considerable surface brightness but very small subtended angle as bright as the full moon ( -12.6 magnitude) or even brighter.  A supernova would easily qualify, depending on the distance.

 However, if we are talking about building artificial objects of such visibility, we need first to 1) quantify what counts as brightness to the eye and 2) consider the practicalities of doing so.

For jaded urban dwellers, used to light pollution, wanting to navigate by night by a bright starlike object, it is not really fair to ask them to try to seek out something much less bright than Jupiter.  For even moderate thin cloud cover, only Venus really punches through reliably.

Even the Moon of course,  can be defeated by heavy clouds. But for navigational purposes a tightly located moonglow can be almost as good as the visible disk.

So the range of brightness of Jupiter (around -2) Venus (-4.5) and the Moon (-12.6) are of interest to a discussion of artificial pole stars and navigation aids.

Venus is at -4.5 compared to -12.6 that is 2.8 times  less bright on the magnitude scale. However remember that each five magnitudes is 100 times brighter so that apparently small 8.1 magnitude difference is really thousands of times brighter. (~1738 times brighter)  I have read but never seen that on cold snowy winter mornings (dark ones) that Venus before sunrise can cast a detectable shadow. I have never seen it myself but everyone has seen full Moonlight and especially on snow it can have haunting beauty.

 What I never saw, but others of course have, was a daylight reentry fireball of the Space Shuttle Orbiter, often cited as comparable to Venus.  The International Space Station can occasionally get as bright as -5.9.

An excellent page on what it was like to visually observe the Space Shuttle Orbiter http://www.satobs.org/shuttle.html

Yes, experts can navigate with far fainter objects in dim skies by knowing precisely where to look. (In the early 60s the massive Echo satellites or briefly orbiting booster stages were often quite visible to warriors in  the hills of Indochina., and in the 80’s I occasionally saw the Space Shuttle Orbiter moving through the cold winter Chicago sky).

  But that is not navigation on demand that you can teach to a child. An ideal artificial navigation star would be of useful brightness and location and designed for ease of use.

The natural full Moon is of apparent magnitude –12.6, far fainter than the blinding –26.73 apparent magnitude of the Sun—about 449,000 times less bright. So the Moon is 14.13 apparent magnitudes fainter than the Sun. As each unit of apparent magnitude is 2.512 times fainter or brighter than its’ neighbor (five magnitudes of difference are, by the Pogson scale of 1856, exactly 100 times brighter or fainter)– we can therefore conclude that the Sun is 2.513 to the 14.13th power (449032.16 times) brighter than the Full Moon.

 (Note below Wiki’s calculation for about the same number (~400000 times dimmer  full Moon than Sun)

The Moon’s area in the sky is about 0.2 square degrees. The sky itself has an area of 41253 square degrees. Thus the Moon’s area is 1/206265 of the sky! It seems bigger, especially at Moonrise—

Convenient guide to magnitude system http://www.icq.eps.harvard.edu/MagScale.html

From Wikipedia:  https://en.wikipedia.org/wiki/Apparent_magnitude
In 1856, Norman Robert Pogson formalized the system by defining a firstmagnitude star as a star that is 100 times as bright as a sixth-magnitudestar, thereby establishing the logarithmic scale still in use today. This implies that a star of magnitude m is 2.512 times as bright as a star ofmagnitude m+1.
What is the ratio in brightness between the Sun and the full moon?

The apparent magnitude of the Sun is −26.74 (brighter), and the mean apparent magnitude of the full moon is −12.74 (dimmer).

Difference in magnitude :

 x = m_1 – m_2 = (-12.74) – (-26.74) = 14.00 
Variation in Brightness :

 v_b = 2.512^x = 2.512^{14.00} approx 400,000 
The Sun appears about 400,000 times brighter than the full moon.

So my own calculations were somewhere in the reasonable range.
And, remember, the Full Moon is about 2000 times brighter than Venus, which itself is about 10 times brighter than Jupiter in tonight’s evening sky.

So how do we build artificial pole and other navigation stars?

