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The Solar System
Overview
A survey of overall properties
Age of solar system:
- from radio-dating of Earth rocks, Moon rocks and meteorites that contain radioactive elements
- age = 4.5109 years (4.5 Giga-years (Gyr))
Planetary orbits:
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all planets have orbits with following properties:
- nearly circular (eccentricity, e < 0.1)
- orbit counter-clockwise (CCW) around Sun
- lie in almost same plane (inclination, i, with respect to ecliptic  0o)
- exception: Pluto: i = 17o
almost all planets rotate with following properties:
- rotational equators lie in plane of orbits
 rotation axes almost perpendicular to plane of orbits
- rotate in same direction as revolution, ccw (“top-spin”)
 properties suggest that planetary orbits part of a rotating disk
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Inner solar system:
- four planets closest to Sun
- in order of increasing distance from Sun: Mercury, Venus, Earth, Mars
- orbits relatively closely spaced; radius of Mars’ orbit is 1.5 AU (Astronomical
Units – see notes, Set 1)
Outer solar system:
- five planets furthest from Sun
- in order of increasing distance from Sun: Jupiter, Saturn, Uranus, Neptune,
Pluto
- orbits relatively widely spaced; radius of Neptune’ orbit is 30 AU
Two classes of planet: Terrestrial and Jovian
I Terrestrial planets: Mercury, Venus, Earth, Mars
- Earth-like planets (“Terra”: Latin for Earth)
- found in inner solar system
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solid surface
interior composed of solid and molten rock and metal
relatively small radius (R) and mass (M)
relatively large average density,  (kg/m3)
 ρ = M/Volume
Volume of a sphere = 4πR3/3
 density,  = 3M/4πR3  relatively large ratio of M to R
relatively few moons, no rings
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II Jovian planets (gas giants): Jupiter, Saturn, Uranus, Neptune
Jupiter-like planets (“Jove”: Latin name of Roman God, Jupiter)
found in outer solar system
apparent surface NOT solid
interior composed mostly of Hydrogen (H) and Helium (He) fluid (gas and liquid)
 “gas giant” planets
relatively large radius (R) and mass (M)
relatively small average density, 
 ρ = M/V = 3M/4πR3  relatively small ratio of M to R
many moons, rings
NOTE: Pluto is a special case; neither Terrestrial nor Jovian
Moon: a natural object that orbits directly around a planet
- large moons: seven moons are larger than Pluto or Mercury: Earth’s Moon, 4 moons
of Jupiter, 1 moon of Saturn, and 1 moon of Neptune
- small moons: most moons are asteroid sized: 2 moons of Mars, many dozens of the
Jovian planets
Atmospheres of planets (and large moons!):
-
planetary atmosphere: layer of gas surrounding a planet (or moon)
may contain atoms and molecules (eg. carbon dioxide (CO), methane (CH4))
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Motivating question: why do some bodies have atmospheres while other bodies do
not?
- eg. Mercury and Saturn’s Moon Titan are approximately the same size, but
Mercury does not have an atmosphere while Titan does – why?
