ASTR 1210 (O'Connell) Study Guide
11. PLANETARY SYSTEMS:
OURS AND OTHERS
Comparison of the planets, based on
Sizes are to scale, but separations are not.
The four large satellites of Jupiter discovered by Galileo in 1610
with his small telescope were the first new members of the Solar
System identified in recorded history. They instantly increased the
known membership of the Solar System from 8 to 12. Since that time,
astronomers have identified tens of thousands of Solar System bodies
(planets, satellites, and smaller rocky or icy objects) with telescopes
Most remarkably, after thousands of years of speculation about other
worlds like ours in the universe, we have recently discovered planets
in orbit around other
This lecture describes the general properties of our planetary system and
those around other stars and how we believe these originated.
A. Inventory of the Solar System
By terrestrial standards, the density of matter in the Solar System is
extremely low, and the planets are separated by enormous gaps.
Other than the Sun, no solar system object is self-luminous at
visible wavelengths, and all shine by reflected sunlight. Seen
from the Earth, the second and third-brightest celestial objects are
Earth's Moon and Venus.
Contents of the Solar System:
For a diagram of the current location of the planets,
- The Sun (99.8% of total mass)
- 8 "classical" planets (0.1% of the mass). Jupiter's mass
is greater than the masses of the other planets combined.
- Over 170 satellites of planets
- Tens of thousands of smaller rocky or icy bodies,
ranging in size down to a few hundred meters. The largest of these,
including Pluto, are now called "dwarf planets."
Most of these are
members of the asteroid belt between Mars and Jupiter or the
"Kuiper Belt" in the outer solar system, beyond Neptune. There
has been much recent controversy over what to call the larger
ones, but we will postpone discussion of this until Study Guide 20.
Objects smaller than dwarf planets but larger than about 50-m
diameter are called "asteroids" if they are composed
of rocky materials or "comets" if they are icy.
- Meteoroids (rocky or icy bodies smaller than
50-m), dust, gas
An oblique view of the planetary orbits drawn to
(though the planet sizes shown are not to scale).
B. Systematics of Planet Orbits
Systematic characteristics of the orbits of "classical" planets:
It is important to understand that none of the above is required by
- Orbits for all lie close to the plane of the
Earth's orbit (the ecliptic plane)
In the picture above, you can see the "cozy" inner solar system
(Mercury through Mars) separated from the vast outer solar system by
the asteroid belt.
edge-on plot of the orbits showing the near-coincidence of the orbital
planes, click here.
The orbits of the "dwarf planets," including Pluto, can be more highly
inclined to the ecliptic plane.
- The orbits, though technically ellipses, are nearly circular
- The direction of revolution of the planets in their orbits is the
same (counterclockwise from above Earth's N. pole); the direction of spin
on their rotation axis is the same for most.
- The orbits show systematic spacing (Bode's "Law"): the
separation between orbits increases with orbit size.
For example: Newton's laws imply the orbit of a given planet will be in a
fixed plane, but the orbits of other planets can be in different
planes; revolution directions do not have to be the same; orbits can
be highly elliptical rather than nearly circular; etc.
Instead, these systematics must be the product of special
physical conditions prevailing during formation of the planets. That is,
they provide clues to the process that forms planets.
C. Segregation of Physical Properties
The four "inner" or "terrestrial" planets (Mercury, Venus,
Earth Mars) show a striking dissimilarity from the four large
"outer" or "Jovian" planets (Jupiter, Saturn, Uranus, Neptune):
|Size & Mass**
**See the image at the top of this page for a graphic comparison
of planet sizes.
These differences constitute another major clue about the
processes that formed the planetary system.
Note: we are deliberately omitting Pluto here, since it is not
representative of the "classical" planets.
D. Origin of the Solar System
Since the time of Galileo, there have been many models for the origin
of the solar system. They all fall into two main categories:
- "Catastrophic/tidal theory": a passing star pulls material from Sun, which cools
to form planets
This would imply planets are rare, since close encounters
between stars are extremely rare.
