Wednesday, July 23, 2003

Eclipse mad science:

Asked by Ernest, a teacher in California: Would it be possible to create an artificial solar eclipse using a circular object in earth orbit to cast a shadow on our planet's surface? If such an orbiting object were at a distance of the international space station, how big would it have to be? Could an artificial eclipse be used as a weapon by denying sunlight to a certain city or country? What might it's potential be as a tourist attraction?

It would certainly be possible to create an artificial eclipse by orbiting a circular object around the Earth, but it wouldn't be very practical.

If the object were orbiting at the height of the International Space Station, or about 380 kilometers high, then we can figure out how large it would have to be to just cover the face of the Sun. The Sun is, on the average, 149,600,000 km from the Earth, and its diameter is 1,392,000 km. Using some trigonometry, that means that it subtends an angle s of about s=2*arcsin(1,392,000/2/149,600,000) or about 0.533 degrees. It's hard to believe the Sun is that small in the sky, isn't it? [Of course, the Moon is also approximately this size, otherwise we'd never see a total solar eclipse!]

Now the object we are thinking about has to subtend the same angle, so again we can use trig to find that if it is 380 km away, it will have a diameter d of about d=2*380*sin(s/2)or about 3.5 km.

Building something this big in orbit is pretty difficult, but possible---the best thing would probably be to simply fire an enormous balloon into orbit and then inflate it until it reached this size. Still, a pretty great feat.

However, notice two things about our scheme: one, the shadow only just touches the ground, and two, the shadow is moving along the ground at least at 17,000 km/hr as the object orbits the Earth (at the same speed as the International Space Station, since it is at the same height). So, unless the shadow were a lot larger (by making the balloon larger), the eclipse would not last long at all. Even the Moon can only cover the Sun for about 4 minutes. The physics of orbits make it impossible to keep the shadow still.

"Aha," you say, "...but what about geostationary and Lagrange orbits?" Well, these orbits are much farther away, and that means that our object needs to get proportionately larger. A geostationary orbit, which is one that orbits the Earth once a day (and so keeps up with the ground underneath it, and therefore seems to stay still in the sky), is 35,767 km from the Earth---our object would have to be 329 km across! The Sun-Earth Lagrange point, where the gravitational pulls of the two bodies are equal, is at about 1,500,000 km, so our object would now have to be 13,816 km across! But note that even for both of these ideas, the shadow would still not stay over the same point on the Earth.

There is actually a satellite called SOHO that is orbiting around the LI Lagrange point 1,5000,000 km sunward from the Earth, and it uses a special camera with a disc in the middle to create its own "artifical eclipses." This is used so that SOHO can observe the solar corona all the time to study the Sun and give us warnings when there are particularly dangerous flares.

The above calculations give us the answer to your question about denying people sunlight, and about creating a tourist attraction where the Sun was always in eclipse---it is pretty much impossible to do it from orbit. The only way to tackle this from orbit would be to build a ring around the Earth (like a ping pong ball with the ends cut off). I will leave it to you to calculate what the surface area of a shell like this would be, but even for a really narrow one, it would take an enormous amount of material.

The opposite idea, that of putting more light on the surface, has actually been tried. Reflecting light off large orbiting mirrors has been proposed to help increase solar arrays generate power or simply to illuminate areas during winter. The Soviets and Russians seriously investigated trying to shine sunlight on Siberia during their long winter months, but gave up after they calculated the size of mirrors and the cost of systems to keep them properly pointed. The idea was also probably strongly opposed by their own astronomers, who need dark skies for observing---read this ABC article about the project.

From Energiya's Znamya site:

Illumination from space - "Tretie svetilo" (Third light):

Solar light from space: This program was also developed during the Columbus-500 project. Illumination by space mirrors was originally proposed by scholars of the past: F. Tzander, H. Obert. Conceptually however, it was developed and refined by Kraft Ericke. Using the solarcraft as a basic component, a whole system can be configured.

The following parameters are considered to be suitable in the near future.

  • Size of reflector---200 m,
  • circular orbits of 1500--4500 km of attitude,
  • size of light spot---15--45 km,
  • brightness 10--100 lunettes (full moon),
  • number of reflectors in a cluster ~ 12,
  • one cluster could provide illumination to 5 large cities.

Here are some stories on the June 21 eclipse, visible in Southern Africa, "Africa Marvels at First Eclipse of New Millennium" and "Africa Marvels at Solar Eclipse," and here's a description of eclipses in general. [You might also check out The Eclipse Home Page.]

Hope this helps!