Solar System Lecture Notes

Solar System Review

SOLAR SYSTEM - GENERAL

Solar System Inventory

The Sun

The sun is the dominant component of the solar system.  It contains 99.9% of the mass of the solar system.   The nuclear fusion reactions within the sun generate about 4 X 1026 watts of power.  This provides most, but not all, of the energy to heat the planets.  The gravitational field of the sun holds the planetary system together.  The sun is also the source of most of the thin gas which permeates the solar system.  This solar wind consists of electrons and ionized atoms which stream away from the upper atmosphere of the sun at several hundred kilometers per second.   Upon striking the planets the solar wind interacts with their atmospheres and magnetic fields.

    Visit the virtual sun at: http://www.michielb.nl/sun/kaft.htm

The Planets

The planetary system consists of the Earth, the five "naked eye" planets known to the ancients - Mercury, Venus, Mars, Saturn, Jupiter - and three discovered since the invention of the telescope - Uranus, Neptune, and Pluto.  Most of the mass of the planetary system resides in jupiter.  The planets all revolve around the sun in approximately the same plane - the plane of the ecliptic.  In addition, each planet rotates on an axis, and in most cases the direction of this rotation is the same as the direction of revolution.   This is usually interpreted as being closely connected with the process by which the solar system formed.

The planets are commonly grouped as follows: (1) the four inner planets are referred to as the terrestrial planets (the moon is often included in this group); (2) the five remaining planets are called the outer planets; but (3) Jupiter, Saturn, Uranus, and Neptune are known as the jovian planets (or giant planets); (4) Pluto is neither terrestrial nor jovian, being similar to the satellites of the jovian planets.  The terrestrial planets are primarily composed of rock and metal.  The jovian planets consist mainly of ices, liquids, and gases.

Other Solar System Members

Satellites and Rings

Each planet, except Mercury and Venus, has one or more satellites.

Planet

Satellites

Mercury

0

Venus

0

Earth

1

Mars

2

Jupiter

16

Saturn

19

Uranus

15

Neptune

8

Pluto

1

Of these moons, six are comparable in size to Earth's Moon or Pluto.  Each jovian planet has a ring system (Saturn/1610, Uranus/1977, Jupiter/1979, Neptune/1985).

Comets

Comets are large chunks of frozen gases, ice, and dust which revolve around the sun in highly elongated orbits.   Typically a few kilometers in diameter, comets become visible when heating by the sun causes atmospheres and tails millions of kilometers long to form.

Asteroids

Asteroids are rocky in composition, and are primarily located in the region between the orbits of Mars and Jupiter.

Other

A huge number of objects too small to be observed with even the most powerful telescope complete the inventory of the solar system.  These range from boulder size down to the tiniest grains of dust.   When one of these objects encounters the Earth's atmosphere friction causes it to be partially (meteorite being the object which survives to reach the Earth's surface), or completely (meteor), vaporized. 

    For extensive data and images of solar system objects check:
    http://pds.jpl.nasa.gov/planets/index.htm
or http://seds.lpl.arizona.edu/nineplanets/nineplanets/nineplanets.html
or http://www.hawastsoc.org/solar/eng/homepage.htm

Origin of the Solar System

Apart from intrinsic interest in each of the planets themselves, one goal of the study of the solar system is to understand the process(es) by which it was formed.  The entire solar system formed some 4.5 billion years ago, and as a result many of the planets share certain basic properties.   The study of our solar system, and others now in the process of forming about other stars, reveals that the planetary system probably formed from a hot rotating cloud of gases and dust - a solar nebula.  The nebula was composed largely of hydrogen and helium, with the sun forming from the inner part of the nebula and the planets and smaller bodies forming in the large disk surrounding the new star.

Discoveries of the Planets

The five "naked eye" planets have been known by most civilizations since antiquity.  The remaining three planets were each, insome sense, discovered.

Discovery of Uranus

Uranus was discovered by the English astronomer William Herschel in 1781 during a systematic survey of the constellation Gemini.  At first he thought it to be a comet, but subsequent observations showed it to be in a nearly circular orbit beyond that of Saturn.   Uranus can actually be seen with the unaided eye, but only under the best of conditions.  It had been plotted as a star on at least 20 different star charts prepared during the preceding 90 years, and this enabled astronomers to determine perturbations that were minutely altering Uranus' orbit.

Titius-Bode Law

The discovery of Uranus convinced the German astronomer Johann Bode of the correctness of a progression for the sizes of the planetary orbits suggested in 1766 by Daniel Titius.  The "Titius-Bode law" gives the approximate planetary orbit radii by adding 4 to the sequence of numbers 0, 3, 6, 12...., and then dividing the result by 10.

Planet

Calculated Dist.

Actual Dist.