The process is also physically unlikely: expelled (hot) material would
diffuse quickly before it was able to condense.
- "Nebular theory": planets form from the cloud ("nebula")
of cool debris surrounding a forming star.
This would imply planets are common because they are byproducts
of normal star formation.
There is now excellent supporting evidence for the nebular theory,
not least of which is item "G" below
E. The Interstellar Medium and Star Formation
We know that stars are forming
continuously out of the "interstellar medium"
at a rate of about 1 solar mass/year throughout our Galaxy:
Dust plays the essential role of a refrigerant for interstellar
gas. Parts of the ISM, if well shielded by dust grains against
heating by surrounding stars, can become very dense and cold (only
about 10o K above absolute zero temperature). These are
the regions which are primed to turn into nurseries for newly born
stars. A beautiful example of a likely stellar nursery is shown in
the picture below:
- The interstellar medium (ISM) is the dilute matter between stars.
It constitutes a few % of the mass of our Galaxy
Gas (atoms, molecules)
Composition: hydrogen 71%; helium 27%; all other elements (C,N,O,Fe,
etc) only 2%. When hot, or "ionized," this gas is visible as
"gaseous nebulae" (producing optical spectra containing, among other
features, bright emission lines of hydrogen, as discussed
in the Supplements). Where the gas
is cold, and in atomic or molecular form, we can detect it using
Very small solid particles
or "dust grains". These are
smoke-like. They absorb and redden light passing through them.
Absorption by concentrations of dust creates
"dark clouds" seen
against bright background sources such as the Milky Way.
| This is the "Eagle Nebula" imaged by the Hubble Space
Telescope. The extended, dark, sculpted "elephant trunk" running
across the image is a cold, dusty region. It is surrounded by hot gas
(greenish-blue), which is evaporating the cold material away. The
small globules on the end of the finger-like protuberances are the
densest regions of the cloud, possibly containing protostars with
masses like the Sun. Click on the image for a full view. For more
pictures and information, click here.
here is an MPEG video of a zoom into
the Eagle Nebula.
For Hubble Space Telescope images of another spectacular star-forming
region in the Carina
F. Planet Formation in the Nebular Theory
- A dense, cold cloud in the ISM collapses under gravity:
- As it collapses, it spins up & flattens because of the conservation of
angular momentum (first illustrated by Kepler's Second Law).
A rotating, flattened "protoplanetary" disk is a natural
consequence of the collapse of the interstellar cloud and is expected
to accompany star formation in all enviroments. In the case of our
solar system the disk is called the "solar nebula."
Note! The scale of this picture is much smaller, by
several 1000x, than the scale of the previous picture.
- The dense concentration of material in the center of the disk is
the "protostar" ("protosun" in the illustration here).
The protostar heats up, first from energy released by
gravitational collapse, and later, once its core reaches a critical
density and pressure, by nuclear reactions.
- The protostar heats the inner protoplanetary disk to
a higher temperature than the outer disk.
Here is a typical
temperature profile for the disk.
- The heating determines the kinds
of solids which
can survive in a given part of the disk and generates
the segregation of planetary properties:
Only "refractory" (high melting point) solids survive in
the inner disk. These tend to be heavy, rocky materials. Only
a small fraction of the total inner disk is in this form since
heavy elements are not abundant.
"Volatile" materials are those with low melting points.
They include the ices of water, methane, and ammonia (H2O,
CH4, NH3). These will be vaporized in
the inner disk.
On the other hand, these ices can persist in solid form in the
cool outer disk. These are hydrogen-rich compounds, and ecause
H is abundant, there is a large amount of such icy material in
the outer disk.
The innermost radius in the disk where icy materials can remain solid
is called the "frost line".
Solids in the outer nebula are more similar in chemical
composition to the Sun than are inner nebula solids
- Larger bodies grow from the solids, not from gas, through
collisions and sticking together (or "accretion").
Accretion produces solid bodies with a range of sizes in the sequence
grains ==> "planetesimals" ==> "protoplanets," where
the distinction in size between the two latter classes is not firmly
defined. A protoplanet is an object over about 500 km in diameter.
