ASTR 1210 (O'Connell) Study Guide

Comparison of the planets, based on NASA images.
Sizes are to scale, but separations are not.

A. Inventory of the Solar System

• 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.

• Tens of thousands of smaller rocky or icy "minor" planets, 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.

• Over 170 satellites

• Comets (small, icy bodies; perhaps a trillion of these)

• Meteoroids (small, rocky bodies), dust, gas

An oblique view of the planetary orbits drawn to scale
(though the planet sizes shown are not to scale).

B. Systematics of Planet Orbits

• Orbits for all (except Pluto) 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.
  For an edge-on plot of the orbits showing the near-coincidence of the orbital planes, click here.

• 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.

C. Segregation of Physical Properties

**See the image at the top of this page for a graphic comparison of planet sizes.

Note: we are deliberately ignoring Pluto here. It is not representative of the "classical" planets. Instead it is a member of a huge group of small, rocky/icy bodies that reside the outer solar system. See Study Guide 20.

D. Origin of the Solar System

• "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
  Also physically unlikely: expelled material would diffuse, not condense

• "Nebular theory": planets are byproducts of normal star formation
  Planets form from the cloud ("nebula") of debris surrounding a forming star
  Would imply planets are common
  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

• The interstellar medium (ISM) is the dilute matter between stars. It constitutes a few % of the mass of our Galaxy

• Contents:
  Gas (atoms, molecules)
  Composed of: hydrogen 71%; helium 27%; all other elements (C,N,O,Fe, etc) only 2%. When hot, this gas is visible as "gaseous nebulae" (producing spectra containing, among other features, bright emission lines of hydrogen, as discussed in the Supplements).

  "Dust"
  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 sources such as the Milky Way.

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 Nebula, click here.

F. Planet Formation in the Nebular Theory

1. A dense, cold cloud in the ISM collapses under gravity:

   
   

2. 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 star formation. 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.

3. The dense concentration of material in the center of the disk is the "protosun."
   The protosun begins to heat up, first from energy released by gravitational collapse, later by nuclear reactions

4. The protosun heats the inner protoplanetary disk to a higher temperature than the outer disk.

5. 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 exist in solid form in the cool outer disk. These are hydrogen-rich compounds. Because 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

6. 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" proto-planets form.

   
   

   
   Computer simulation of protoplanetary disk

7. Final assembly: violent infall of fragments, which heats the protoplanets. Collisions between protoplanets and large fragments can have drastic effects, producing extensive melting/resurfacing or even shattering them.

8. Elapsed time is short by cosmic standards: probably a few million years (though is possible could occur much faster).

9. Interiors of proto-planets that are large enough are heated amd partially melted by the energy dissipated by accretion and by the decay of short-lived radioactive isotopes. The interiors differentiate, with heavy metallic materials settling to the center and lighter, rocky materials rising to exterior.

10. 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.

Detection Methods

Doppler 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, though 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 planets.)
  The motions can be detected by the Doppler effect on the spectrum of the star (see the Supplements), although special spectrographs, with high sensitivity and stability, are required.

  
• Shown at the right is the Doppler-derived velocity curve 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 speeds!

• The shape of the velocity curve allows us to determine the planet's orbital shape.

• By applying Kepler's Third Law (see Study Guide 8), 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.)

Transit Method
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 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. Note that the amplitude of the eclipse is only 1.5% of the star's normal brightness.
This method can catch only the small fraction of planets whose orbital plane has 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.
The transit method is important because, by determining the fraction of the parent star's surface that is occulted, it provides an estimate of the radius of the exoplanet.

Exoplanet Count

As of February 2013 we have found 861 planets in 677 planetary systems. 128 of these are multiple planet systems. Over 250 are transiting planets. For a complete list, see the Extra Solar Planets Encyclopaedia.

Properties

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. Their 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 great than 5 AU, and it is thought (see above) that they cannot form at small distances from the Sun. Probably, these planets form at large distances but, because of interactions with the protoplanetary disk, they migrate over time nearer the star.
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 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. About a dozen of these have been detected so far. Some have masses and radii that suggest they are made of rocky materials, like Earth, or of ice/water. Some Super Earths are in or near their star's habitable zone.
Earth-Like Planets? Only one Earth-mass exoplanet has been tentatively identified yet. It is a member of the nearest star-system to the Sun, Alpha Centauri (a triple star). It is too close to its parent star to be able to host Earth-like life. A number of Earth-sized candidates have been found by the Kepler mission, but none of these are confirmed yet; see next section.

The Kepler Mission

Kepler is a small space telescope carrying a huge electronic camera (42 CCD detectors) which steadily surveys 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 here will be 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 so far it has detected over 2700 planetary candidates---but each of these must be confirmed by the Doppler radial velocity method before they are accepted as planet detections (over 100 to date).
By design, Kepler is able to detect the very tiny eclipses (0.01%) caused by Earth-sized planets. It has identified several dozen candidates of near-Earth size, but none of these have yet been confirmed to have Earth-like masses; only four are in the habitable zone of their parent star.
COROT is another space mission with goals similar to Kepler's.

How Many Planets in the Galaxy?

Based on the excellent statistics from Kepler, astronomers estimate there are 50-150 billion planets in our Galaxy, though again most of these are not Earth-like nor in a habitable zone. There are probably at least as many planets in the Galaxy as there are stars.

Artist's concept of an evaporating "Hot Jupiter"
in orbit around nearby star 51 Pegasi

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.

Bennett textbook: Secs. 8.5, 9.1, 9.6
Study Guide 12

More information on systematics of the Solar System (SEDS)
Java Simulations of Solar System Orbits (UMd)
Multimedia Tour of the Solar System
Best color images of interstellar gas and dust nebulae (Anglo-Australian Observatory, David Malin)
Tutorial on ExtraSolar Planets (ASU)
University of California Extra Solar Planets Search Page
Extra Solar Planets Encyclopaedia
NASA Exoplanet Archive
Techniques for Detection of Extra Solar Planets
Detection of Extra Solar Planets by Transit Photometry (STARE Project)
Extra Solar Visions (artwork by John Whatmough)
Java Simulations of Orbits for Selected Extra Solar Planets (UMd)
MEarth Project (an automated transiting planet survey observatory)
The Kepler Mission (NASA)

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Last modified March 2013 by rwo

Drawings of stages in the nebular theory from ASTR 161, University of Tennessee. Computer simulation of protoplanetary disk by G. Bryden. Artwork of extra-solar planet from Extra Solar Visions, copyright © 1996 John Whatmough. Velocity curve of 51 Peg from G. Marcy & P. Butler. Text copyright © 1998-2013 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 Virginia.