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Physics 202: Introduction to Astronomy – Lecture 4. Carsten Denker Physics Department Center for Solar–Terrestrial Research. Jupiter. The Jovian Moons Io Europa Ganymede Callisto. Laws of planetary motion Kepler’s laws Elliptical orbits Astronomical unit

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physics 202 introduction to astronomy lecture 4

Physics 202: Introduction to Astronomy – Lecture 4

Carsten Denker

Physics Department

Center for Solar–Terrestrial Research

jupiter
Jupiter
  • The Jovian Moons
    • Io
    • Europa
    • Ganymede
    • Callisto

Center for Solar-Terrestrial Research

chapter 1 4 1 5
Laws of planetary motion

Kepler’s laws

Elliptical orbits

Astronomical unit

Dimensions of the solar system

Radar measurements of Earth/Venus distance

Newton’s laws

Mechanics

Force

Mass

Inertia

Acceleration

Gravity

Gravitational force

Inverse-square law

Chapter 1.4 – 1.5

Center for Solar-Terrestrial Research

orbital paths of planets
Collection of 20 years of accurate planetary positions by Tycho Brahe (1546 – 1601)

Johannes Kepler (1571 – 1630)

1609: Astronomia Nova

1619: Harmonice Mundi

1627: Rudolphine Tables

Orbital Paths of Planets

Center for Solar-Terrestrial Research

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

Center for Solar-Terrestrial Research

ellipses
Ellipses
  • Focal points F1 and F2(sun in principal focus)
  • Distance from focal points r1 and r2
  • Semimajor axis a
  • Semiminor axis b
  • Eccentricity0 e  1
  • Ellipse defined:

Center for Solar-Terrestrial Research

distances in the planetary system
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

Center for Solar-Terrestrial Research

isaac newton 1642 1727
Isaac Newton (1642 – 1727)
  • 1686: Principia Mathematica, universal law of gravitation
  • Stable planetary orbits result from a balance between centripetal and gravitational acceleration
  • Sun–to–Earth mass ratio (MEarth/MSun= 28700 instead of 332945), wrong value for solar parallax, better estimate in later edition of the Principia (within factor of two)

Center for Solar-Terrestrial Research

newtonian physics
Newtonian Physics
  • Galileo Galilei (1564–1642)
    • 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 (1642–1727)
    • 1687 Philosophiae Naturalis Principia Mathematica mechanics, gravitation, calculus
    • 1704 Optiks  nature of light and optical experiments

Center for Solar-Terrestrial Research

laws of motion
Laws of Motion
  • Newton’s 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.
  • Newton’s 2nd Law: The net force (the sum of all forces) acting on an object is proportional to the object’s mass and it’s resultant acceleration.
  • Newton’s 3rd Law: For every action there is an equal and opposite reaction.

Center for Solar-Terrestrial Research

gravitational force
Gravitational Force

(Kepler’s 3rd law, circular orbital motion, M >> m)

(constant velocity)

(centripetal force)

(law of universal gravitation)

Universal gravitational constant: 6.67  10–11 Nm2 / kg2

Center for Solar-Terrestrial Research

gravity near earth s surface
Gravity Near Earth’s Surface

Center for Solar-Terrestrial Research