The world finder: searching for the Earth's twin. (Try this!) Edward H. Carlson.

Look up into the clear night sky. If you are away from city lights you see about 2500 stars with your naked eye. (Seems like a lot more, doesn't it?) Astronomers believe many of these stars have planetary systems. Which ones? Could you be looking toward worlds that are similar to Earth in size, temperature, atmosphere, and living conditions? Let's explore our Milky Way galaxy, using the computer as a spaceship on a journey to find the Earth's Twin. In this quest, we will come across many strange worlds inhabited by fantastic lifeforms.

We must first make the standard science fiction assumption--that we have a deep space hyperdrive to tunnel through space-time and thus greatly exceed the speed of light. We don't want our journey to take millions of years. But this is our only concession to the fiction folk. We will otherwise stick to what the astrophysicists believe about planets and their habitability--that is, when these wizards can agree in this rapidly developing field of study.

One short article cannot teach a whole book full of astronomy, so refer to your encyclopedia when you run across unfamiliar terms. On the other hand, the program in Listing 1 will crunch the numbers and spit out the particulars on any planet we run across--its size, surface gravity and temperature, length of day and year, satellites, composition, life chemistry, and geological age.

To find out what kinds of planets we might find roving about what kind of stars, we peek under the cabbage leaf and watch the birth of stars and planets.

Planets form at the same time their central star is born--from the same cloud of gas and dust swirling chaotically in a spiral arm of the galaxy. The gigantic, cold, tenuous cloud is mostly hydrogen gas mixed with 20% helium gas and containing about 2% dust--specks containing water ice, other ices (ammonia, methane) with smaller amounts of "sand" (silicate grit) and iron.

As the cloud contracts under its own gravitational attraction, its swirling must speed up, obeying the same principle by which an ice skater, starting in a slow spin, speeds up by pulling her arms in to her body. What happens next is the subject of immense computational effort on the world's fastest computers. Most often the cloud breaks up into pieces, each contracting to form a star, so binary, triple, or multiple star systems result. Such systems may be too unstable to allow planets to form. But in about 10% of the cases, a single star with planets is born from a cloud fragment spinning so fast that it flattens into a disk, the planetary accretion disk, whose central bulge becomes the star.

The contraction process heats the disk, and the central regions become so hot that the ices evaporate. Near the central bulge, the silicate and iron also vaporize. In the central bulge itself (if hot and massive enough) thermonuclear reactions create the life spark of the newborn star which cannot cool off again until its hydrogen fuel is used up. But the disk itself does cool by radiating its heat away, recondensing its gases back into iron particles, silicate grains, and far enough away from the star, ices. These particles collide and stick together, forming planetesimals which attract each other gravitationally, forming the planets and satellites. Gas, dust, and vapors that are not captured by the growing planets eventually escape into interstellar space.

The whole process takes somewhere in the range of a million to tens of millions of years--a short time compared to the 4.55 billion year age of the solar system and the approximately 13 billion year age of our galaxy.

From the largest clouds come massive stars and perhaps massive planets. I say "perhaps" because massive stars are so bright and hot that they may evaporate the cloud before the planets can properly form. Then again, they may not. We have good data for only one case, our own solar system, and the sun is not particularly massive (though it is more massive than the average star).

You might think a massive star would take a long time to burn its hydrogen into helium, but this is not so. A star 30 times more massive than the sun burns 150,000 times more brightly, running through its fuel in only a few million years versus the 10 billion year life span the sun can expect. We may satisfy our curiosity by looking for planets near the really bright stars we see in the sky, such as Spica, Rigel, and Vega, but we won't want to settle down on one of their planets--raw and uncivilized by life--because the star may "soon" swell up into a red giant, engulfing the innermost planets, and then later explode as a supernova.

The composition of a growing planet depends on how hot its part of the gas-dust cloud is, which in turn depends on the distance of the planet from the central star. The central parts of the accretion disk are too hot to allow ices to condense, so the planets formed there are rocky--composed of a dense iron core surrounded by silicate rocks. In our solar system, Mercury, Venus, Earth (and its Moon), Mars, and probably the asteroids are rocky.

