Physics 320: Astronomy and Astrophysics

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Physics 320 Astronomy and Astrophysics Lecture
II

• Carsten Denker
• Physics Department
• Center for SolarTerrestrial Research

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Celestial Mechanics

• Elliptical Orbits
• Newtonian Mechanics
• Keplers Laws Derived
• The Virial Theorem

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Elliptical Orbits

• Keplers 1st Law A planet orbits the Sun in an
  ellipse, with the Sun at on focus of the ellipse.
• Keplers 2nd Law A line connecting a planet to
  the Sun sweeps out equal areas in equal time
  intervals.
• Keplers 3rd Law The
  average orbital distance a
  of a planet from the Sun
  is related
  to the planets
  sidereal period P by

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Ellipses

• Focal points F1 and F2 (sun in principal focus)
• Distance from focal points r1 and r2
• Semimajor axis a
• Semiminor axis b
• Eccentricity 0 ? e ? 1
• Ellipse defined

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Conic Sections
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Distances in the Planetary System

• Astronomical unit AU, average distance between
  Earth and Sun 1
  AU 1.496 ? 108 km
• Light year 1 ly 9.461 ? 1012 km
• Light minute 1.800 ? 107 km
  (1 AU 8.3 light minutes)
• Parsec 1 pc 3.0857 ? 1013 km 3.262 ly

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Newtonian Physics

• Galileo Galilei (15641642)
• Heliocentric planetary model
• Milky Way consists of a multitude of stars
• Moon contains craters ? not a perfect sphere
• Venus is illuminated by the Sun and shows phases
• Sun is blemished possessing sunspots
• Isaac Newton (16421727)
• 1687 Philosophiae Naturalis Principia Mathematica
  ? mechanics, gravitation, calculus
• 1704 Optiks ? nature of light and optical
  experiments

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Laws of Motion

• Newtons 1st Law The law of inertia. An object
  at rest will remain at rest and an object in
  motion will remain in motion in a straight line
  at a constant speed unless acted upon by an
  unbalanced force.
• Newtons 2nd Law The net force
  (the sum of all forces) acting
  on an
  object is proportional to the
  objects mass and its resultant
  acceleration.
• Newtons 3rd Law For every
  action there is an equal and
  opposite reaction.

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Gravitational Force
Universal gravitational constant 6.67 ? 1011
Nm2 / kg2
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Gravity Near Earths Surface
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Potential Energy
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WorkKinetic Energy Theorem
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Escape Velocity
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Group Problem

• What is the minimum launch speed required to put
  a satellite into a circular orbit?
• How many times higher is the energy required to
  to launch a satellite into a polar orbit than
  that necessary to put it into an equatorial
  orbit?
• What initial speed must a space probe have if it
  is to leave the gravitational field of the Earth?
• Which requires a a higher initial energy for the
  space probe leaving the solar system or hitting
  the Sun?

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Center of Mass
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Binary Star System in COM Reference Frame
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Energy and Angular Momentum
In general, the twobody
problem
may be treated as
and
equivalent onebody problem
with the reduce
mass moving about a fixed mass M at a distance r.
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Keplers 2nd Law
The time rate of change of the area swept out by
a line connecting a planet to the focus of an
ellipse is a constant.
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Keplers 3rd Law
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Keplers 3rd Law (cont.)
Virial Theorem For
gravitationally bound systems in equilibrium, it
can be shown that the total energy is always
onehalf of the time averaged potential energy.
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Class Project
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Homework Class Project

• Read the Storyline handout
• Prepare a onepage document with suggestions on
  how to improve the storyline
• Choose one of the five topics that you would like
  to prepare in more detail during the course of
  the class
• Homework is due Wednesday September 23rd, 2003 at
  the beginning of the lecture!

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Homework Solutions
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Homework

• Homework is due Wednesday September 16th, 2003 at
  the beginning of the lecture!
• Homework assignment Problems 2.3, 2.9, and 2.11
• Late homework receives only half the credit!
• The homework is group homework!
• Homework should be handed in as a text document!