Mercury

(0+4)/10=0.4 0.39

Venus

(3+4)/10=0.7 0.73

Earth

(6+4)/10=1.0 1.00

Mars

(12+4)/10=1.6 1.5

(Asteroids)

(24+4)/10=2.8  

Jupiter

(48+4)/10=5.2 5.2

Saturn

(96+4)/10=10.0 9.6

Uranus

(192+4)/10=19.6 19.2

Neptune

(384+4)/10=38.8 30.1

Pluto

(768+4)/10=77.2 39.5

Discovery of Neptune

The existence of Neptune was mathematically predicted.  Perturbations of the orbit of Uranus indicated the presence of an as yet undiscovered planet.  By 1844 discrepancies between calculated and observed positions of Uranus had accumulated to nearly 2", easily resolvable with a modest telescope.

Leverrier and Adams solved (independently) the gravitational problem assuming (based on the Titius-Bode law) the new planet to be about 39 AU from the sun.  Although this distance is incorrect, it turns out to have little bearing on the direction to the planet.  Although Cambridge astronomers under the direction of astronomer royal George Airy looked for the new planet, they had no up-to-date star charts for comparison, so their progress was slow.   Meanwhile, at the Berlin Observatory a young astronomer, Johann Galle, quickly found the predicted planet in September of 1846.

A scan of earlier records revealed that Neptune had been seen twice in 1795, but not identified as a planet.   These observations coupled with the new (1846) ones allowed calculation of an improved orbit and indicated that Neptune is only about 30 AU from the sun.  So long Titius-Bode!

Discovery of Pluto

While the search for the planet that would be named Pluto began as a result of reported perturbations of the orbits of Neptune and Uranus.  Percival Lowell based calculations mainly on Uranus, since the newly discovered Neptune had not moved sufficiently to allow meaningful conclusions to be drawn.  Lowell's calculations indicated a planet mass of about 6.6 Earth masses, and a most likely location in the constellation Gemini.  Lowell searched from 1906-1916 without success.  Others continued to search after Lowell's death, but progress was slow due to the fact that Gemini is near the Milky Way, and so each photographic plate had nearly 300,000 stars images.  Finally the development of the blink microscope resulted in Clyde Tombaugh finding Pluto in February 1930.  In fact, Lowell's calculations were incorrect, and subsequent determination of Pluto's mass showed it to be less than the Moon's.

pluto.jpg (45202 bytes)
Pluto's shift in position during 24 hour period (Hale 200-in.)

Note that Pioneer and Voyager craft show no drift that might be attributed to unidentified mass.  Also, IRAS full-sky infrared surveys show no additional planets.

Basic Ideas of Planetary Science

The study of the planetary system has progressed through three stages: (1) celestial mechanics (antiquity through Newtonian mechanics), (2) astronomy (physical and chemical properties of planets as revealed by telescopic observations), (3) direct exploration (adding to the above planetary geology, meteorology, and space physics).

Fundamental Characteristics of the Planets

The basic properties of a planet are its mass, chemical composition, and distance from the sun.  From these basics many other features can be predicted.  Determination of masses and distances are found by application of Kepler's laws and Newton's laws of motion and gravitation.

Rotation

All the planets are found to rotate.  This has been determined by three primary methods:

(1) Motion of permanent surface features.  In the case of Pluto and some jovian satellites periodic variation of brightness is used.

(2) Doppler radar.  Doppler shifting of the reflected radar waves from the approaching and receding limbs of the target cause the reflected signal to be broadened in proportion to the rotation rate.

radarrot.jpg (74113 bytes)

(3) Rotation rate of magnetic field.  For gaseous jovian planets radar waves are not reflected, and "surface" features only indicate the rate of motion of the upper atmosphere winds.  Planetary magnetic fields are (in the most reliable models) produced in, and coupled to, the planetary core.

Surface Temperature

Since most energy comes from sunlight, planetary temperatures depend primarily on the distance from the sun.  The effective temperature provides an estimate of the expected temperature, with no consideration given to complicating effects such as atmospheres, variations in reflectivity, and internal heat sources.  The effective temperature is a balance between incident sunlight and the re-emission of infrared radiation back into space.

Since the intensity of incident radiation depends inversely on the square of the distance from the sun, and the emission from a surface is proportional to the fourth power of the temperature (Stefan's law), the effective temperature varies with the inverse square root of the distance from the sun.

Teff ~ d-1/2

Planet

Distance

Reflectivity

Calc. Teff

Measured Teff

Mercury

0.39

0.1

420

440

Venus 0.72 0.7 300 250
Earth 1.00 0.5 260 280
Mars 1.52 0.2 210 230
Jupiter 5.2 0.5 115 125
Saturn 9.6 0.5 85 95
Uranus 19 0.5 60 60
Neptune 30 0.5 50 60
Pluto 40 0.4 40 ?