For larger protoplanets (about 15x the mass of the Earth),
gravitational fields begin to attract gas from the nebula.
In the inner disk, small, rocky proto-planets form.
In the outer disk, beyond the frost line, large, "gas-giant"
Computer simulation of protoplanetary disk
- Final assembly: the violent infall of fragments heats
the protoplanets. Collisions
between protoplanets and large fragments can have drastic effects,
producing extensive melting/resurfacing in a merged protoplanet or
even shattering the originals into smaller pieces.
- The elapsed time for proto-planet formation is short by
cosmic standards: probably a few million years (though under the right
conditions it could occur much
- The interiors of proto-planets that are large enough are heated
and partially melted by the violent accretion and by the
decay of short-lived radioactive isotopes. The melted interiors will
differentiate, with heavy metallic materials settling
to the center and lighter, rocky materials rising to the exterior.
- Gravitational interactions between planets, or between planets and
the residual protoplanetary disk (as in the image above), can
drastically change the orbits of the new planets, moving large
planets inward, tossing small bodies outward, or pushing planets into
more strongly elliptical orbits.
- Here is a pictorial
summary of the nebular model.
The nebular model successfully explains the systematics in the orbital
geometry, motions, and compositions listed in Sections B and C
Strong support for the nebular theory has emerged. We now
have direct detections of protoplanetary disks around nearby
Hubble Space Telescope,
infrared telescopes, and
millimeter-wave array, operated by the National Radio Astronomy
Observatory here in Charlottesville. A high priority goal for the
infrared James Webb Space
Telescope, to be launched in 2018, is to probe in detail the
physics of star and planet formation. An HST image of a young planetary
disk is shown at the right (this star is in a stage where it is
producing a gas jet perpendicular to the disk). Yet stronger
evidence, based on the expectation in the nebular theory that planets
will be common, is found in the next section.
Speculation about planets around other stars extends as far back in
history as the ancient Greeks. The philosophical implications of
discovering other planetary systems for the context in which we should
view the Earth and the human race have been widely discussed. But
for hundreds of years, despite much effort, no planetary companions
to other stars were found.
Finally, extra-solar planets around other Sun-like stars were
detected in October 1995. ("Extra-solar" means planetary systems
other than that around the Sun, now usually abbreveviated simply
to "exoplanets".) We have not only detected exoplanets, but
we have established that they are relatively common around Sun-like
stars in the Galaxy. And, using special techniques and highly
sensitive detectors, we have begun to probe the composition and
structure---even the meteorology---of some exoplanets.
The initial detections of exoplanets were technically very
difficult (or they would have been found sooner!).
We cannot simply take a picture and see the planet. The
images of the star and planet are blended together in an
ordinary telescope (see the discussion of telescope resolution
in Study Guide 14), and the feeble
reflected light of the planet is
completely overwhelmed by the bright star.
Instead, several sophisticated methods have been been developed for
article). We discuss below only the two most widely used of
those. The "Doppler method" is particularly important because it is
the primary means by which we can obtain estimates of an exoplanet's
Both of these techniques are biased in the sense they are much
more sensitive to larger planets at small distances (say
less than 1 AU) from a star.
Doppler Velocity Method
- The Doppler method for finding exoplanets is based on
detecting the tiny changes in the star's
motion induced by the gravity of an orbiting planet.
These amount to only a few times 10 meters/sec.
Recall that in Newtonian gravity, a planet exerts the same force on
its parent star as the star exerts on the planet. The star therefore
accelerates in response, though the acceleration is very
small because it is in inverse proportion to its mass. The animation
at right shows how their mutual gravity causes both the star
and its planet to move around a common "center of gravity." (The
stellar motion in the animation is greatly exaggerated compared to the
motion induced by normal planets.)
