Astronomy 121, Winter 2005

Exam 1 Review

posted Jan. 17, 2005, jeb

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TOPICS FOR EXAM Basic Laws The Solar System The Earth The Moon Mercury

go to Earth go to the Moon go to Mercury

The Solar System:

An Introduction to Comparative Planetology

The nine planets of the solar system:

• 4 terrestrial planets:
  • Mercury, Venus, Earth, Mars
• 4 Jovian planets:
  • Jupiter, Saturn, Uranus, Neptune
• Pluto

Planetary orbits generally lie in a plane ( ecliptic plane)

• largest deviations from plane: Pluto (17^o) Mercury (7^o)

The planets orbit the Sun in a counterclockwise direction, as seen from above the Earth's North Pole.

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Properties of the Terrestrial and Jovian planets

Large densities (= mass/volume) of inner planets => iron-nickel cores

density (=mass/volume) is a measure of the compactness of the matter within an object

Planetary atmospheres depend on escape speed => which depends on gravity (or total mass of planet),
competing against the temperature of the atmospheric gas (which exerts an upward pressure against the gravity)

Table of Solar System Properties

Some extremes of the Solar System:

Closest to the Sun - Mercury
Farthest from the Sun - Pluto
Largest and most massive planet - Jupiter
Planet with the most known moons - Jupiter
Planets with no moons - Mercury and Venus
Planet with fastest rotation - Jupiter
Planet with slowest rotation - Venus
Planet with fastest retrograde rotation - Uranus
Planet with highest density - Earth
Planet with lowest density - Saturn

Kepler's Laws (orbits of the planets)

1. The orbital paths of the planets are elliptical (not circular) with the sun at one focus
   
   a measure of the size of an ellipse is the semi-major axis
   
   
2. An imaginary line connecting the Sun to any planet sweeps out equal areas
   of the ellipse in equal intervals of time
   
   
3. The square of the planet's orbital period is proportional to the cube of its semi-major axis

Kepler's Laws follow from Newton 's Law of Universal Gravitation:

Planetary motion is determined by The Sun's inward pull of gravity competing with the planet's tendency to continue moving in a straight line.


• F = G m₁m₂ / R²
  
  This is an inverse-square law

Astronomical Unit (A.U.)(Distance from Earth to Sun)

• = 150,000,000 kilometers (km) = 93,000,000 miles = 1 astronomical unit (A.U.)

which means it takes light about 8 minutes to travel from the Sun to the Earth
• time = distance/speed
• time = 150,000,000 km / 300,000 km/sec = 500 sec = 8 min, 20 sec.

Interplanetary debris:

• Asteroids & meteoroids (small asteroids, rocky)
• Comets (icy)
• Interplanetary dust

Asteroid belt

• Between orbits of Mars and Jupiter

Mass of the Solar System

• Sun 99.80%
• Jupiter 0.10%
• Comets 0.05%
• Other 8 planets 0.04%
  • Total of Sun + Planets + Comets = 99.99%

Age of the Earth & Solar System

• 4.6 billion years (4,600,000,000 years)

History of Discovery in the Solar System

• Greeks of old knew inner planets

  Study of the sky revealed that some objects were "wanderers", undergoing retrograde motion. They did not following the consistent pattern of motion of the rest of the objects in the sky.
  
  

  These were identified as the planets, which circle the Sun.

  
  

  Nicholas Copernicus (1473-1543) developed the heliocentric model of the Solar System.
  
  Galileo Galilei (1564-1642) convinced many of the correctness of Copernicus.

  • Mercury
  • Venus
  • Mars
  • Jupiter
  • Saturn
• Moons of Jupiter - 1609/1610 (Galileo)
• Saturn's rings - 1659
• Uranus - 1758
• Ceres (largest asteroid) - 1801
• Neptune - 1846
• Pluto - 1930

Spacecraft Exploration of the Solar System

• All planets but Pluto have been visited by U.S. or Soviet craft
  
• Mercury
  • 1974 - Mariner 10
• Venus
  • Venus is most visited planet
  • since 1970 - Soviet
  • 1990 - US Magellan - detailed survey and map from orbit
• Mars
  • since 1976 - US Viking 1 & 2 land
  • 1997 - Pathfinder/ Sojouner
  • 2004 - Spirit and Opportunity
• Outer Planets
  • Pioneer 10 & 11 (launched 1972 & 1973)
  • Voyager 1 & 2 ( launched 1977)
    (Voyager 1 & 2 used Jupiter's gravity to send them on to Saturn)
  • Galileo (launched 1989, arrived Jupiter 1995)
  • Cassini ( launched 1997, arrives Saturn 2004)