Planets formed farther out are more massive but less dense, composed mostly of ices. If they are massive enough to attract and hold hydrogen and helium gases, they become giant gas balls. (If the gas ball is large enough, its central regions heat to the ignition point of fusion nuclear reactions, and the "planet" becomes a small star.) Jupiter, Saturn, Uranus, and Neptune are gas ball planets. Pluto is probably an icy planet--most likely an escaped moon of Neptune.

Thus a sharp boundary occurs at the "condensation-of-ice radius" of a planetary system. Inside this radius are the rocky "terrestrial" planets, outside are the icy and gas ball planets. The condensation-of-ice radius is about 4 AU in our solar system--between the asteroid belt and Jupiter. (AU stands for Astronomical Unit, the 93 million mile yardstick used to measure distances in planetary systems. It is the distance of the sun from the earth.)

Using the Program

In the program in Listing 1, you first pick the mass of the star you wish to investigate. The brightness of the star and its lifetime depend only on its mass. A cube five light years on a side in our part of the Milky Way galaxy would probably contain one star of mass and brightness similar to the sun and several that are fainter. To find a star that is a hundred times brighter than the sun, we should look in a cube that is at least 30 light years on a side. (The center of our Milky Way galaxy lies about 30,000 light years away. You are looking toward it when, in the summer sky, you look near the "pouring spout" of the "teakettle" in Sagittarius.)

The program then semi-randomly generates a typical planetary system for the star you picked. The program uses our understanding of the physical processes that give rise to planets, which are best understood for our own planetary system. So the planets generated for stars of mass M=1 (that is, a mass equal to one solar mass) are most plausible. The systems generated for stars of much different mass are, frankly, speculative.

The radii of the orbits come from a modified Titius-Bode Law--the radii increase roughly in a geometrical series as you move out from the sun or star. I also assumed that the mass of the planetary accretion disk was proportional to the mass of the star. Then using the inverse square law of light intensity vs. distance from a source (star) to determine the condensation-of-ice radius, and Kepler's Laws of planetary orbits, the planetary system can be constructed. By the way, when I say "the surface radius" of a gas planet like Jupiter I mean the radius of the gas ball, not the radius of the small solid core that may lie deep within the planet.

As you run the program, it quickly becomes obvious that few planets match the Earth in temperature, gravity, and composition. If the orbit of Earth were somewhat larger or smaller in radius, the oceans would freeze or boil. If the gravity were weaker, our atmosphere would escape. If stronger, the atmosphere would differ in composition from the familiar 80% nitrogen and 20% oxygen we breathe.

An iceball world, even one having Earth gravity, may be very difficult to live on. Earth astronauts will test this out first hand in the next century, visiting the satellites of Jupiter, Saturn, Uranus, and Neptune.

Expanding the Program

The program as it stands is fun and instructive, but leaves many topics you may want to develop further. After visiting your local library for astronomy books, you can tune up the calculations in many places, for example the length of planet days and the density of the planets. Finish the satellite construction that I began. The satellites come from two sources: The gas ball planets have some satellites--the Galilean moons of Jupiter, for example--that apparently formed in a miniature accretion disk, just like the solar system as a whole. Other satellites are apparently captured asteroids or large planetesimals. So you may want to give your planetary systems some asteroids, formed in a belt inside the orbit of the largest planet. The gravitation of the giant planet disrupts the process of planetesimal accretion for the next inner planet. Comets--kilometer sized ice balls formed far out in the planetary accretion disk--add a decorative touch.

If you like chemistry, play around with the composition of the planets, moving on to geology, then to weather and climate. Finally, explore the implications all this has for biology. Invent lifeforms to fit the various living conditions on the planets. Drop me a letter (c/o Creative Computing) or leave a message on the Creative Computing CompuServe SIG (type GO PCS 22 at any function prompt) about your extensions. If I perceive enough interest, I will reopen the subject in a later column. I am especially eager to become acquainted with the creatures, gentle and ferocious alike, of the other worlds.

But the first task is to locate our home away from home. I suggest you modify the program to search automatically many suitable stars for earthlike planets, keeping track of the number of systems investigated. Start it running at bedtime and see if morning brings a rosy dawn on the Earth's Twin.