The Origin of the Solar System 51
Unfortunately, the Doppler method determines only one
component of the star’s velocity, so the orientation of the
orbital plane is not known in general. This means one can
obtain only a lower limit on the planet’s mass. For randomly
oriented orbits however, the true mass of the planet is most
likely to lie within 30% of its minimum value.
Some extrasolar planets have been detected when they
transit across the face of their star, typically causing the star
to dim by 1–2% for a few hours. Only a small fraction of
extrasolar planets generate a transit since their orbital plane
must be almost edge on as seen from the Earth. When a
planet is observed using both the Doppler and transit meth-
ods, its true mass can be obtained since the orientation of
the orbital plane is known. If the stellar radius is also known,
the degree of dimming yields the planet’s radius and hence
its density. The densities of extrasolar planets observed this
way are generally comparable to that of Jupiter and substan-
tially lower than that of Earth. This suggests these planets
are composed mainly of gas rather than rock or ice. In one
case, hydrogen has been detected escaping from an extraso-
lar planet. A few objects have been found whose minimum
masses are below 15 Earth masses, and it is plausible that
these are more akin to ice giants or even terrestrial planets
than gas giants.
Stars with known extrasolar planets tend to have high
metallicities; that is, they are enriched in elements heavier
than helium compared to most stars in the Sun’s neighbor-
hood (Fig. 21). (The Sun also has a high metallicity.) The
meaning of this correlation is hotly debated, but it is consis-
tent with the formation of giant planets via core accretion
(see Section 8). When a star has a high metallicity, its disk
will contain large amounts of the elements needed to form a
solid core, promoting rapid growth and increasing the likeli-
hood that a gas giant can form before the gas disk disperses.
Both the Doppler velocity and transit techniques are bi-
ased toward finding massive planets since these generate a
Stellar Metallicity (Sun = 1)Fraction of Stars with Planets
0.40 0.63 1.0 1.58 2.51305010152025FIGURE 21 The fraction of stars that have planets as a function
of the stellar metallicity (the abundance of elements heavier than
helium compared to the Sun). Here the iron-to-hydrogen ratio
relative to the Sun is used a proxy for metallicity.
stronger signal. Both are also biased toward detecting plan-
ets lying close to their star. In the case of transits, the proba-
bility of suitable orbital alignment declines with increasing
orbital distance, while for the Doppler velocity method, one
generally needs to observe a planet for at least a full orbital
period to obtain a firm detection. Despite these biases, it is
clear that at least 10% of Sun-like stars have planets, and
this fraction may be much higher. The fraction of planets
with a given mass increases as the planetary mass grows
smaller, despite the strong observational bias working in
the opposite direction. Roughly 10% of known extrasolar
planets have orbital periods of only a few days, which im-
plies their orbits are several times smaller than Mercury’s
orbit about the Sun. These planets are often referred to as
hot Jupiters due to their likely high temperatures. Theoret-
ical models of planet formation suggest it is unlikely that
planets will form this close to a star. Instead, it is thought
that these planets formed at larger distances and moved in-
ward due to type-I and/or type-II migration. Alternatively,
they may have been scattered onto highly eccentric orbits
following close encounters with other planets in the same
system. In this case, subsequent tidal interactions with the
star will circularize a planet’s orbit and cause the orbit to
shrink.
Roughly 20 stars are known to have two or more planets.
In a sizable fraction of these cases, the planets are involved
in orbital resonances where either the ratio of the orbital
periods or precession periods of two planets is close to the
ratio of two integers, such as 2:1. This state of affairs has
a low probability of occurring by chance, which suggests
these planets have been captured into a resonance when
the orbits of one or both planets migrated inwards.11. Summary and Future Prospects
Thanks to improvements in isotopic chronology, we now
know the timescales over which the Earth, Moon, Mars, and
some asteroids formed. Terrestrial-planet accretion started
soon after the solar system formed, leading to the growth
of some Mars-sized and smaller objects within the first few
million, and in some cases only a few hundred thousand,
years. This early accretionary phase was accompanied by
widespread melting due to heat generated by short-lived
isotopes and the formation of planetary cores. The Moon
formed relatively late, 30–55 Ma after the start of the solar
system, with the most likely date being 40–50 Ma. This was
the last major event in Earth’s formation. These isotopic
timescales are consistent with theoretical models that pre-
dict rapid runaway and oligarchic growth at early times, to
form asteroid-to-Mars-sized bodies within a million years,
while predicting that Earth took tens of millions of years to
grow to its final size.
The presence in Earth’s mantle of nonnegligible amounts
of siderophile elements such as platinum and osmium ar-
gues that roughly 1% of Earth’s mass arrived after its core