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Kepler’s Breakthrough
• Kepler used Brahe’s data to develop three
laws that could be used to describe
planetary motion.
• All of the laws are based upon an
understanding of the ellipse.
After Tycho Brahe’s death,
Johannes Kepler (pictured here
with Tycho in the background)
used Tycho’s observations to
deduce the three laws of
planetary motion.
KEPLER’S THREE LAWS OF PLANETARY MOTION
LAW #1. The orbit of a planet around the Sun is an ellipse with the
Sun at one focus.
The amount of elongation in a planet’s orbit is defined as its
orbital eccentricity. An orbital eccentricity of 0 is a perfect
circle while an eccentricity close to 1.0 is nearly a straight line.
In an elliptical orbit, the distance from a planet to the Sun
varies. The point in a planet’s orbit closest to the Sun is
called perihelion, and the point farthest from the Sun is
called aphelion.
KEPLER’S THREE LAWS OF PLANETARY MOTION
LAW #2: A line joining the planet and the Sun sweeps out equal
areas in equal intervals of time.
Planet moves slower
in its orbit when
farther away from
the Sun.
Planet moves faster
in its orbit when
closer to the Sun.
KEPLER’S THREE LAWS OF PLANETARY MOTION
LAW #3: The square of a planet’s sidereal period around the Sun is
directly proportional to the cube of its semi-major axis.
This law relates the amount of time for the planet to complete one
orbit around the Sun to the planet’s average distance from the Sun.
If we measure the orbital periods (P) in years and distances (a) in
astronomical units, then the law mathematically can be written as P2
= a3 .
Newton’s Physics—Motion and
Gravity
• Newton’s Three Laws of Motion
– A body remains at rest or moves in a straight line at a
constant speed unless acted upon by an net outside
force.
– The acceleration of an object is proportional to the
force acting on it and dependent upon its mass.
– Whenever one body exerts a force on a second body,
the second body exerts and equal and opposite force on
the first body.
• Newton’s Universal Law of Gravitation
– Fgravity = G x m1m2
d2
Newton’s Physics—Angular
Momentum
• Angular momentum depends upon three things
1. Speed of rotation or revolution
2. Mass
3. How spread out the mass is
• Angular momentum is related to the amount of energy
stored in an object due to its rotation and revolution
• Angular momentum is also related to the sideways or
tangential velocity of an orbiting object
• Angular momentum is conserved--as the spread of mass
decreases, the rotation rate must increase.
• This is important to the understanding of the formation of
stars and the solar system.
The Newtonian Physics of
Earth Orbiting the Sun
4
3
5
Not to scale
As a result, centripetal force
(which means centerseeking force) due to
gravity, accelerates or pulls
Earth toward the Sun.
Earth has less mass, less
inertia, same gravitational
force; thus, more easily
accelerated
Sun
1
E
2
Sun contains 99.9% of
mass in the solar
system, tremendous
inertia or resistance to
acceleration.
Sun and
Earth experience equal
and opposite forces of
gravity
However, due to tangential velocity as a result of angular momentum gained during formatio
the solar system, the Earth moves away at the same time it is pulled toward the Sun.
Planetary configurations are defined for the location of the planets as
they orbit the Sun from our point of view.
Orbital Periods for Planets
• Sidereal Period
– The true orbital period of a planet with respect
to the background stars.
• Synodic Period
– The period of time that elapses between two
successive identical configurations as seen from
Earth (example: for Venus, greatest eastern
elongation to greatest eastern elongation)
The cycle of these positions for a synodic period is
different from the actual orbital period of the planet
around the Sun (a sidereal period) because both the
Earth and the planet orbit around the Sun.
©1996-2002 Scott R. Anderson
Last update: 2002 October 22
Please send questions, comments, suggestions, or corrections to
[email protected].
Determining the Distances to
Astronomical Objects
Parallax
• Parallax view: the variation in angle that occurs
when viewing a nearby object from different
places.
• Importance of parallax: Danish astronomer
Tycho Brahe reasoned that the distance of
the object may be determined by measuring
the amount of parallax. A smaller parallax
angle meant the object was further away.
The apparent
change in the
location of an
object due to the
difference in
location of the
observer is called
parallax.
Their views
differ because
of a change in
position
relative to the
mountain
Because the parallax of the “star” was too small to
measure, Tycho knew that it had to be among the other
stars, thus disproving the ancient belief that the “heavens”
were fixed and unchangeable.
http://www.astronomy.ohiostate.edu/~pogge/Ast162/Movies/p
arallax.gif
http://instruct1.cit.cornell.edu/cours
es/astro101/java/parallax/parallax.h
tml
Limitation to using parallax
• Eventually, the parallax shift will no longer
be measurable.
• This is because the distance is too great for
the effect to be observed.