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