The motions can be detected by the Doppler effect on the
spectrum of the star (see
spectrographs, with high sensitivity and stability, are
- Shown at the right is the Doppler-derived velocity curve (velocity
plotted against time) for the
parent star of the first identified extra-solar planet around a
Sun-like star. Click for an enlargement. The amplitude of the
velocity change is +/-50 m/s, but the precision of the data is better
than 10 meters/sec--- a velocity that can be achieved by a fast
sprinter. So we can now detect stars moving at human
- The shape of the velocity curve allows us to determine the
planet's orbital shape. A markedly elliptical orbit
will produce an asymmetrical curve.
- By applying Kepler's Third Law (see Study
Guide 8) to the observed orbital period and velocity amplitude,
this method provides an estimate for the mimimum mass of the
planet. (It is a minimum because we usually do not know the
inclination of the plane of the planet's orbit to the line of sight; a
tilt of this plane will reduce the observed radial velocities.)
After a number of planets were detected by the Doppler technique,
astronomers realized that they could also find them by searching
for planetary transits, that is, the very tiny change in light
from a star when a planet crosses its disk seen from our point of view
(a partial eclipse). In principle, astronomers could have
detected these with many of the electronic devices available since the
1950's---but they had never configured their observing techniques to
look for effects this small.
For a diagram showing the viewing configuration for a
transit, click here.
The picture at the right shows a typical "light-curve" for a planetary
transit --- i.e. the observed brightness plotted against time. Note
that the amplitude of the eclipse is only 1.5% of the star's normal
This method can catch only the small fraction of planets whose orbital
planes have the right orientation such that eclipses occur from the
Earth's point of view. However, with stable and sensitive digital
cameras, it has proven possible to detect many transiting planets even
with modest-sized telescopes. Many groups around the world, including
amateur astronomers, are now surveying the sky for planet transits.
Normally, a transiting detection is not counted as a confirmed planet
until a corresponding Doppler detection is made. However, in the case
of systems with multiple transiting planets, the various phenomena
that can lead to false positives can be confidently ignored,
and the transiting objects are regarded as validated.
Aside from identifying new planets, the transit method is invaluable
because, by determining the fraction of the parent star's surface that
is occulted, it provides an estimate of the radius of the
exoplanet. (We know the sizes of stars based on our understanding of
their internal and atmospheric physics.) It also allows precision
timing of exoplanet motions in their orbits and changes in those.
The Kepler Mission
Kepler is a small space telescope carrying a huge electronic
camera (42 CCD detectors) which steadily surveyed a large patch of sky
in the Milky way between Lyra and Cygnus searching for planetary
transits in the tens of thousands of stars observable in the
field. Planetary systems identified here are very distant
(typically over a thousand light years away), but the strength of the
mission is that it can find a large number of potential planets. The
Kepler survey field is shown at the right.
Kepler was launched in 2009 and has identified thousands of
planetary "candidates" --- but most of these must be confirmed by
the Doppler velocity method before they are accepted as planet
detections. By January 2015, Kepler had found
4175 candidate planets, 1004 of which had been confirmed.
By design, Kepler is able to detect the very tiny changes in starlight
(0.01%) caused by eclipses by Earth-sized planets. It has
identified scores of candidates with sizes less than 3 Earth radii.
In May 2013, Kepler lost a key component of its attitude-control
system and its ability for precision pointing, regretfully just as it
was exploring the Earth-like planetary regime around Sun-like stars in
both size and orbital period. However, some clever engineering
innovations to stabilize the spacecraft make it possible to continue
the mission while observing fields other than the original one. It
may still be possible to detect Earth-sized planets around types of
stars significantly smaller than the Sun ("red dwarf" stars).
As of March 2017 we had found over 3500 confirmed planets in 2600 planetary
systems. 600 of these are multiple planet systems. Over 2700 are
For a complete list, see the
Extra Solar Planets Encyclopaedia.
Hot Jupiters: "Hot" Jupiters are gas giant planets (~ Jupiter
mass or larger) in very small orbits---less than 0.4 AU,
the radius of the orbit of Mercury. The tightest orbits are
less than 0.01 AU in radius. Hot Jupiter atmospheres are heated
to high temperatures by their parent star; many are puffed-up
or losing material. Under some circumstances, the atmospheres
may evaporate altogether.
