Stadyshell

Statite Dynamic Shell, aka, Stapledon Dyson Shell

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1. The Standard Story

The continued increase of the human population, expanding into the solar system and later to other star systems, is a common assumption in 20th century science fiction. People move into orbiting space habitats at the L4 and L5, terraform Mars, etc. When planetary systems are exhausted, the expansion continues into more space habitats orbiting the sun, perhaps manufactured from the asteroids, Mercury, and Venus. Some propose dismantling the Earth to build more habitats, eventually capturing most of the energy from the Sun.

This is unlikely, and dismantling the Earth is unnecessary and wrong.

Nikolai Kardashev characterized future supercivilizations by the energy they capture and use.

• A type I supercivilization captures all the power reaching their planet from their star for artificial uses. For the Earth, that is 174 petawatts, 1.74e17 watts incoming, of which perhaps 120 petawatts reaches the surface - the rest is reflected into space. Plants intercept about 20 petawatts (2e16 W), and convert 200 terawatts (2e14 W) into material animals (and now biofuel-guzzling machinery) can eat. Current global artificial power production is about 15 terawatts (1.5e13 W).

  A type II supercivilization captures all the power emitted by their star. Our sun emits 380 yottawatts (3.8e26 W) visible light, UV, and infrared, 2 billion times more power than the earth intercepts, and 25 trillion times more power than human artificial power production.

  A type III supercivilization captures all the power emitted by all the stars in their galaxy. Our galaxy emits perhaps 40 trillion yottawatts, (4e37 W), more than two heptillion (2e24) times more power than human artificial power production.

So, a supercivilization capturing all the power emitted by the Sun with a shell of habitats would be a Type II supercivilization.

Olaf Stapledon wrote about type II and type III supercivilizations in his 1937 space fantasy novel Starmaker. Freeman Dyson wrote about how such supercivilizations might appear as highly luminous, compact infrared sources in 1960, Search for Artificial Stellar Sources of Infrared Radiation. Dyson described them as shells, a constellation surrounding a star - he did not claim they would be solid or spherical.

Because of this paper in Science, a journalist misleadingly named these sources Dyson Spheres, a source of confusion ever since. Dr. Dyson wishes they were named something else, as I will do below.

What do Type II Humans Need?

Intelligent life resembling us is probably very rare. There may be many possible substrates for many kinds of intelligence, though, and we may invent other forms that are more compatible with long-term goals for intelligence.

Earth life needed more than a billion years to invent oxygen-producing photosynthesis, and did so only once. This involved the development of more than 100 proteins in a complex configuration with two coupled photosynthesis systems; it took a long time for nature to develop and combine all the elements out of anaerobic predecessors. The conditions that produced us are required for our survival. What do unmodified humans need?

The last is the reason to build a Type II civilization in the first place. A billion years of resources may be impossible to provide, if we are limited to the earth, with imperfect recycling and our ore-derived materials slowly eroding into the sea. The sun is heating up, and the earth may be uninhabitable within a few hundred million years. We will need to be active in space to protect our planet, and restore it after a major catastrophe.

Gravity is a recent addition to the list, based on work by Joan Vernikos MD of NASA Ames, and experience with a relative who spent way too much of her life in a recliner chair, developing blistering, swelling, and infections in her legs. There are valves in the legs that augment blood flow in the body; without that pressure modulation, we eventually (years) get sick and die. Ask an MD physical therapist.

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The "Dyson" "Sphere"

The scare quotes are intentional - the attribution is wrong, as is the noun. I will describe the idea the label has come to describe, before disposing of it.

For many science fiction readers, this is a large solid sphere, inhabited on the inner surface with the sun overhead. Details intentionally vague ... because a solid sphere doesn't work, for numerous reasons.

A Miscellany of Physical Pathologies

light from above, tiny gravity

The area of a sphere is 4πR² - the area of a planet facing the sun is πR², so the average surface illumination is ¼ of the total. Add in atmospheric reflection, and the average illumination (visible light and near IR < 2 μm wavelength) reaching the Earth's surface is about 240 W, averaged over 24 hours. If this was somehow duplicated across the inner surface of a huge sphere, and radiated into deep space on the outer surface with an emissivity ε of 1, the black body temperature would be T = 255 K = /sqrt(4){240 / \epsilon \sigma} where σ = 3.567e-8 W/m²K⁴ $. A temperature of 13℃ (55℉) is considered optimal - a black body temperature of 286 K. We can achieve that with an emissivity of ε = 0.63. Except - if we want to preserve the diurnal and annual cycles of nature, we will want to modulate the light on a 24 hour and an 8766 hour cycle. Easy; we put reflective shutters on a region and the sun, and turn the shutters open to closed on a 24 hour cycle. The light not used by one area will be reflected into the sphere, and used elsewhere, perhaps creating a daily cycle ranging from zero light to 750W at "noon", more in some regions ("the tropics"), less in others ("the poles"), with these regions interspersed in such a way as to create winds, migrations, etc.