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a planet (or moon) can ONLY retain an atmosphere IF its gravity can prevent
surrounding particles (atoms and molecules) from escaping
- recall from Newton’s Laws of Motion and Law of Gravity:
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- if v >> a  particle escapes on hyperbolic trajectory
(where: a is acceleration toward center of planet due to force of gravity, v is
velocity perpendicular to a)
 vesc = (2GM/R)1/2
where: vesc = escape velocity (velocity needed to escape planet’s gravity) in
m/s
M = mass of planet (or moon) in kg
R = distance from particle to center of planet (> radius of planet) in m
G = Newton’s gravitational constant (6.6710-11 N m2 / kg)
 makes sense: vesc is larger for larger M, and smaller for larger R
- let vave = average velocity of particles in planet’s atmosphere
 if vave < 1/6 × vesc  particles trapped by planet’s gravity  planet retains
atmosphere
 if vave ≥ vesc  particles escape from planet’s gravity  planet cannot
retain atmosphere
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kinetic theory: atoms and molecules are always in motion
average velocity, vave, depends on heat content  depends on temperature, T
 vave = (3kT/m)1/2
where: vave = average velocity of particle (atom or molecule) in m/s
T = temperature of gas in K
m = mass of particle in kg
k = Boltzmann’s constant = 1.3810-23 J / K
 higher T  larger vave
 particles moves more quickly in a hotter gas
 larger m  smaller vave
 in a given gas, heavy particles (large molecules) move more slowly than
lighter particles (small atoms)
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 to determine if a particular planet or moon retains an atmosphere of a
particular type of particle:
- atmosphere retained if for any particles vave < 1/6  vesc
 if (3kT/m)1/2 < 1/6  (2GM/R)1/2
where: T = temperature of gas in K
m = mass of particle (atom or molecule) in kg
k = Boltzmann’s constant
M = mass of planet (or moon) in kg
R = distance from particle to center of planet in m
≈ radius of planet
G = Newton’s gravitational constant
 to retain an atmosphere:
- need large M and/or small R  high density (=3M/4R3)
- need low T  further from Sun
- need large m  heavier particles (CO2, CH4) more easily retained than light
particles (H, He)
Significance: where in solar system are bodies with atmospheres found?
1) Planets of outer solar system
- large M; far from Sun  low T
 Jovian planets have thick atmospheres, contain light atoms (H, He) as well as
heavier molecules
2) Largest moons of outer system
- far from Sun  low T
- small  low R  moderate 
 larger Jovian moons have moderate atmospheres, eg. Titan
3) Some planets of inner solar system
- closer to Sun  higher T
- small and moderate mass  low R and moderate M  high 
 some inner planets have moderate atmospheres, contain heavier molecules
only, eg. Earth, Venus
Interior composition of solid bodies:
- solid bodies: inner solar system planets, and all moons
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inner solar system: solid or molten rock and metal only
- rock and metal are refractory materials
 high melting temperature, high vaporization temperature (> 1000 K)
 can remain solid at high T closer to Sun and at low T far from Sun
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outer solar system: even mixture of ices and rock and metal
- ices are volatile materials
 low melting temperature, low vaporization temperature (< 200 K)
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 cannot remain solid at high T closer to Sun, can ONLY survive at low T far
from Sun
- ices: many light molecules form ices when they freeze (eg. ices of H2O, CO2
(“dry ice”), CH4 (methane), NH3 (ammonia) …)
NOTE: the inner solar system planets Earth and Mars have a small amount of
volatile material on surface because atmosphere protects surface from Sun’s radiation
Minor bodies (debris): asteroids, meteoroids, comets
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orbit the Sun directly (like planets)
Asteroids (minor planets) and Meteoroids:
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found in inner solar system
asteroids: largest (Ceres): D = 900 km  larger than many minor moons
- most have D < 10 km
- most found in asteroid belt
 region of concentrated asteroid population between 2.5 and 3 AU from Sun
 between orbits of Mars and Jupiter
meteoroids: smaller than asteroids; D < 1 m, as small as pebble size
 size in ONLY distinction from asteroids
composition: solid refractory materials; ie. rock and metal
Comets:
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found in outer solar system
asteroid sized or smaller
composition: mixture of volatile and refractory materials
 mixture of ices and rock and metal
most found in outer solar system, beyond orbit of Neptune, in Kuiper belt
apparition: a few comets are on highly elliptical orbits that cross into inner solar
system
 high T vaporizes volatile materials  produces tail visible on Earth
NOTE: composition reflects composition of other solid bodies (moons and terrestrial
planets)
 inner solar system minor bodies (asteroids & meteoroids) composed only of
refractory materials
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 outer solar system minor bodies (comets) composed of a mixture of volatile and
refractory materials
The origin of the solar system – the Solar nebula theory
Nebula: large cloud in interstellar space composed of gas and dust
- the interstellar medium is observed to contain many such nebulae
Solar nebula:
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interstellar cloud composed of gas and dust
- gas: independently moving atoms and molecules
- dust (solid aerosol): microscopic particles of solid material, ie. grains
- a dust grain is composed of ~106 atoms
mass, M ~106 MSun  much larger than mass of present solar system
radius, R ~several light-years (LY)  much larger than size of present solar system
cloud slowly rotating  has a rotation axis
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chemical composition by number of atoms same as composition of overall Universe:
- 92% Hydrogen (H) – the lightest element
- 7.8% Helium (He) – the next lightest element
- 0.2% Everything else!
 ie. elements needed for making solids, and organic material (Carbon (C),
Nitrogen (N), Oxygen (O), etc. are VERY RARE!