Earth

Our Home in Space

Earth's Evolution

• First hot and molten
• Heavy material sank toward center
  • Differentiation
    • Heavy material sinks over time toward the center of the Earth while lighter material rises to the surface.
• Earth cooled from outside in
• Radioactivity continues today to heat interior
  
  
• Oldest Earth rocks found on the surface today are about 3.9 billion years old
  • this is known from radioactive dating
  • therefore, Earth formed at least 3.9 billion years ago
    • it actually formed 4.6 billion years ago with the rest of the Solar System

Internal Structure of the Earth

• P- waves (pressure or primary waves)
  • refracted at the surface of the core
• S- waves (shear or secondary waves)
  • cannot pass through the liquid core

Six Regions of the Earth

• Core
  • metallic (mostly nickel and iron)
  • Core is high density (12,000 kg/m³) => 5000K
• Mantle
  • rocky structure (80% of Earth's volume)
  • Mantle is medium density (5,000 kg/m³) => T rises to 4000K
• Crust
  • thin surface covering mantle
  • Crust is low density (3,000 kg/m³) (water is 1,000 kg/m³)
  • Plate tectonics (continental drift)
    • Continental Drift
      • Earth's surface => a dozen plates
      • Plates slowly move => few centimeters/year
      • Interactions at plate boundaries
        • => large deformations
        • => earthquakes, volcanism, mountain building
          • an excellent example is the clash of the Pacific and North American plates at the San Andres fault
      • Plate motion driven by convection in mantle
• Hydrosphere
  • Liquid oceans
  • Earth is only planet with large quantities of surface water
    • 70 % of surface covered by oceans
  • Surface water is deformed by tidal force of Moon (and Sun)
    • enormous forces of tides continuously eroding surface
  • Earth rotation rate is slowing as a result of tidal force
    • slowed from 400 days/year to 365 in 500 million years
• Atmosphere
  • nitrogen and oxygen
    • 78% Nitrogen, 21% Oxygen, few % Water
    • Radiation shield (ozone)
    • Burns up most asteroids
    • Insulates surface, keeps warm (greenhouse effect => CO₂)
    • Oxygen came from life which appeared 3.5 billion yrs ago
    • Blue sky results from preferential scattering of blue light
  • Origin of Earth's atmosphere
    • Early Earth atmosphere - common gases of early Solar System
      • hydrogen, helium, methane, ammonia, water vaper
    • These early gases, being light, escaped from Earth (over 1/2 billion years)
      • especially hydrogen and helium
    • Secondary atmosphere created from volcanic activity - lots of Nitrogen
    • Life appeared over 3.5 billion years ago -> oxygen appears
  • Atmospheric Layers
  • Important Physical Processes in the Atmosphere
    • Convection
    • Greenhouse Effect
    • Surface temperature of Earth averages about 290 K
  • Why is the sky blue?
    • blue wavelengths of light are preferentially scattered by molecules in the atmosphere, comnpared to red.
      • Rayleigh scattering
    • This is also the reason sunsets and sunrises are reddish
• Magnetosphere
  • charged particles trapped in Earth's magnetic field
  • Earth's magnetic field
    • => circulating internal iron (magnetic) fluid
  • Trapped charged particles => Van Allen Belts
    • Aurora
    • Aurora from the Space Shuttle

The Moon

A Scorched and Battered World

Like Mercury:

• heavily cratered, ancient surfaces
• no air, no water
• wild temperature swings, day to night

The Moon - General Properties

• Radius = 1738 kilometers (about 1/4 of Earth)
• Mass = 7.4 x 10²² kilograms (about 1/80 of Earth)
• Average density = 3340 kg/m³
  • => fewer heavy metals (like iron) than Earth
• Atmosphere (NO)
  • => very weak gravity
  • => low escape speed (2.4 km/s, while earth is 11 km/s)
• Temperature
  • 400K (daytime)
  • 100K (nightime)
• Earth-moon distance = 384,000 km = 1.28 light-seconds

The Moon's Orbit around the Earth

• Orbits Earth in 27.3 days
• Rotates synchronously with orbit
  • the same side of the Moon always faces the Earth
  • on the Moon, the Earth appears to hang fixed in one place in the sky, slowly rotating on its axis
• Elongated shape of the Moon results in the synchronous orbit
  • Presumably, the Moon's elongated shape was created long ago by the Earth's tidal influence when the Moon was young, and the moon is now "tidally locked"