This was the first class of exoplanets to be discovered around
Sun-like stars because they produce large Doppler signals. However,
they were a great surprise because in our solar system the
large planets are all at distances greater than 5 AU, and it is
thought (see above) that they cannot form at small distances
from their parent star. Probably, these planets form at large
distances but, because of gravitational interactions with the
protoplanetary disk, they migrate over time nearer the
Because early planet searchers thought massive planets
would always be distant from their parent stars, with long orbital
periods, most did not look for short-period oscillations of the stars
(until after the first detection).
[Note: objects with masses larger than 13 x Jupiter's are considered
"brown dwarf" stars, not planets.]
Super-Earths: These are exoplanets with masses significantly
larger than Earth's but smaller than 10 Earth masses. They are
smaller than Uranus or Neptune. Scores of these have been
detected so far. The exoplanet system Kepler-62 has four
Super-Earths. Some Super-Earths have masses and radii that suggest
they are made of rocky materials, like Earth, or of ice/water. A
number are in or near their
star's habitable zone, where
surface temperatures allow the presence of liquid water. These would
be excellent candidates for Earth-like biospheres, but we have
no evidence to date that such exist.
A number of Earth-sized
candidates have been found by the Kepler mission. In April
2014, Kepler announced the confirmation of Kepler-186f, the first
Earth-sized planet in its star's habitable zone. K186f is 11%
larger than Earth and orbits a so-called "M dwarf" star about 500
light years away with a period of 130 days. Because its star is
fainter than the Sun, the small (0.4 AU) orbit of K186f places it
within the habitable zone.
Another tantalizing Earth-mass exoplanet in the habitable zone
Centauri b, which was detected by the Doppler method in orbit
around a small, red dwarf star. In this case, however, it happens to
be the star nearest to the Sun (only 4 light years away), so
the planet instantly became a target for extensive exploration.
(Proxima Centauri is part of the triple-star system Alpha
The champion system for Earth-like planets was announced in February
2017, using transit data from the Spitzer Space Telescope and
terrestrial telescopes. It is
very small, cool star, 36 light years away, which hosts a total
of seven Earthlike planets in or near the habitable zone. The
orbital periods range from 1.5 to 20 days. (Because the star is so
cool, the habitable zone lies much closer to it than in the case of
the Sun.) Spectroscopic searches for evidence of water in the
atmospheres of the planets are already underway.
How Many Planets in the Galaxy?
Based on the excellent statistics from Kepler, astronomers estimate
there are 100-400 billion planets in our Galaxy, though again most of
these are not Earth-like nor in a terrestrial habitable zone. There
are probably at least as many planets in the Galaxy as there are
Think about that the next time you look at the sky on a clear
night or a deep image of a
Milky Way star field.
The discovery of exoplanets inspired an explosion of artists'
impressions of exoplanet systems and surfaces. Some nice ones are
shown in the composite below. Bear in mind that no telescope is
powerful enough to produce images like this, so they are all entirely
speculative. Almost all contain some unphysical features (like
showing the shape of other planets in the parent system).
Reading for this lecture:
Alert! Most lectures from now on will cover more material in the text
than has been the case up to now. Try to keep up with the reading.
Study Guide 11
Bennett textbook: Chapter 7 except pp. 202-212; Chapter 8; "Summary of Key Concepts" for Chapter 13.
Reading for next lecture:
Bennett textbook: Secs. 8.5, 9.1, 9.6
Study Guide 12
June 2017 by rwo
Drawings of stages in the nebular theory from ASTR 161,
University of Tennessee. Computer simulation of protoplanetary disk
by G. Bryden. Velocity curve of 51 Peg from G. Marcy & P. Butler.
Text copyright © 1998-2017 Robert W. O'Connell. All rights
reserved. These notes are intended for the private, noncommercial use
of students enrolled in Astronomy 1210 at the University of