## Probability That The Presence Of A Second Star Has Not Rendered The Planet Uninhabitable

In order to assess this probability, it is necessary to know the probability that a star is a member of a binary star system, and if so, the probability that the stars are spaced, or move around each other, in such a manner that they will affect the existence of a normal ecosphere.

As discussed earlier, habitable planets can exist in binary star systems if the two stars are so close together that there is a single ecosphere around the pair or if they are so far apart that at least one can have an ecosphere without interference from the other.

Tables 14 and 15 give the proportion of stars that are spectroscopic doubles (closely spaced binaries) as a function of spectral class. In spectral classes F, G, and K, the proportion is 4 to 7 per cent according to Allen (1955) and 28 to 30 per cent according to Jaschek and Jaschek (1957). The periods of revolution of spectroscopic doubles made up of main-sequence stars are typically measured in days. This means that the two stars must be quite close together, generally having separations of less than 0.1 astronomical unit. From Figure 31 (see page 80), it may be seen that this would be compatible with the existence of an ecosphere around both stars.

On the other hand, the great majority of visual doubles are so widely separated that their orbital elements can not be determined with much accuracy. For the 12 per cent of visual doubles with measurable orbital motions, typical separations are great enough to permit the existence of a suitable ecosphere around either star. Since 4 to 9 per cent of stars in spectral classes F, G, and K are visual doubles, probably no more than a fraction of 1 per cent have separations in the critical distance range that would prevent the existence of an ecosphere.

According to van den Bos (1956), the median period of the binaries near the Sun has been given by Hertzsprung as 80 years and by Luyten as 300 years. Wide separations appear to be typical.

Some authors have assumed that binary systems, unless the components are very widely separated, can not have stable planetary systems (Huang, 1959). Considerations of the stability limits for orbits in the three-body problem, however, strongly suggest that stable planetary orbits can exist within ecospheres in the majority of binary systems of interest, although the general conditions for stability of planetary orbits are difficult to estimate when the two stellar components are revolving in eccentric orbits about their common center of mass.

From the foregoing, it appears that practically all of the closely spaced binary star systems (spectroscopic doubles) could possess habitable planets and that, among visual doubles, spacings that would prevent the existence of a normal ecosphere are rare. In view of the incomplete state of our knowledge, however, let us estimate that generally, for any arbitrary star, there will be interference in 5 per cent of all cases, or PB is equal to 0.95, to allow for possible underestimates of the numbers of binary star systems

Table 14. Data on Binary Stars

### Spectroscopic doubles Spectral class

Proportion of the stars in each class with duplicity in radial velocity (per cent) Median period of revolution (days) for spectroscopic doubles composed of main-sequence stars

Visual doubles (of apparent visual magnitude brighter than + 9)

Spectral class O B A F G K M

Proportion of the stars in each class that are visual doubles

Visual doubles with measurable orbital motions

Proportion of visual doubles with measurable orbital motions is 12 per cent

(others are too widely separated for determination of orbital elements). Mean and modal elements (from Arend, 1950) mean mode

Semimajor axis of true orbit (A.U.) 26 18

Period (years) 76 32

Eccentricity 0.54 0.46

Source: Allen (1955).

Table 15. Corrected Percentages of Spectroscopic Binaries along the Main Sequence

Spectral class B A F G K M

Percentage of spectroscopic binaries in each class 21 27 30 29 28 32

Source: Jaschek and Jaschek (1957).

having awkward separation distances. For isolated stars or for stars in binary systems where the orbital parameters are known to be favorable, PB should be taken as 1.00.

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