Note the importance of reflectivity, atmosphere/greenhouse effect (Earth, Venus), internal heat sources (jovian planets).

Age of Rocks

Prior to the 20th century estimates of the age of the Earth varied from a few thousand years to infinity.  With the discovery of radioactivity it became possible to measure the ages of rocks.  Most naturally occuring rocks contain several radioactive isotopes with suitable half-lives for determination of their solidification age.

Parent Isotope Daughter Isotope Decay Half-Life (109 yrs)

Samarium-147

Neodymium-143

Alpha

106

Rubidium-87 Strontium-87 Beta 48.8
Thorium-232 Lead-208 Alpha 14.0
Uranium-238 Lead-206 Alpha 4.47
Potassium-40 Argon-40 Beta 1.31
Radioactive Decay

Although a random process for any given nucleus, statistically one half of a large sample of nuclei will decay in a time interval of one half life.  There will then be equal numbers of parent and daughter nuclei.  At any given time the relative amounts of parent and daughter determine the elapsed time since the parent was produced.

radioact.jpg (52219 bytes)

Chemistry of the Planetary System

In the case of the planetary system the matter involved is primarily in solid and liquid form, as opposed to stars where individual atoms or fragments of atoms are in a gaseous state.  Thus the chemistry of molecules and minerals must be considered.  For this purpose five primary types of matter need be considered.

Five Types of Matter

Fluids

The jovian planets are primarily composed of hydrogen and helium, but at the pressures encountered in the interiors of these planets these gases are transformed into the liquid state.  Thus, most of the solar system (by weight) is fluid - either liquid or gas.

Plasmas

A plasma is a dilute hot gas composed of ionized atoms.  That is, negatively charged electrons and positively charged ions.  Unlike an ordinary gas, a plasma responds to electric and magnetic fields.  The solar wind is a plasma, as are the charged particles trapped in the magnetic fields of some planets.

Ice

The abundant (cosmically) elements hydrogen, oxygen, carbon, and nitrogen all form simple compounds that freeze at the temperatures found in the outer solar system: H2O, NH3, CH4, CO2, and CO.  These are the basic building blocks of comets and (possibly) cores of jovian planets.

Rock

Complex compounds of silicon, oxygen, magnesium, calcium, sulfur, carbon, iron, and other elements. These are the primary materials found in the inner planets and asteroids.

Metal

Since most metallic elements readily form compounds with oxygen, they are found in rocky material.  In some locations (the cores of planets) the metals separate from the rocky material.


For a specific planetary object we find various proportions of rock, metal, ice, and fluid, all immersed in an interplanetary plasma.

Oxidized and Reduced Environments

Most of the chemistry of the solar system is dominated by the two elements hydrogen and oxygen.  These elements are abundant and chemically quite reactive.  The chemical evolution of a planet will largely depend on the relative amounts of these two elements.

When there are less than two hydrogen atoms per oxygen atom in an envirnment, it is said to be an oxidized environment.  For example, on the Earth hydrogen is relatively rare since it easily escapes from the atmosphere (see below).  Most of the crustal rocks are compunds of oxygen, and there is free oxygen to spare in our atmosphere.  When hydrogen or hydrogen rich compunds are formed on Earth they are quickly broken down by chemical interaction with oxygen.  In such an environment pure metals are also unstable and become oxidized (e.g. rusting).  All of the terrestrial planets are to some degree oxidized environments.

A reduced environment results when there are two or more hydrogen atoms per oxygen atom.  Any available oxygen is combined with hydrogen to form water (H2O) and remaining hydrogen combines with other elements to produce compunds such as ammonia (NH3) and various hydrocarbons.  The giant planets are reduced environments with free hydrogen, and clouds of ammonia and methane (CH4).

Rocks and Minerals

Rocks are mixtures of compounds composed partially of silicon and oxygen.  Rocks (heterogeneous) are conglomerations of minerals (single compounds).  Typical minerals include silicates like quartz (SiO2), metallic oxides such as hematite (Fe2O3), sulfides like iron pyrite (FeS2), and carbonates including calcite (CaCO3).

Rocks are generally classified as to their history, rather than composition.

Igneous Rock

Formed by the cooling of molten material.  On Earth the primary examples of this type are basalt (ocean basin) and granite (continental).

lavaflow.jpg (91097 bytes)
Lava flow producing new basaltic rock

Sedimentary Rock

Formed by the deposition of fragments of igneous rock and/or organic material.  Common terrestrial examples are sandstones, shales, and limestones.

Metamorphic Rock

Produced by chemical and/or physical alteration of igneous or sedimentary type rocks at high temperatures and/or pressures.  On Earth this type occurs frequently due to ongoing geologic activity.

Primitive Rock

Original material from which the solar system formed.  Unaltered by heating.  No primitive rock is found on terrestrial planets due to heating above melting point of rock early in planet histories.   Comets, asteroids, meteorites.

