The Solar System

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The Solar System
Isaac Newton (1642)

• 1665-1666 new version of natural philosophy
• Three Laws of Motion
• the natural state of motion is a constant speed
  in a straight line (based on Galileo)
• an object's motion changes as a result of forces,
  larger force produces larger change, heavier
  masses are more resistant to change
• objects' interactions are mutual
  (action/reaction) (based on Descartes)

• developed Calculus to apply the laws
• allows prediction of motion, given forces
• allows prediction of forces, given motion

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• deduced inverse-square nature of gravitational
  attraction from Keplers laws (for circular
  orbits)

• Hooke (1674) asks Newton to consider motion
  under influence of inverse-square force
• Newton finds orbits would be elliptical
• Edmond Halley (1684) asks Newton same question
• urges Newton to publish his ideas on forces and
  motion

• Philosophia Naturalis Principia Mathematica
  (Mathematical Principles of Natural Philosophy -
  1687)
• Law of Universal Gravitation any two bodies
  will attract each other with a force that depends
  on the masses of the objects and the distance
  separating them. (inverse-square law)

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• inverse-square law leads to elliptical orbits

• also reproduces Keplers Laws

Gravity is the underlying force that governs the
motions in the solar system
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Advances in Instruments

• Refracting Telescope
• use refraction (bending of path of light by
  glass) to concentrate light

• two lenses gives greatly magnified image

• improved by increasing diameter and focal
  length of lens (increases length of telescope)

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17th century Solar system observations

• Huygens (1656) resolves rings around Saturn,
  moon of Saturn
• Cassini  rotation of Jupiter (1663), rotation
  of Mars, moons of Saturn

• Micrometer adjustable scale and pointer attached
  to telescope (1638-1666)
• allows accurate measurement of position within
  telescope field of view

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Pendulum clock (1656 Huygens)

• pendulum regulates movement of clock mechanism
• allowed more precise timing of observations
• critical when examining motion

• Size of Solar System
• Cassini and Richer  (1670's)
• based on observations of position of Mars

• observations made at same time from different
  places
• once distance to Mars known, other
  distances follow

Earth-Sun distance 150 million km 1
Astronomical Unit (AU)
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• Sizes of Planets
• determined from
  known distances and apparent
  size (from micrometer)

Speed of Light (Roemer 1675)

• eclipses of Jupiter's moons occur slightly
  later than expected when Earth moving away from
  Jupiter, slightly earlier when Earth moving
  towards Jupiter
• changes are a result of light having to travel
  further to reach Earth as Earth moves in orbit

• c 3?108 m/s 300,000 km/s

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Reflectors

• light is concentrated using reflection from
  curved mirror (1668, Newton)
• improved by making mirror larger, smoother

• became more popular towards end of 1600's due
  to lighter weight and high magnification

• Equatorial mount
• one axis is parallel to Earth's axis
• telescope only has to rotate around one axis to
  compensate for Earth's rotation
• much more stable

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Titius-Bode "Law"
The Discovery of New Members of the Solar System

• William Herschel discovers Uranus, 1781

• The Asteroids
• 1766 - Titius Law radii of planets' orbits
  (up to Saturn) described by numerical sequence

• gap at 2.8 AU
• Uranus fit into sequence when discovered

  0 3 6 12 24 48 96 (192) (384)
  4 7 10 16 28 52 100 196 388
Prediction 0.4 0.7 1.0 1.6 2.8 5.2 10.0 19.6 38.8
Orbit Size(AU) 0.39 0.72 1.00 1.52   5.20 9.54 19.2 30.1
  Mercury Venus Earth Mars  ? Jupiter Saturn (Uranus) (Neptune)
Titius-Bode "Law"

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• Von Zach (1800) calculates orbital path for
  hypothetical object at 2.8 AU, initiates search 
• Piazzi (Jan 1, 1801) notes movement of 8th mag.
  object in Taurus
• observes until Feb. 11 - motion appears more
  planetary than cometary
• notifies Bode in Germany (March 20 1801),
  object no longer visible
• orbital calculations too primitive - object
  lost
• Gauss develops method for finding orbits on
  basis of 3 observations, applies to Piazzi's
  data and produces ephemeris
• Von Zach uses ephemeris to re-locate object
  (Dec 31 1801)
• Piazzi names object (planet) "Ceres"
• location at 2.77 AU reinforces Titius-Bode Law

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• Herschel determines size of Ceres 260 km 
  (modern value 1000 km)
• "asteroid"  (star-like in appearance - much
  smaller than planet)

• Olbers discovers another object in similar
  orbit - 2.67 AU (Pallas)
• Juno (1804) and Vesta (1807) in similar orbits
• many smaller ones discovered through 19th and
  20th cent.
• Asteroid belt large pieces of rock (10 - 100
  km diameter) orbiting between 2.2 and 3.3 AU
• left over material from formation of
  solar system

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Celestial Mechanics

• can predict motion of planets, comets,
  asteroids etc. using Newton's Laws of Motion and
  Law of Universal Gravitation
• position and velocity at initial time can be
  used to predict future
• need 6 pieces of data knowledge of forces
• 3 observations of location in sky (R.A. and
  dec.)
• data transformed into 6 orbital elements

                Mars

• orbital elements change over time due to
  gravitational influences of other planets and
  shapes of planets
• osculating orbit the elements of the ellipse
  that best describes orbit at given time
• Kepler's Laws are approximations

Jan. 30 1995 Nov. 19 1995
a 1.523664  a 1.523741
e 0.093418  e 0.093354
i 1.8498 i 1.8497
W 49.522 W 49.529
v 336.020 v335.948
L 119.2770 L 307.9440