Robert L. Forward was a great science fact and entertaining science fiction writer and futurist.–Greatly missed.
Remembering how Arthur C. Clarke’s 1945 description of the geostationary communications satellite did nothing to make Clarke a rich man, he patented starting in the late ‘ 80s a new concept– the statite. In simplest form a giant solar sail hovering by light pressure not in orbit but in co-location above a given spot on Earth, he invented the polesitter satellite.  (Although it need not be located over a pole, but that would certainly be a convenient fixed spot for communications purposes)

From the patent:

(NOTE: The pictures can be seen in greater detail if you follow this direct link to the PDF and zoom in:  https://docs.google.com/viewer?url=patentimages.storage.googleapis.com/pdfs/US5183225.pdf)

The minimum distance from the earth for a Statite is sixty Earth radii or about nine times the geostationary orbit distance. 

 Statite (301) will always be kept at a fixed angle beta from the polar axis (303) of the Earth (305). This angle will have to be greater than 23.5% because the tilt of the polar axis of the Earth takes each pole 23.5% to the sunward side of the earth during one of the solstices and the Statite has to stay over the dark side of the Earth. FIG. 3 shows the position of the Statite at the summer and winter solstices. 

In practice the angle could range from 30% to 45%. Statites at these angles could provide communication services to the United States, Europe, Alaska, Canada, all of the USSR, northern China, Argentina, Chile, New Zealand, southern Australia, and, of course, the Arctic and Antarctic.

At the summer solstice, and at an angle from the polar axis where beta equals thirty degrees (30%), the angle at the incoming sunlight will strike the sail at 6.5 degrees. 

At this angle to the sunlight, the performance of a flat solar sail is severely degraded. 

In such a situation, the Solar Photon Thruster has a considerable advantage over the simple solar sail in Statite operation.around the Earth, at all times of the year, even over the sunlit side, at the expense of slightly greater operating distance. 

Instead of the Statite being balanced by sunlight in the gravitational field of the Earth, the Statite would be placed in orbit around the Sun, at such a distance from the earth that the gravitational field of the Earth plus the moon is only a perturbation on the gravitational field of the Sun.

In this embodiment of the present invention, the solar propulsion system would be controlled so the Statite moves in a slightly ecliptical orbit around the Sun with a period equal to the Earth orbital period of one year. 

Light pressure is used to “levitate” the plane of this Statite’s solar orbit above or below the ecliptic plane, and to vary the radius of the orbit during the year so that the Statite moves inside and outside the orbit of the Earth. The result would be that, to an observer on the Earth, the Statite remains fixed above one of the Poles of the Earth. 

Thus, although the spacecraft would be a “satellite” of the sun, it is a Statite of the Earth because it is adjacent to the Earth, but not in orbit around it. This embodiment is shown in FIG. 4 showing the Statite above the North Pole at the equinoxs and the solstices. T

he 1976 JPL solar sail technology has ample propulsive capability to allow it to carry out the orbit levitation and orbit ellipticity maneuvers necessary to place a Statite over the Poles of the Earth at all times of the year using the solar orbit embodiment of the present invention. 

Another mode of Statite system operation would place the Statite in an orbit around a fixed point adjacent to the Earth. In this mode of operation, although the Statite is moving relative to the Earth, it is not in orbit around the Earth, and, therefore, is not a satellite of the Earth. 

As is shown in FIG. 5, if Statite  (501) keeps its orientation inertially fixed while it is displaced off of its normal fixed operating point (503), the light pressure force Fp will compensate for the component of the gravitational force Fgz normal to the sail, but there will be a component of the gravitational force Frg tangent to the sail that will attempt to pull the Statite back to its normal fixed operating point; just as if there were a mass located at that point. The Statite can thus be induced to move through or circle about that point in a “halo orbit”.

Finally, there is an interesting distance of three hundred and forty Earth radii where the period of such a “halo” orbit for a Statite is one year. The Earth’s gravity at this distance is so weak that it could easily be reached by a 1976 JPL technology sail carrying a five ton payload. The center of this halo orbit would be chosen at some distance over the dark side of the Earth that would yield a comfortable sail tilt angle. Such a Statite would circle above the arctic circle, just 23.5 degrees from the polar axis, keeping itself positioned over that point where the northern most portion of the terminator crosses the arctic circle. To an observer on the ground, the Statite would appear to spin around the Pole once a day, staying on the opposite side of the Earth from the Sun. Such a Statite could be continuously observed anywhere north of twenty-four degrees north latitude.

A very different mode of Statite system operation is possible that would allow the Statite to be placed at any point around the Earth, at all times of the year, even over the sunlit side, at the expense of slightly greater operating distance. Instead of the Statite being balanced by sunlight in the gravitational field of the Earth, the Statite would be placed in orbit around the Sun, at such a distance from the earth that the gravitational field of the Earth plus the moon is only a perturbation on the gravitational field of the Sun.