Moon's Gravity on its Surface

The Moon's Surface Features

• Maria - large flat areas resulting from lava flows
  • Fourteen (14) named maria, the largest being Mare Imbrium (1100 km diameter)
• Highlands - lighter appearing, elevated areas
• Craters - very old => mostly from meteoritic impact - very old
• Far side surprise
  • no major maria => due to asymmetric crust
  • almost entirely highlands
• Moon's surface is frozen in time: very little surface erosion
  • no wind or running water, to cause erosion
  • no plates on surface to cause volcanism or seismic activity
  • some erosion from micrometeroids
    • cumulative effect of micrometeroids => dust

Character of the Moon's Surface

• Highlands
  • rich in aluminum
  • somewhat lower density (2900 kg/m³)
  • material originated in crust
• Maria
  • more iron
  • greater density (3300 kg/m³)
  • material originated from mantle
• Lunar Dust
  • about 20 meters deep
  • pulverized by meteroids
• Volcanism
  • explains some craters
    • some lava found in maria
  • but volcanism ended early in the Moon's history

The Moon's Internal Features

• Moon's average density (3340 kg/m³) is similar to surface rock
  • No dense core
• No magnetic field => iron deficiency
• Cooler (1500K) interior than Earth
• Crust is thicker on the lunar far side
  • resulted from tidal forces
  • and explains absence of maria on far side

Origin of the Moon

• Likely origin from collision of large object (Mars-sized) with young Earth
  • Moon is similar to Earth's mantle

Planet order from Sun Orbital period Semi-major axis Mass Radius Density Surface Gravity Escape speed Rotational Period Inclination Surface Magnetic Field Surface Temperature Number of Moons

Mercury 1 0.24 years (88 days) 0.39 AU 0.055 x Earth 0.38 x Earth 5430 kg/m3 0.38 x Earth 4.2 km/s 58.6 days 0.0° 0.011 x Earth 100-700 K 0

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Mercury

A Scorched and Battered World

Like the Moon:

• heavily cratered, ancient surfaces
• no air, no water
• wild temperature swings, day to night

Observing Mercury from Earth

• Mercury never separates from the Sun by more than 28^o, as viewed from the Earth

Character of the Mercury's Surface

• Craters from meteoritic bombardment
  • less densely packed than Moon (covered at some time by lava?)
  • lower crater walls than on Moon (stronger gravity)
  • little evidence of Maria-like features (not much lava flow)
• Conclusion: some lava flow (not all craters remain) but not much (no maria)
• Scarps are evidence for collapse of surface when interior cooled
  
• Caloris Basin - 1400 kilometer diameter impact feature
  • "Weird" terrain

Mercury - General Properties

• Radius = 2440 kilometers (about 2/5 of Earth)
• Mass = 3.3 x 10²³ kilograms (about 5.5% of Earth)
• Average density = 5430 kg/m³
  • => pretty similar to Earth's 5500 kg/m³
• Atmosphere (NO)
  • => very weak gravity
  • => low escape speed (4.2 km/s, while earth is 11 km/s)
• Temperature
  • 700K (daytime)
  • 100K (nightime)
• typical Sun-Mercury distance (semi-major axis) = 58,000,000 km = 0.39 A.U.
  • Except for Pluto, Mercury has most eccentric ("out of round") orbit of the planets
    • perihelion = 0.31 A.U
    • aphelion = 0.47 A.U.
  • Orbital plane is inclined 7^o relative to the plane of the Solar System (the ecliptic), second largest deviation of the planets from this plane
• Weak magnetic field (1/100 x Earth)

Mercury's Spin-orbit Resonance

• Mercury rotates on its axis once every 59 days, exactly 2/3 of the planet's orbital period
• The spin-orbit resonance is similar to the tidal lock seen in the Moon's rotation
  • Here the large eccentricity of the orbit, moves the dominate tidal influence to the perihelion point, resulting in the 3:2 resonance
• Tidal lock also explains 0^o inclination (no tilt of rotation axis)
  • rotation axis exactly perpendicular to orbital plane

Mercury's Internal Features

• Mercury's average density (5430 kg/m³)
  • much larger than Moon's 3340, but about the same as Earth
• Small magnetic field => about 1/100 x Earth
  • This is surprising:
    • Dynamo Theory of planetary magnetic field generation requires rapid rotation of conducting liquid core
      • Mercury rotates slowly
      • There is thought to be little, if any molten iron in Mercury (there must be some)
  • But the field is small, so perhaps the slow rotation does it
  • or the core may have solidified, but still carries magnetic imprint
• Differentiated
  • explains large average density and weak magnetic field

Temperature Scales