The surface of the sphere must be ( 3.8e26 W / 240 W/m² ) = 1.6e24 m² = 4πR² so R = 3.5e11 meters = 2.4 AU (Astonomical Units = 1.492e11m), around the middle of the asteroid belt.

But what about gravity? The sun's gravitational parameter is 1.327e20 m³/s², so the gravitational force at that distance is 1e-3 m/s². And it is inward, in the same direction as the sun. That won't work!

Compression strength

Assuming the sphere is all structural material (nothing hanging on it, which is pointless) with a thickness of t and a density of \rho . We will consider a hemisphere with radius R in solar gravity \mu / R^2 . Assume \theta is the angle from the center of the hemisphere to the side, ranging from 0 to \pi / 2 . The incremental mass d M of a hoop segment between angles \theta and \theta + d \theta is the diameter of the hoop 2 \pi R \sin{ \theta } times the width R d \theta times the thickness t and density \rho :

\Large d M = ~2 \pi ~\rho ~t ~R^2 ~\sin{ \theta } ~d \theta

Some of the gravitational force is perpendicular to the bearing surface of the hemisphere; the component adding to the compression force on the bearing surface is proportional to cos{ \theta } . The gravitational acceleration from the sun is \mu / R^2 .

Multiplying all these together, we get the total compression force on the bearing surface per hoop element:

\Large d F = ~2 \pi ~\mu ~\rho ~t ~sin{ \theta } ~cos{ \theta } ~d \theta

Integrating for the total force F :

\Large F = ~\pi ~\mu ~\rho ~t

The bearing surface is 2 \pi R t , so the compression stress per unit area S is

\Large S = \mu ~\rho / 2 R

The necessary compression strength to weight ratio Y is:

\Large Y \LARGE = { S \over \rho } = { \mu \over { 2 R } } in m²/s².

The solar gravitational parameter \mu is 1.327e20 m³/s^{2, and $ R $ is 3.5e11 m, so $ Y $ = 1.9e8 m}2^/s2^{. The space elevator community dubbed the m}2^/s2 ^{unit the "Yuri" (after Yuri Artusanov) so this is 190 !MegaYuris. For comparison, the tensile strength of a [[ https://nanohub.org/resources/12251/download/msa334.pdf | multiwall carbon nanotube ]] is 0.15 TPa, the assumed density (graphite) is 1300 kg/m}3^, so that material cannot deliver more than 115 MegaYuris - probably much less in bulk material with a crosslinking matrix. This does not include the dead load we want to hang on this structure. That won't work!

Stability

The bending strength of this huge, thin shell is almost nonexistent. If a bulge occurs, the restoring forces are negative - the bulge grows, either pushed outwards by reduced gravity or pulled inward by increased gravity. That won't work!

Air, Water, Cycles of Nature

The earth's biosphere is complex, and humans are exquisitely tuned to it. As the Biosphere 2 experiment revealed, a robust (and large) global biosphere is essential (and perhaps too small with current technology) to support the Earth's many human inhabitants. How much biomass per person? It is about 10 tonnes per person (WAG) on Earth - how this scales to a sphere environment is difficult to say. A lot of that is cattle and cattle feed, so perhaps that can be reduced.

Humans breath 1 kg/m³ air - if we substitute helium (extracted from Uranus) for nitrogen, perhaps people can breath air that is 200g/m³ of oxygen and 200g/m³ helium. However, we can't grow plants in that - which need a lot of room and air to grow. Perhaps the humans live on algae cake and farmed fish.

But what is the point?

Protective Environment

The earth's magnetic field and thick atmosphere also provides protection against space radiation (cosmic rays, supernovae, solar mass ejections), meteorites, and thermal extremes. Again, substitutes are difficult, heavy, and expensive.

Unmodified Humans are Fragile

Humans break - way too easily. We are designed to replace ourselves, not endure beyond a century or so. A few of our constructions span centuries, but most happen fast or grow incrementally, so we can expect a secular project like a Dyson Sphere to either be complete within a human lifetime, or "deliver the goods" in a shorter time.

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