- C, N, and O are more common that other elements heavier than He
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collapse:
solar nebula collapsed due to force of gravity (ie. collapsed under its own weight)
 during collapse: R decreases, but M remains constant
 density, ρ, increases  nebula is compressed
Formation of Sun:
-
central region of cloud collapsed into dense sphere
 formed proto-Sun (object that became the Sun)
Kelvin-Helmholtz contraction: as gas collapsed gravitational energy converted to
kinetic energy of particles (atoms, molecules, and dust grains)
 vave of particles increases
 collapsing central sphere heated up (T increased)
107 years after collpase started: central T in proto-Sun = 106 K
 ignition of nuclear Hydrogen (H) fusion reactions at center of proto-Sun
 proto-Sun begins to shine due to generation of nuclear energy
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 proto-Sun became Sun (a star)
total time for Sun to fully form: 108 years
Formation of planetary disk:
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as cloud collapsed  rotation rate increased
 due to conservation of angular momentum – the same priniple that causes a
figure skater to spin more rapidly when they pull their arms and legs in
cloud collapsed preferentially parallel to rotation axis
 due to centrifugal force – the force that causes a revolving object to be flung off
at a tangent if the oppositely directed centripetal force suddenly goes to zero
 cloud collapsed into disk (only central region formed spherical proto-Sun)
 formed proto-planetary disk (object that became planetary system)
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Proto-planetary disk:
rotating disk composed of gas and dust centered on proto-Sun
planets and moons formed in disk
radiation and outflowing gas from proto-Sun pushes lightest atoms (Hydrogen (H)
and Helium (He)) out of inner part of disk
 explains some overall properties of planetary system:
 planetary orbits and rotational equators lie in same plane
 planets revolve around Sun and rotate in same direction
 gas giant planets with huge H & He envelopes found in outer solar system
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Planet Building:
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takes place in stages
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Stage 1: Condensation
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condensation: atoms and molecules in a gas collide and stick together to form
microscopic grains of solid material
 a gas-to-solid phase transition
 microscopic solid grains are first stage building blocks
condensation aided by compression of disk due to collapse
-
condensation sequence: which types of material can condense depends on gas
temperature (T)
- high T (T > 1200 K): only refractory (rock and metal) materials can condense
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- low T (T < 350 K): both volatile (ices) and refractory materials can condense
- NOTE: the condensation sequence is a temperature sequence, NOT a time
sequence
proto-planetary disk temperature (T) gradient:
- T decreases with increasing distance from proto-Sun
 T > 1500 K around orbit of Mercury
T < 50 K near orbit of Neptune
 inner solar system: grains of rock and metal ONLY condense
- mineral elements (Na, Mg, Si, S, Al, P, K, Ca, Fe, etc.) are rare in solar nebula
 relatively small amount of material condenses
 outer solar system: grains of ices AND rock and metal condense
- ice elements (H, C, N, O) are abundant in solar nebula
 relatively large amount of material condenses
-
NOTE: if ice grains that formed in outer solar system enter inner solar system 
vaporized by heat of Sun
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Stage 2: Accretion
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accretion: smaller objects colliding and sticking together to form larger objects
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accretion is a heierarchical process
- smaller objects accrete to form larger objects  larger objects accrete to form
even larger objects  … (similar to avalanching particles)
 accretion produces progressively larger and larger building blocks, starting with
microscopic grains and ending with proto-planets
- grains  pebbles  gravel  boulders  planetesimals  proto-planets
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planetesimals: asteroid-sized objects (D > 1 km) produced by accretion
- building blocks of proto-planets
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proto-planets: moon-sized objects (D > 1000km) produced by accretion of
