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Kepler’s Laws
AP Physics C
Mrs. Coyle
Geocentric View Points
Aristotle (Greek) 384-322 BC
Ptolemy (Alexandrian Greek) 85-65AD
Heliocentric Viewpoints
Aristarchus (Greek)310-230 BC
Copernicus (Poland and Italy) 1473-1543
Galileo Galilei (Italian) 1564-1642
Compromise Theory: The Sun orbits
the Earth, but the remaining planets
orbit the Sun.
Brahe passed along his observations
to Johannes Kepler, his assistant.
German Astronomer
Kepler’s First Law (Law of Orbits):
Planets move in elliptical orbits with the Sun at one of the
focal points.
 e=c/a
 For
a circle e=0
 Pluto has the highest e=0.25
in our system.
 Earth’s e=0.017
Elliptical orbits are allowed for bound object
An unbound object would pass by and not
Paths that are parabolas(e = 1) and hyperbolas (e > 1)
A line from the sun to a planet sweeps out
equal areas in equal lengths of time.
The torque caused by the
gravitational force on a planet is
zero because it is a central force
and the F is in the same direction
as the r vector.
 τ=dL/dt =0 , so L =constant
The square of the orbital period of a
planet is directly proportional to the
cube of the average distance of the
planet from the Sun.
T  Kr
K for our Solar
K  2.97 x10
s /m
T2 = (4π2 / GMs) r3 ,
K= 4π2 / GMs
1 Astronomical Unit (AU)= average radius of
the orbit of the earth about the sun.
When T is measured in earth years and r in AU
then K for our solar system =1 y2 / AU3 .
Hint: The gravitational force plays the role of
the centripetal force.
( _ T ___ )
( _ r ___ )
An asteroid revolves around the sun
with a mean orbital radius of three
times that of the earth. What is the
period of the asteroid in earth years?
Answer: 5.2y
Two same stars are orbitting about the
center of mass half way between them.
The orbital speed of each star is 220km/s
and the orbital period of each is 14.4
days. Find the mass M of each star.
Ans: 1.26x1032kg