The late Harlow Shapley was perhaps the first astronomer ever to seriously attempt quantitatively to estimate the frequency of extraterrestrial life in the universe.⁸¹⁶ It is said that Shapley was more optimistic than his published estimates indicate, but that he deliberately chose extremely conservative numbers to forestall possible criticism from the scientific quarter. His calculation went something like this.

• Suppose that only one star out of every 1000 has any planets at all.
• Further, let us presume that out of every 1000 worlds, only a single one is located an appropriate distance from its sun (and thus has a climate suitable for life).
• Then assume that out of all these well-placed planets only one in 1000 is big enough to hold an atmosphere, and that of these worlds, only one in 1000 has a chemical composition appropriate for the origin of life.
• Combining all of these factors, we find that only 1 star in 10¹² is graced by life.
• There are at least 10²¹ stars in the universe so, according to Shapley, we may expect to find about 1,000,000,000 life sites in the cosmos.

At first blush this seems like a very large number, but upon further reflection we see it is actually quite pessimistic. Since the typical habitable galaxy has about 10¹¹ stars, only one galaxy out of ten will harbor any life at all. If this calculation is correct, humanity is very much alone.

It appears that Shapley selected his step-factors of 1000 largely out of cautious conservatism without any real basis in genuine, established scientific findings. Subsequent formulations have been devised in an attempt to deal with this major failing of the Shapley calculation. The most popular alternative among xenologists today is the so-called Drake Equation¹³¹⁷ (or "Green Bank Formula"²³⁵⁸), named for its originator Frank D. Drake, a well-known American radioastronomer currently associated with the Center for Radio-physics and Space Research at Cornell University.

Where might we expect to find alien life and civilization in nearby extrasolar space?
The following three tables may serve as starting points for discussions of this speculative question.

Due to unavoidably deficient data, Table 23.4 is complete only out to about 40 light-years. From 40-100 light-years, data are available only for about 25% of the "good suns" expected to lie at this range. The deficiency is almost exclusively among the class K stars (which are harder to measure at great distances) beyond 40 light-years, although many late class G suns are also missing beyond 50-60 light-years.

Table 23.2  lists the 75 brightest named stars in the night sky of Earth. Table 23.3  gives a complete inventory of all luminous stars within 20 light-years of Sol. Table 23.4  includes a listing of all "good suns"* within 100 light-years (30 parsecs) of Sol.

Table 23.2 Table 23.3 Table 23.4

Table 23.2 The 75 Brightest Named Stars in the Night Sky of Earth(modified after Robinson3086) 0.000016 - 63 ly 64 - 210 220 - 1600    0.000016 - 63 light-years    64 - 210 light-years    220 - 1600 light-years Table 23.3 Complete Inventory of Luminous Stars with 20 Light-Years of Sol (modified from Mattinson1114) 4-11 ly 11-15 ly 15-18 ly 18-20 ly    4.29 - 11.48 light-years    11.57 - 15.31 light-years    15.38 - 18.43 light-years    18.53 - 19.89 light-years Table 23.4 Inventory of Good Suns* (F5-K2) within 100 Light-Years of Sol (selected from Hofflied575) 4-35 ly 36-48 49-55 56-67 67-76 76-88 88-96    4-35 light-years    36-48 light-years    49-55 light-years    56-67 light-years    67-76 light-years    76-88 light-years    88-96 light-years

* In this context, a "good sun" is a Main Sequence dwarf (Sol-like) belonging to stellar classes F5-K2. The nearest to Sol is the α Centauri star system,³⁰⁸⁹ which recently has been discovered to be 6 eons old and significantly richer in heavy elements than our own solar system.³²²⁴

Table 23.5 Possible Planetary Companions of Nearby Stars

Assuming habitable worlds circle some or all of these distant stars, how might they be detected from Earth? There are four basic techniques, none of which has as yet provided absolutely unambiguous evidence for the existence of extrasolar planets.* The present state of the data is summarized in Table 23.5, at right.

Certainly the most fruitful approach to date has been the technique of astrometry.

This requires a bit of explanation.

• It will be recalled that all stars in the Milky Way orbit the galactic center much as planets circle a sun.
• Since each star moves with a slightly different velocity, celestial objects appear slowly to change position relative to each other over the years.
• Slowly, inexorably, the familiar constellations are torn asunder as the component stars move off in different directions at different speeds.
• For instance, the stars Sirius, Betelgeuse, Aldebaran and Arcturus have moved about the apparent diameter of the moon (Luna) since Ptolemy mapped them two millennia ago.
• The path traced in the sky by a wandering star is referred to as its "proper motion" by astronomers.

A lone sun traces a straight path across the sky, but a star with a retinue of invisible companion bodies should wobble slightly as it traverses the celestial vault. This is because the presence of the unseen planetary masses shifts the center of mass away from the center of the sun.