planetesimals
- cores of planets
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gravity assisted accretion:
- initially collisions between small particles due to random encounters
- later collisions between planetesimals and proto-planets enhanced by
gravitational attraction between colliding bodies
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Final stage:
- the final stage of planet building differs for terrestrial planets and Jovian planets
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Terrestrial planets:
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heavy bombardment era: era during first 5.0108 yrs of solar system with relatively
frequent collisions between planetesimals and proto-planets
 produced heavy cratering of proto-planets
 cratering rate declines as remaining planetesimals swept up
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differentiation of interiors:
- kinetic energy of most violent impacts melt entire proto-planet
 heavier elements (Iron (Fe), Nickel (Ni)) sink to center of planet
lighter elements (Carbon (C), Silicon (Si), Magnesium (Mg), …) rise to
outer layers
- planet cools and re-solidifies  differentiated structure locked in
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Heat of formation:
- outer layers of solid planet are a good insulator
 heat from kinetic energy of impacts trapped in interior of planet
 central region of terrestrial planets hotter than surface layers, even now
- heat of formation gradually flowing out toward surface as interior cools
 drives geological and volcanic activity
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thin atmospheres:
- only rare heavier gas atoms (C, O) available in inner solar system
- terrestrial planets have small mass (M)  small escape velocity (vesc)
- terrestrial planets have high surface temperature(Ts)  average velocity of
particles in atmosphere, vave, large
 can only retain atmosphere of rare heavier gas atoms (C, O)
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Jovian planets:
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gas giant planets:
- solid proto-planets composed of volatile and refractory materials (ice and rock)
- ices made of abundant light atoms  lots of ice available
 Jovian proto-planets more massive than terrestrial proto-planets
 larger vesc  can retain atmosphere of abundant light (H, He) AND rare
solid proto-planets bombarded by remaining planetesimals
 proto-planets sweep up remaining planetesimals
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heavier atoms
- outer solar system contains abundant light atoms (H and He)
 lots of gas available
- T lower  vave of light atoms smaller  vave of H and He < 1/6 vesc
 Jovian proto-planets enshrouded by very thick gas envelopes
 gas envelope contains most of mass and volume of Jovian planet
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moons of Jovian planets:
- larger moons are smaller proto-planets left over from planet building
- formed near Jovian planet  orbit around Jovian planet
- smaller moons are left over planetesimals trapped in orbit around Jovian planet
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Minor bodies - debris:
- asteroids: left over planetesimals that formed in inner solar system
 composed of refractory materials
- comets: left over planetesimals that formed in outer solar system
 composed of both volatile and refractory materials
Earth & Moon
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best known objects
 points of comparison and contrast for other objects
Earth as a planet:
Surface temperature:
-
radiation from Sun is primary energy source on Earth’s surface (photons carry
energy, E=hν)
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albedo (A) of Earth (reflectivity): fraction of incident radiation that is reflected
 1-A = fraction of incident radiation absorbed by Earth
-0<A<1
- A = 0.39  39% incident radiation reflected; 61% incident radiation absorbed
- significance: ONLY the fraction of solar radiation absorbed (1-A) heats the
surface  determines surface T
- the fraction of solar radiation reflected (A) allows Earth to be seen in visible band
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rate of heating by solar radiation = energy, E, absorbed per unit time
= fTot  aE  (1-A) in Watts, W
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- where: fTot = total flux of radiation from Sun at Earth (W/m2)
= LTot/4d2, where LTot = total Luminosity (L) of Sun (W)
d = Earth’s mean distance from Sun (m)
