Project Cyclops, A Design... - Department of Earth and Planetary ...

Black at NASA's Ames Research Center reanalyzed Van
de Kamp's data and found that an even better fit
between the theoretical and observed wobbles could be
obtained by assuming three bodies in circular orbits. Van
de Kamp's two planets and Suffolk and Black's three
planet solutions are given in Table 2-3.
Barnard's star is an M5 star with only 15 percent of
the Sun's mass. It is tempting to regard Suffolk and
Black's solution as evidence for a scaled-down solar
system with three gas-giant planets at 1.8, 2.9, and 4.5
AU, rather than four at 5.2, 9.5, 19, and 30 AU, as in
our Sun's family. However, the data do not appear to
support this simple interpretation.
A single planet in orbit about a star causes the star to
execute an orbit of the same shape (same eccentricity)
about the common center of gravity. If the planetary
orbit is circular, the observed stellar motion should be
simple harmonic in both right ascension and declination,
and the Fourier spectrum of both motions should
therefore contain a single frequency. If the orbit is
highly elliptical, the motion of the primary will occur
rapidly when the two bodies are near periapsis, with
relatively slow motion for the long intervening period.
Thus, the spectrum of the motion will contain harmonics
of the fundamental frequency of revolution.
TABLE 2-3
CHARACTERISTICS OF POSSIBLE PLANETS
ORBITING BARNARD'S STAR
Mass Orbit
Planet Distance (AU) (Jupiter = 1) Period (Trs)
Source
BI 4.7 1.1 26 van de Kamp
4.5 1.26 24.8 Suffolk & Black
B2 2.8 0.8 12 van de Kamp
2.9 0.63 12.5 Suffolk & Black
B3 1.8 0.89 6.1 Suffolk & Black
Examination of the periods of the "planets" in Table
2-3 shows them to be very nearly in the ratio of 2:4 for
Van de Kamp's solution and l:2:q '_,r Suffolk and
Black's solution. This raises the ql, estion as to whether
the perturbations ascribed to planets/32 and B3 may not
in reality be harmonics produced by a highly elliptical
orbit for B1 as originally proposed by Van de Kamp.
It is significant that the "harmonic content" of the
wobble of Barnard's star is different in right ascension
and declination. This could not be the case for multiple
planets in coplanar circular orbits. The reduction in
residual errors in Suffolk and Black's solution as
compared with Van de Kamp's solutions is obtained
only if the orbit of BI is steeply inclined (_> 40 °) to the
orbits of B2 and B3.
Thus, it appears likely that Barnard's star has more
than one orbiting companion and that either the orbits
are not coplanar or at least one is highly elliptical. The
evidence for three bodies will not be conclusive until a
longer observation time shows that the periods of B1,
B2, and B3 are indeed incommensurate. A solution that
allowed ellipticity but required coplanarity would be
interesting to pursue.
Table 2-4 lists several other stars known to have dark
companions. For the first six the companion has from
1/10 to 1/35 the mass of the visible star. These we might
classify as binary stars in which the smaller companion
has too little mass to initiate thermonuclear reactions in
its core. (It is generally agreed that this requires about
0.05 solar masses.) The last examples, 61 Cyg A and
Proxima Centauri, are borderline cases where the star is
55 or more times as massive as the companion. (The Sun
is 1000 times as massive as Jupiter.) Like Barnard's star,
70 Ophiuchi appears to have more than one unseen
companion. We infer from these examples that a more or
less continuous spectrum of systems exists between
symmetrical binaries at one extreme and single stars with
a giant planet, or planets, at the other.
It will be noticed that with one exception all the stars
listed in Table 2-4 are K5 or smaller. The size of the
wobbling to be expected from planets orbiting stars of
one solar mass or larger is too small to be detected with
present instruments. That we find an unseen companion
of giant planetary size about nearly every star for which
we could hope to detect the perturbations argues that
most single stars have their retinue of planets.
ATMOSPHERIC
EVOLUTION
If all planets had simply condensed from the early
disk one would expect them to have essentially the same
composition as the Sun: less than 2 percent heavy
elements and the remainder hydrogen and helium. The
giant planets appear to have approximately this composi.
tion. The inner planets, on the other hand, are composed
almost entirely of heavy elements. (It is perhaps worth
noting that, without their hydrogen and helium atmospheres,
the outer planets would be comparable in size to
the inner planets. Jupiter would be about 4 times as
massive as Earth, Saturn about 2 times, Uranus 0.3
times, and Neptune 0.35 times.) Earth has almost no
helium and relatively little hydrogen, most of it in the
form of water. It is believed that the inner planets either
formed without hydrogen or helium atmospheres or else
lost these gases soon after formation.
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