Physics 202: Introduction to Astronomy – Lecture 4 Carsten Denker Physics Department Center for Solar–Terrestrial Research

January 27, 2006Center for Solar-Terrestrial Research Jupiter  The Jovian Moons Io Europa Ganymede Callisto

January 27, 2006Center 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

January 27, 2006Center 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

January 27, 2006Center for Solar-Terrestrial Research Elliptical Orbits  Kepler’s 1 st Law: A planet orbits the Sun in an ellipse, with the Sun at on focus of the ellipse.  Kepler’s 2 nd Law: A line connecting a planet to the Sun sweeps out equal areas in equal time intervals.  Kepler’s 3 rd Law: The average orbital distance a of a planet from the Sun is related to the planets sidereal period P by:

January 27, 2006Center for Solar-Terrestrial Research Ellipses  Focal points F 1 and F 2 (sun in principal focus)  Distance from focal points r 1 and r 2  Semimajor axis a  Semiminor axis b  Eccentricity 0  e  1  Ellipse defined:

January 27, 2006Center for Solar-Terrestrial Research Distances in the Planetary System  Astronomical unit [AU], average distance between Earth and Sun: 1 AU =  10 8 km  Light year: 1 ly =  km  Light minute:  10 7 km (1 AU = 8.3 light minutes)  Parsec: 1 pc =  km = ly

January 27, 2006Center for Solar-Terrestrial Research 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 (M Earth /M Sun = instead of ), wrong value for solar parallax, better estimate in later edition of the Principia (within factor of two)

January 27, 2006Center for Solar-Terrestrial Research 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

January 27, 2006Center for Solar-Terrestrial Research Laws of Motion  Newton’s 1 st 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 2 nd 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 3 rd Law: For every action there is an equal and opposite reaction.

January 27, 2006Center for Solar-Terrestrial Research Gravitational Force (Kepler’s 3 rd law, circular orbital motion, M >> m) (constant velocity) (centripetal force) (law of universal gravitation) Universal gravitational constant: 6.67  10 –11 Nm 2 / kg 2

January 27, 2006Center for Solar-Terrestrial Research Gravity Near Earth’s Surface