aE = Earth’s cross-section (projected area of Earth) (m2)
A = albedo
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 rate of heating by solar radiation (Watts) = LTot/4d2  RE2  (1-A)
- where: LTot = total Luminosity (L) of Sun (W)
d = Earth’s mean distance from Sun (m)
RE = Earth’s radius (m)
A = albedo
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Earth is a Blackbody
- Earth has a surface Temperature, TSurf > 0 K  emits Blackbody radiation
- emitted Blackbody radiation differs from reflected sunlight
- significance: emission of Blackbody radiation cools Earth  determines surface
T
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rate of cooling by B-body radiation = rate of energy loss
= B-body Luminosity (L) of Earth = FE  AE in Watts, W
- where: FE = Total surface flux of B-Body radiation (w/m2)
AE = total surface area of Earth (m2)
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 rate of cooling by B-body radiation = TSurf4  4RE2
- where: TSurf = surface temperature of Earth (K)
RE = radius of Earth (m)
 = Stefan-Boltzmann constant (see “Blackbody radiation”)
Earth surface T (TSurf) is approximately constant in time; ie. Earth neither heating
up nor cooling down
 (rate of cooling by Blackbody radiation) = (rate of heating by solar radiation)
 TSurf4  4RE2 = LS/4d2  RE2  (1-A)
 TSurf 4 = (1-A)  LS/16d2
 TSurf = 246 K = -27o C
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Apply Wien’s Law of B-body radiation:
- max = 0.0029 m K / TSurf = 0.0029 m K / 246 K  1.210-5 m = 12 m
 Earth emits B-Body radiation in the IR band (visible band light from Earth is
reflected Sun light)
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Actual average TSurf = 9o C
 Actual TSurf > Calculated TSurf
- due to Greenhouse effect of Earth’s atmosphere
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 atmosphere effects Tsurf of a planet!
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Atmospheric activity (weather):
- B-body radiation from surface heats atmosphere just above surface
 in lower atmosphere T decreases with increasing height
- warm air more buoyant than cool air
 convection currents: circulation cells made of hot updrafts and cool
downdrafts
 cause of weather
- ie. the atmosphere is active due to heating by Sun
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Interior:
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interior is chemically differentiated
- heavier elements (Iron (Fe), Nickel (Ni)) concentrated toward center
lighter elements (Carbon (C), Silicon (Si)) concentrated toward surface
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interior is Temperature (T) and density () stratified
- T and  increase inwards toward center
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chemical differentiation and T stratification both due to heat of formation in final
stages of planet formation (see “Planet Building”)
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evidence:
- surface = 3000 kg/m3, but average = M/V = 5500 kg/m3  core > surface
- seismology:
seismic waves: vibration from Earthquakes cause sound waves to travel
through interior
- waves refract as they travel through interior due to T and  stratification
- seismographs around surface detect vibrations transmitted by waves
 can determine interior  and T structure
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three main zones: core, mantle, crust
core:
- central point: T = 5000 K,  = 13000 kg/m3,
- Pressure, P = weight of overlying 1 m2 column of rock and atmosphere
= 106  atmospheric P at sea level
- Tcore > melting point of Iron (Fe)  outer core is molten  composed mostly of
liquid Fe
- Pcore too large to allow Fe to melt  inner core is solid Fe
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mantle:
- composed of rock
- mantle hot (high T), under large pressure (P)  solid rock behaves like fluid
 mantle flows slowly
crust:
- composed of rock
- tectonic (crustal) plates: crust divided into separate rigid plates
 plates float on top of fluid mantle
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interior activity:
- Earth is geologically active
- central region hotter that outer layers
 heat slowly flowing outward through interior
- mantle is fluid  outward heat flow drives slow convection currents in mantle
 circulating currents in mantle drag tectonic plates around; rate = few cm yr-1
 causes volcanic and geological activity on surface (plate tectonics)
 surface is active as a result of trapped heat of formation
 Earth’s surface is geologically young
 surface features are much younger than planet itself
