Physics 202: Introduction to Astronomy – Lecture 4
Carsten Denker
Physics DepartmentCenter for Solar–Terrestrial
Research
January 27, 2006 Center for Solar-Terrestrial Research
Jupiter
The Jovian Moons Io Europa Ganymede Callisto
January 27, 2006 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
January 27, 2006 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
January 27, 2006 Center for Solar-Terrestrial Research
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:2 3P a
January 27, 2006 Center for Solar-Terrestrial Research
EllipsesFocal points F1 and F2 (sun in principal
focus)
Distance from focal points r1 and r2
Semimajor axis aSemiminor axis bEccentricity 0 e 1Ellipse defined:1 2 2r r a
2 2 21 2
2 2 2
( )
(1 )
r r r a r b ae
b a e
2(1 )
1 cos
a er
eA ab
January 27, 2006 Center for Solar-Terrestrial Research
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 kmLight minute: 1.800 107 km
(1 AU = 8.3 light minutes)Parsec: 1 pc = 3.0857 1013 km =
3.262 ly
January 27, 2006 Center 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 (MEarth/MSun= 28700 instead of 332945), wrong value for solar parallax, better estimate in later edition of the Principia (within factor of two)
January 27, 2006 Center 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, 2006 Center for Solar-Terrestrial Research
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.
net1
net
( )
n
ii
F F ma
dv d mv dpF m
dt dt dt
12 21F F
January 27, 2006 Center for Solar-Terrestrial Research
Gravitational Force2 3P kr (Kepler’s 3rd law, circular orbital motion, M
>> m)
2 rP
v
(constant velocity)
2 2 2 23
2 2
4 4r v mkr m
v r kr
(centripetal force)
2
2 2
4 m MmF G
kr r
(law of universal gravitation)
Universal gravitational constant: 6.67 10–11 Nm2 / kg2
January 27, 2006 Center for Solar-Terrestrial Research
Gravity Near Earth’s Surface
2 2( )
M m M mF G G
R h R
( )h R
2
MF ma mg g G
R
24
23
5.974 10 kg m9.799
s6.378 10 km
Mg
R