• The star, like its planets, actually circles this center of mass, which distant observers may observe as a tiny sinusoidal wobble with a period on the order of decades.
• Astrometry is a form of careful positional measurement which allows astronomers to calculate the mass and orbit of the hidden worlds based on the amplitude and frequency of wobble in the proper motion of the target star.

Imagine an hypothetical alien astronomer located 10 parsecs (33 light-years) away who wishes to demonstrate the existence of planets around Sol using astrometry. How accurate must his measurements be?

• Viewed from this distant observatory, our sun would subtend only 10^-3 arcsec (seconds of arc, or 1/3600 of a degree) in the sky.
• One-half an arcsec away from this minute yellow disk is found the giant planet Jupiter, a shining pinprick of light 10^-4 arcsec in diameter.

It is helpful to put these numbers into proper perspective in order to fully appreciate their smallness.
A second of arc is considered extremely high accuracy in all normal circumstances.

• One arcsec is the equivalent of hitting a buzzing horsefly with a rifle bullet at a range of 2 kilometers.
• But Sol would subtend only 10^-3 arcsec, which is like hitting the same horsefly in New Orleans by firing a rifle in Los Angeles (more than 2000 kilometers).
• To use another example, consider a level tabletop. When you touch it lightly, it tilts by at least a second of arc.
• At the 10^-3 arcsec level the table is like the surface of a sea — acoustic waves from people talking wash back and forth across its surface and "tilt" it by more than milliseconds of arc.
• To observe Sol’s wobble due to Jupiter, our hypothetical ET astronomer would have to be able to measure variations in proper motion of about arcsec at a range of 10 parsecs.
• The displacement of our sun due to the presence of Earth is considerably smaller, less than 10^-6 arcsec at 10 parsecs.
• The state-of-the-art of astrometric precision was roughly 3 × 10^-3 arcsec for human technology in the mid-1970s, which means that mankind is now at the threshold of the capacity to detect jovian planets circling neighboring stars.²²⁰⁰
• Scientists believe that sophisticated interferometric techniques²³⁸⁷ can increase ground-based accuracy to 50 × 10^-6 arcsec, and that large spaceborne telescopes specially designed for the task can reach 10^-6 arcsec accuracies.^3092,2865 (NASA’s 2.4-meter Space Telescope has pointing stability of 0.007 arcsec.)

The major difficulty with astrometry is that several cycles of the alien planet must be observed to identify and validate a discovery, which means several decades’ worth of data must be accumulated. Furthermore, the presence of more than one perturbing planetary body (Sol has 9) greatly complicates the mathematical analysis of periodicities in the wobble in proper motion of the target star.

To date, only astrometry has been exploited in the search for extrasolar worlds. But three other promising techniques have been discussed at length in scientific circles. The first of these is called the spectroscopic or "radial velocity" method.

Whereas proper motion is the apparent movement of a star across the sky, stellar "radial motion" is its velocity towards or away from us. We recall that light emitted from a moving object undergoes a Doppler shift in wavelength depending on the relative velocity of source and observer.

• By measuring the Doppler shift in a star’s visual spectrum, astronomers are able to determine its radial velocity.
• If a massive planet is present, then its orbit will cause the star’s radial velocity to oscillate much like the wobble in proper motion discussed in connection with astrometry.
• Rather than a positional undulation, however, the planet-hunting spectroscopist is looking for minute cyclical variations in Doppler-shifted starlight.
• This requires an instrument accurate to 0.08 mm visible light, able to detect variations in radial velocity on the order of 5 meters/second.¹⁵⁶⁸
• To date, the most sophisticated equipment has accuracies about an order of magnitude too low, but astronomers estimate that the state-of-the-art should progress enough in a decade or two to make the spectroscopic method feasible.²⁸⁶⁵

Photometry is another promising technique.

• If the orbital plane of the target solar system happens to lie precisely in our line of sight, then at some point planets will cross the face of the star and partially eclipse its light.
• If a planet the size of Jupiter crossed in front of a star like Sol, the decrease in brightness would amount to about 1% change in total luminosity. (Passage of Earth would only cause a minute 0.008% eclipse, and so on.¹²⁵⁹)
• Astronomers believe that the colorimetric and photometric eclipse signature should be fairly easy to detect and to identify.¹²⁶⁶
• One writer has calculated the probability of the onset or termination of an eclipse by any one of Sol's planets during a typical 6-hour observation period (a single night’s work at the telescope).
• For a randomly situated extraterrestrial observer, using the techniques proposed, the expected detection rate could be as high as one new solar system per year.
• About one star in a hundred should have a line of sight close enough to the orbital plane around Sol to allow all four of our inner planets to be detected by alien astronomers.**¹²⁵⁹
• Human astronomers should prove equally lucky.

The third most promising method for spotting other worlds is direct observation.
There are two main difficulties involved in this.