- due to volcanic renewal of surface
Magnetism:
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Fe is an electrical conductor  outer core composed of electrically conducting fluid
molten Fe is circulating around rotation axis due to Earth’s rotation AND is
circulating up and down due to convection currents
 molten core is a natural dynamo  generates a magnetic field
 existence of Earth’s magnetic field is evidence for molten Fe core
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magnetosphere: volume of space around Earth that is filled with Earth’s magnetic
field
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magnetic field: a type force field (like gravity)
- graphically depicted with lines of force
 indicate which direction a compass needle would point
 show shape of field
- magnetic charge: particles that feel magnetic force have a magnetic charge,
analogous to electric charge
- two polarities of charge: North (N) and South (S); like charges repel, opposite
charges attract (like + and – charges in electricity)
- only particles that have a magnetic charge (ie. are magnetic), OR that have an
electric charge are affected by magnetic force
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- magnetic pole: point in space where lines of force converge
- every magnetic field has at least two poles: one North (N) and one South (S)
pole with opposite magnetic charge
- magnetic dipole: a magnetic field with only two poles, one N and one S
- Earth’s field is a dipole
- magnetic axis: imaginary line connecting N and S poles in a magnetic dipole
- magnetic axis of Earth’s field is approximately aligned with rotation axis
- relationship with electricity: electricity and magnetism are both aspects of one
force: electromagnetism
 a magnetic field exerts a force on electrically charged particles
 electrically charged particles are not free to travel straight through a
magnetic field
magnetic interaction with solar wind:
- solar wind: particles ejected from Sun
- flows outward in all directions from Sun at ~450 km/s
- made up of electrically charged particles: electrons and ions
- solar wind mostly deflected by magnetosphere
 magnetosphere protects Earth from high energy particles
- magnetosphere deformed by solar wind
 field compressed on Sunward side, stretched out on opposite side
magnetopause: boundary where most solar wind particles deflected
- indicates shape of magnetosphere
some particles break through outer field and are trapped in inner field
 Van Allen belts: belts of electrically charged particles from solar wind trapped
in magnetosphere
- inner belt: contains protons (positively charged particles)
- outer belt: contains electrons (negatively charged particles)
terrestrial effects:
- occassional clump of particles in solar wind (from solar flare) breaks through
magnetic field, enters Earth’s atmosphere
- particles deflected toward poles by field  enter atmosphere over poles
- charged particles entering atmosphere excite gas atoms  atmosphere glows
 Aurora Borealis (“northern lights”) and Aurora Australius (“southern
lights”)
Atmosphere:
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composition of modern atmosphere very different from composition of solar nebula
 atmosphere changed over time
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primordial atmosphere:
- two most common gases in solar nebula, H and He, escaped into space from
Earth’s vicinity
 H & He mass small  average velocity > escape velocity
- outgassing: gas baked out of hot rock
- young Earth was hotter than modern Earth  heavier molecules outgassed
from rock retained in atmosphere
- composition: H2O (water) (in gas form), CO2 (carbon dioxide), N2 (molecular
Nitrogen)
- T > 100oC at sea level  H2O in gas phase (“steam”)
- note: there was NO O2 (molecular Oxygen)
- O2 very reactive  bonds with other atoms to make oxide
compounds  does NOT remain free
- eg. Iron Oxide (“rust”): O2 + 2Fe  2FeO
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Greenhouse effect:
- blocking by the atmosphere of IR band blackbody radiation emitted by the Earth
 decreases Earth’s ability to cool by radiating energy
 increases surface T
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- greenhouse gasses: gases of which the atoms or molecules absorb IR radiation
and thus contribute to the greenhouse effect in the atmosphere
 the larger the concentration of greenhouse gases in atmosphere  the larger
the greenhouse effect  the higher the surface T
- H2O and CO2 are both Greenhouse gases
 primordial Earth had large Greenhouse effect  higher surface T
