Tycho Brahe
Tycho’s Solar System
<Solar System>
http://janus.astro.umd.edu/javadir/orbits/ssv.html
<Alternate Solar
Systems>
http://www.niu.edu/geology/stoddard/JAVA/ptolemy.html
The Perfect Solids
Tetrahedron
Cube
Octahedron
Dodecahedron
Icosahedron
The Solar System
The Inner Solar System
Kepler’s First Law
Kepler’s First Law
Planets travel around the sun in ellipses, with the sun at one
focus
Planets travel around the sun in ellipses, with the sun at one
focus
Kepler’s First Law
Planets travel around the sun in ellipses, with the sun at one
focus
Kepler’s First Law
Kepler’s First Law
Planets travel around the sun in ellipses, with the sun at one
focus
Kepler’s First Law
Planets travel around the sun in ellipses, with the sun at one
focus
Planets travel around the sun in ellipses, with the sun at one
focus
<Ellipse demo>
http://csep10.phys.utk.edu/guidry/java/kepler/kepler.html
<Ellipses of Actual Planets>
http://www.walter-fendt.de/ph14e/keplerlaw1.htm
Kepler’s Second Law
Planets sweep out equal areas in equal times
Kepler’s Third Law
The square of the period of the orbit of a planet is proportional
to the cube of the average radius of the orbit:
<Second Law animation>
(Period b)2
(Period a)2
=
(Average radius a)3
(Average radius b)3
http://www.sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Kepler/kepler.html
or
Ta2
3
Ra
=
Tb2
3
Rb
<Second Law and Actual Planets>
http://www.walter-fendt.de/ph14e/keplerlaw2.htm
Equivalent to angular momentum conservation (Newton found
this)
Galileo’s use of and inclined plane
I
up the plane – stops and rolls back
I
independent of angles
I
there must be an angle (0◦ ) for which there is no
acceleration
I
<Kepler’s Laws with Data for Law 3>
http://www.physicsclassroom.com/class/circles/u6l4a.cfm
Math of Galilean mechanics
I
d = vt
I
in such a case the body continues to move at constant
speed ⇒inertia
I
motion is parallel to earth’s surface, therefore circular
I
thus natural for objects to travel in circular orbits
uniform velocity
uniform acceleration (starting from 0 velocity)
d=
I
1 2
at
2
thrown object vs. dropped object . . .