Friedlander here again. So we want to build artificial pole stars and navigational aids of surpassing brightness and ease of use, ideally so simple Cub Scouts could use them and learn to navigate by unconscious calculation of angles literally just by looking at where the known location stars are in relation to you.

What might one such system of aids look like?  Imagine two statites  of Venus or better brightness parked over the North and South Poles,  at about ten geostationary radii out, comparable to lunar distances. Imagine four comparably bright (closer but smaller) large solar sail complexes parked in geostationary arc (they need not be active transmitters taking up a precious geo slot, simply solar sails maintaining their position in the arc)  at 0, 90, 180 and 270 degrees longitude.  Imagine for even more luxurious and ease of use sighting opportunities statites parked at 45 degrees north and south  over 0, 90, 180 and 270 degrees longitude. That is four geostationary sails and two polesitters and eight statites hovering on station all the time.

With such a deluxe system a child could learn celestial navigation and sighting, probably literally to the point of doing it without using a sextant. (At least to give you a rough idea of where in the world you were at a glance).  Special forces would love it because it is an entirely passive, signal free way of navigation not detectable by electronics and not disruptable barring some serious celestial weaponry.  Sailing of course would be enormously simplified (in clear weather) and very simple visual aids (keep the guide star on your right and level with this line) would enable even the most obtuse to get celestial navigation. What a boon for solo round the world sailors as well.

It would be a fantastic way to hook kids on math and astronomy. I am sure any enthusiast could generate about a dozen or two lesson plans for any class of bright kids.   Oh, well, thus far the fantasy.

But what of the practicality?
Let’s blithely pass over the practicalities of sail design and stationkeeping, and just treat rough areas of reflector to get an idea of the magnitude of the system.

The Moon has albedo of about 6% (think dark asphalt parking lot but in brilliant sunshine when full) and a typical aluminium surface above 90%. (The planet Venus itself has cloudtop albedo of 70% or so)

The Moon is about 3476 km diameter at around 385000 km  (238000 mi) out.
A little over 10 times geostationary distance.of 35,786 km (22,236 mi) out.
So a body of similar albedo 1/10th the size should be of Lunar size and brightness as seen from Earth. (348 km for a 6% albedo film disk)
But if we can get 96% albedo we can get similar brightness from 1/16th the area or 4 times less apparent diameter in the 4 Geo stations. or around  87 km diameter solar sail parked in Geostationary orbit maintaining station.

At about 5 tons for a conservative sail design per square kilometer (Eric Drexler has designed sails with far less weight than this) you are talking aircraft carrier sized masses for a Full Moon bright GeoStar.

The sail would gain and loose momentum to keep on station. Full Moon bright, all day and all night– and thus probably not going to happen given fears of biologically sensitive species.

in the Server Sky plan (computer satellites on quite a small scale in unbelievable numbers—supplying beamed electrical power and computing to Earth) , Keith Lofstrom has detailed the dangers of too much light in the night sky near the Earth-Moon system.

Corals may be triggered to incorrectly spawn with as little as 10% of full moon illumination (which is 1E-5 full sun), or 1E-6 of full sun illumination in the night sky. 

But Venus or greater illumination (2000 times less) should have no major problem, nor indeed 100 times Venus brightness. Anyway, the less light, the smaller the sails needed. If  1000 times less sail material, that only around 3 kilometers or 2 miles diameter sail material , mass in the mere tens of tons–per Venus brightness GeoStar,  doable today in theory.
The statites, being at lunar distances need 100  times the material for the same light.  But still under a kiloton for a very conservative design.
In conclusion, a constellation of a dozen objects of Venus or greater brightness should be quite buildable in the next century. Mass for the system,  low thousands of tons.  If biological sensitivities were not a problem, Full Moon levels of brightness and utter ease of navigation  even on moderately clouded nights, would shortly follow. (Mass for the deluxe system,  low hundreds of thousands of tons)
Is it likely? Hard to believe. If astronomy and navigation geek fantasies were as catching and addictive as lovers of this blog  feel them to be, you’d probably be reading this on Mars. On the other hand, on other planets such as Mars something like this would be an enormous aid in the settlement phase so maybe us space geeks will have the last laugh after all.

Note: (Added later): In Indistinguishable From Magic, a fact book of his, Forward stated a corrected minimum polesitter distance of 250 Earth radii for stability including  solar tides.