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Evolution of atmosphere:
-1) Earth emitting blackbody radiation  surface temperature, Ts, gradually
decreasing
 eventually T < 100oC at sea level
 H2O condenses  rains out of atmosphere and forms oceans
 decreases H2O concentration in atmosphere  decreases Greenhouse
effect  surface T decreases more
- 2) CO2 easily dissolved in liquid water (eg. carbonated beverages)
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 most CO2 enters oceans  eventually precipitates out as limestone
sediment
 ie. oceans remove most CO2 from atmosphere and turn it into rock
 decreases CO2 concentration in atmosphere  decreases Greenhouse
effect  surface T decreases more
- 3) at age = 0.5 Gyrs: first plant life appears: blue-green algae
- plant photosynthesis converts CO2 to O2 (CO2  O2)
 produced first free oxygen (O2 molecules) in atmosphere
- recall, O2 very reactive
 must be continually replenished by photosynthesis
 ie. emergence of life a factor in evolution of atmosphere
- at low gas pressure in upper atmosphere oxygen forms ozone: O3
- ozone absorbs UV band radiation from Sun  protects fragile molecules
(like H2O on surface from high energy photons)
- Planck’s Law: EPhoton=hν  UV photons have greater E than visible band
photons
 UV photons, γUV, can destroy water by photolysis: γUV + H2O  2H +
O
Modern atmosphere:
- concentration of CO2 and O2 remain approximately stable due to balance of
processes
- CO2: created by vaporization and combustion of carbon (C) bearing
compounds; destroyed by plant photosynthesis
 concentration = 0.035%  enough for significant greenhouse effect
- O2: created by plant photosynthesis; destroyed by animal respiration and
oxidation
 equilibrium concentration = 21%
Moon:
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well studied:
- many manned and robotic missions
- return missions brought back moon rocks from different regions
-
all the differences between the Moon and Earth are ultimately due to their difference
in size
- Radius of Moon, RM, is 3500 km ~ 1/4 R of Earth, RE
- spherical volume, V = 4πR3/3
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 VM/ VE = (RM/ RE)3 ~ (1/4)3 ~ 1/64
 if average density, ρM ~ ρE  mass of Moon, MM, is ~1/64 ME of Earth
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surface gravity, g:
- Newton’s Law of Gravity: Force of Moon’s gravity on an object at Moon’s surface,
F = GMm/R2 = mg
 g = GM/R2
- where: M = Mass of Moon (kg)
m = mass of object (kg)
R = distance between center of Moon and center of object
= radius of Moon (m)
G = Newton’s gravitational constant (6.607×10-11 Nm2 / kg2)
g is gravitational force per unit mass of object  units: N/kg
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Note: g does not depend on mass of object, m, only on mass of Moon
 g is a useful way of expressing strength of gravity at surface of a body
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surface gravity of Moon, gM
- gM = GMM/RM2
- more useful: compare to Earth: gM/gE = GMM RE2/GMERM2 = MMRE2/MERM2 =
≈ (1/64)(42) ≈ 1/4
- ρM < ρE  actual value gM/gE = 1/6
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- Newton II: F = ma
- but: F = mg  g ≡ a  g is also an acceleration
 units are also m s-2
 ie. N/kg = m/s2
 g = acceleration of gravity at Moon’s surface = “surface gravity”
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small mass  small gravitational force
 gas particles have vave > 1/6 vesc  no atmosphere
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atmospheric pressure at surface, P:
- useful way of expressing how much atmosphere a body has
- P ≡ weight at surface of a column of atmosphere of cross-sectional area = 1 m2
- (recall: weight ≡ gravitational force)
- units: force/area  Metric unit are N/m2
relative to Earth’s atmospheric pressure at sea level  units are
Atmospheres
- eg. P of Earth’s atmosphere at sea level = 1 Atmosphere
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 Moon: no atmosphere: P ~ 0 atmospheres
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surface water:
no atmosphere  low gas pressure, P, on surface  low boiling T of water  no
liquid water on surface
 Moon is arid
H2O only in liquid phase over limited T range, Tliquid: Tfreeze < T < Tvapor
 Tliquid = Tvapor - Tfreeze
- if T < Tfreeze  solid phase (ice)
- if T > Tvapor  gas phase (steam)
- values of Tfreeze and Tvapor depend on gas pressure, P
 lower P  lower Tvapor  smaller Tliquid
- eg. in Denver Co., altitude = 5000 ft  P < 1 atmosphere at sea level  Tvapor <
100oC