Planetary Interiors

Study of planetary interiors is difficult, due to inaccessibility, and so probing must be indirect.  One simple approach is the determination of average planet densities.  These give a clue as to interior composition.  For example ices have densities near 1 gm/cm3, while rocks are much more dense at 2.5-3.5 gm/cm3, and metals are more dense yet at nearly 8 gm/cm3.  Thus knowledge of the overall density of a planet may give a clue as to the relative amounts of these three types of materials in the interior.

For example, the moon has a density of about 3.3 gm/cm3, in the range for rock.  Since the moon is too warm for ices to exist, it is safe to conclude that it is predominantly rocky material.   The Earth's higher density of 5.5 gm/cm3 indicates a mixture of rock and metal, in agreement with the theory of a significant metallic core of iron and nickle.   Pluto, on the other hand, has a density of about 2.1 gm/cm3, and so must include ices in addition to rock (and possibly metal).

If seismic waves can be detected, the interior of a planet can be probed in some detail.  The propagation of various types of seismic waves is dependent upon the internal structure of the body.   These seismic waves may be naturally occuring or artificially produced.  The structures of the Earth and moon have been probed in this way.  (See notes pertaining specifically to the Earth.)

When a planet becomes heated during formation, or subsequently due to radioactive heating, to the point where the various consitutent materials become molten (>1300 K for rocky planets, >273 K for icy ones), the materials will layer themselves according to density in a process known as differentiation.   As the planet later cools this layered structure is preserved.

different.JPG (23765 bytes)

Planetary Atmospheres

All of the large planets have atmospheres.  For Venus, the jovian planets, and Jupiter's moon Titan, the atmospheres are opaque so that the atmosphere is the only part of the object available for direct study.

Composition

The composition of many solar system atmospheres have been known for some time due to the analysis of the spectra of reflected sunlight.  These dark line spectra reveal information about composition, pressure, and temperature in the atmosphere in question.

Investigation of the infrared and ultraviolet portions of the spectra have revelaed the presence of new materials in these atmospheres.  Space probes have also gathered extensive information about planetary atmospheres, by direct and indirect analysis.

The specific gases present depend on the material present at the time the planet formed, the details of the chemical evolution of the planet and its geologic evolution (outgassing), and the planet mass.   Note also the dependence on interaction of the atmosphere with sunlight (ozone), presence of biological processes (respiration and aspiration), crustal materials, and comet impacts.  The atmosphere is continually in a state of dynamic equilibrium with a balance between outgassing and losses (escape to space and/or interactions which bind the gases in other forms).

Condensation Clouds

When the temperature in a region of an atmosphere drops to a certain point condensation clouds may form.  In these clouds materials which are normally gaseous condense into small liquid droplets or ice crystals.  The cloud-forming material is usually a minor component of the atmosphere.

Greenhouse Effect

Most planets with significant atmospheres will have some elevation of surface temperature due to the insulating effects of the atmosphere.  (Especially Earth and Venus.)  As sunlight diffuses through the atmosphere it is absorbed by the surface and heats it.  Since most planets have surface temperatures in the range of 100-500 K they strongly re-radiate in the infrared (Wien's law).  However, so-called greenhouse gases, CO2 being the primary example, are opaque to infrared radiation, preventing it from escaping into space.   Eventually an equilibrium is established, but at a higher temperature than would otherwise be expected.

grnhse.jpg (45320 bytes)

Note that without the greenhouse effect the Earth's surface temperature would be about 260 K, below the freezing point of water.  In all likelihood life would not have formed in such an environment.

Kinetic Theory Applied to Atmospheres

Gases consist of individual molecules which are traveling at high speeds and occasionally collide with each other.   In fact, the temperature of a gas (or any system) is simply a measure of the average kinetic energy of its molecules.  The kinetic theory of gases predicts

3/2 kBT = 1/2 mv2

vrms = (3kBT/m)½

An individual molecule may have a speed greater or less than this value.  The actual distribution of molecule speeds is the Boltzmann distribution.  If the rms speed of a particular type of gas molecule exceeds one-sixth of the escape speed of a particular planet, that gas will eventually completely escape from the planet.

vesc = (2GM/R)½

atmosesc.jpg (69932 bytes)

Atmospheric Structure

The gases which make up an atmosphere have weight.  Thus, the gas exerts a pressure which increases with depth of the gas.  At the Earth's surface the atmospheric pressure is about 100 metric tons per square meter.  This pressure decreases with altitude according to

P = Poe-h/H

where h is the altitude and H is known as the scale height, given by

H = kBT/mg

Note that atmospheres with low temperatures and/or heavy molecules will have small scale heights, and therefore be concentrated near the surface, and vice versa.  On Earth H = 8.