Transcript Gravitation and the Waltz of the Planets

Gravitation and the Waltz of
the Planets
Chapter 4
Kepler’s Laws
First Law: Planets orbit in
ellipses with the Sun at one
focus
 Second Law: Planet – Sun line
sweeps out equal areas in
equal time
 Third Law: There is a
relationship between a planets
orbital period (P) and its
average distance from the Sun
(a), P2 = a3

First Law Meaning


An ellipse is like an elongated circle. Instead of
one point in the center, an ellipse has two points
called foci.
For planetary motion then, each planet does not
orbit the Sun in a circle and thus the distance
from the planet to the Sun varies.
Second Law Meaning


A planet’s orbital velocity varies.
The planet orbits the Sun faster at perihelion
and slower at aphelion.
Third Law Meaning



‘P’ is the period of a
planets orbit
‘a’ is the average
distance from the Sun,
or the semimajor axis
A planet that is farther
away from the Sun
has a slower orbital
velocity and thus it
takes longer to go
around once.
Newton’s Laws



First Law: “Inertia” – A body remains at
rest, or moves in a straight line at
constant speed, unless acted upon by
a net external force.
Second Law: If there exists a net
external force, there is an acceleration
produced that is proportional to the
force. F = ma
Third Law: For every force, there is an
equal and oppositely directed reaction
force.
Examples
Newton

Newton’s Law of Universal Gravitation:
Masses attract each other with a force that
is directly proportional to their masses and
inversely proportional to their separation
distance.
m1m2
Fgrav  G 2
r
Newton and Kepler

Newton’s form of Kepler’s Third Law: Is
more general than K3, and applies in any
situation where two masses orbit each
other.

Ex. Two stars, two galaxies, a star and its
galactic center, a star and planet, a planet
and a moon, etc….
 4
 3
P 
a
 Gm1  m2 
2
2