if P low enough  Tvapor = Tfreeze  Tliquid = 0 K
 water cannot exist in liquid phase
eg. inside a freezer at sea level: water only in form of ice or vapor
Moon: P ~ 0 Atmospheres
 Tliquid = 0 K  liquid H2O cannot exist on surface
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Surface features:
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maria: large circular dark areas – cover 15%
(“maria” Latin for sea  misnomer: there is no liquid water on Moon)
- volcanic rock; age ~ 3.5 Gyrs  younger than solar system
terrae (highlands): light areas outside of maria – cover 85%
- low density mineral rocks; age ~ 4.5 Gyrs  same as age of solar system
impact craters: millions; diameters of ~100 km and less
regolith: uppermost layer of surface  powdered rock
 due to constant sandblasting by sand-grain and pebble sized meteoroids
 no atmosphere to protect surface from small meteoroids as on Earth
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Impact craters:
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velocity of minor body with respect to Moon ~ 10’s of km/s = few ×104 m/s
 have large kinetic energy, KE; KE = 1/2mv2
- where: m = mass of body (kg)
v = velocity of body relative to Moon (m s-1)
due to impacts with minor bodies
always circular  do not depend on angle of impact
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 effect of v2 factor: v large  KE huge
 upon impact: KE goes into pulverizing, atomizing, and melting area of surface,
and ejecting debris
rule of thumb for crater size: crater diameter ~ 10  minor body diameter
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maria: huge impact craters  basins excavated by impact of last planetesimals near
end of heavy bombardment era
- impacts melted subsurface layers and cracked surface
 lava welled up through cracks and flooded basin, covered previous craters
 maria are areas that were “re-paved” near end of heavy bombardment era
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distribution of craters: predominantly in terrae, few in maria
age of craters: most are older than 3.5 Gyrs
 most craters formed during heavy bombardment era during last stage of
planet building
 ie. during first 5108 years of solar system
 maria mostly uncratered  must have formed after heavy bombardment era
 maria are geologically younger surfaces than terrae
Interior:
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Interior is differentiated  due to heat of formation
 has dense Fe rich core, a mantle, and a lower density crust
- Moon’s Fe core is disproportionately small
- Earth: mass of Fe core = 0.33 total Mass
- Moon: mass of Fe core = 0.03 total Mass
 Moon missing much of its Fe?  clue to Moon’s formation
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Moon is small (VMoon/VEarth=1/64)  all heat of formation has escaped
 interior is mostly solid (little or magma)
 no magnetic field
 no mantle convection  no plate tectonics
 no volcanism
 Moon is geologically dead
 surface is geologically old
- consequence: still has craters that formed ~4 Gigayears ago
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Moon quakes:
- take place in deep interior, not on surface
 differ from Earth quakes  Moon is geologically dead
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- due to changing tidal force throughout orbit
 Kepler I: Moon’s orbit is elliptical with Earth at one focus
 perigee: point in orbit nearest Earth
apogee: point in orbit furthest from Earth
 Moon squeezed more at perigee than at apogee
 changing stress on rock causes quakes
 cause of tidal synchronization of Moon’s rotation period to its orbital period
(Prot=Porb)
Origin of Moon:
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Moon is odd  indicates an unusual origin:
clues to origin:
- Earth is ONLY terrestrial planet with a major Moon
- Moon’s orbital velocity is large for a body of its Mass
 Earth-Moon system has a an unusually large amount of angular momentum
- Moon’s interior is unusually poor in Fe
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Collision-Ejection Theory of Moon’s formation
- proto-Earth struck in a glancing collision with a slightly smaller proto-planet
- proto-Earth’s interior already differentiated before collision
 Earth’s entire mantle and entire smaller proto-planet pulverized
- glancing collision (not head-on)  produced disk of rapidly spinning debris
- gravity causes debris to re-coalesce:
- heavy Fe-rich gragments gall back onto Earth
 Earth gets Fe-rich mantle
 remaining debris Fe-poor
- remaining debris in disk coalesces into rapidly revolving, Fe-poor Moon