First there is the problem of optical resolution.

• Seen from 10 parsecs away, Sol and Jupiter appear only 0.5 arcsec apart — close to the limits of present-day ground-based telescopes.
• And planets smaller than Jupiter at the same distance, or jovian worlds farther from the star, probably could not be resolved using present instrumentation.
• The image of the star and planet would blur together.

The second main difficulty is that the extrasolar body we seek is very faint.

• Shining in reflected light, the luminosity of the planet is only about 10^-8 that of the stellar primary in the visible wavelengths.
• Dr. Bernard Oliver of the Hewlett-Packard Corporation has estimated that sophisticated "apodization" techniques (a mask fitted over the end of the telescope to selectively reduce the brightness of the star’s diffraction pattern) could be used in a 2-meter spaceborne telescope which would just barely permit a jovian world to be resolved.²⁸⁶⁵
• Indeed the Space Telescope, due to be launched by NASA in the early 1980’s, should fulfill these requirements and permit the first direct imaging of extrasolar planets.²¹⁰³

Another solution to the problem is to shift to lower frequencies where the star is relatively less bright.

• For example, in the infrared the luminosity differential falls from 10^-8 to 10^-4.²⁸⁶⁵
• In the radio things are even better: Fennelly and Matloff have estimated that jovian planets may be detectable out to 10 parsecs using intercontinental interferometry at radio wavelengths.¹⁴⁵³

Ultimately it would be nice to be able to take detailed color photographs of terrestrial worlds across interstellar distances. Is this possible?***

Lyman J. Spitzer, Director of the Princeton University Observatory, has proposed a spaceborne occulter apparatus.³⁰⁸⁰

• In this scheme, an orbiting large space telescope is pointed at the target star.
• A disk of black material is then placed in the instrument’s field of view in such a way that it exactly covers up the image of the star.
• The blazing brilliance of the primary is blotted out, permitting the detection of much fainter planetary bodies.
• According to Spitzer, NASA’s Space Telescope should suffice to resolve a jovian 10 parsecs away if an occulting disk 75 meters wide is placed 10,000 kilometers in front of the telescope.
• To spot an Earthlike extrasolar world at the same distance, a 400-meter-wide disk must be accurately positioned 250,000 kilometers ahead of the telescope.
• Citing the practical problems inherent in such a proposal, a few authors have advocated using Luna as an occulter.^3189,1095
• To pick out jovians at 10 parsecs, a 3-meter space telescope should be placed in a near-polar 8100-km-high lunar orbit.
• The curved limb of the moon periodically would blot out the star light, making possible at least minute-long observations of reflected extrasolar planet light.
• To spot Earthlike worlds, a 7-meter space telescope should be placed in high Earth orbit, again using the distant Luna as an occulter.

Still larger systems could actually begin to resolve features on the surfaces of these faraway celestial bodies. The possibility of constructing orbital and lunar telescopes comprised of giant mirrors or huge multi-mirror arrays has been discussed in the literature.^3091,3085 According to Gerard O’Neill, the fabrication of large space structures should make interstellar imaging a snap:

• It might be preferable to take advantage of a zero-gravity location by building a large number — perhaps 10,000 — of individual glass mirrors, each a meter in diameter, and providing each with a small locator-module, equipped with station-keeping gas jets.
• If the 10,000 elements were linked only by light beams, their spacing could be established by the unvarying number of wavelengths of light between each pair.
• That nonphysical linkage, computer-controlled, would have the further advantage that the mirrors could be programmed to separate and reform, like dancers in a slow-motion ballet. … If located in a cross-shaped array, with individual elements spaced ten meters apart, a telescope of that kind would have the theoretical capability of resolving something as small as a changing weather system, one thousand kilometers on a side — on the planet of a star ten light-years away.²⁷¹⁰

* See reviews by Gatewood,¹⁵⁶⁷ Huang,¹²⁷⁸ Martin^{1452,1088,1092} Matloff and Fennelly,¹⁶¹⁴ Morrison, Billingham, and Wolfe,²⁸⁶⁵ O’Leary,¹²⁴⁴ and Smith.²⁸⁶⁶

** Edward Argyle at the Dominion Radio Astrophysical Observatory in Canada has proposed a clever variation of the photometric method. Planets shine with reflected light and are located several light-minutes from the source of illumination (the star). If the emitted starlight varies, the portion reflected by the planet will be delayed in time behind the rest of the solar output. Careful photometric measurement, says Argyle, should permit the separation of these "light-echoes" from the normal starlight, thus demonstrating the presence of reflective planetary bodies and proving the existence theorem for extrasolar worlds.¹²⁸⁹

*** The surface of Betelgeuse, the giant red star in the constellation Orion, has been successfully photographed using computer-enhanced "speckle interferometry" techniques.^411,3090 Surface structures are clearly visible in the photos.