Transcript Kepler`s Laws - Harnett County High Schools Wiki

Solar System Overview
Early Ideas
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It was assumed that the Sun, planets, and
stars orbited a stationary universe
This is known as a “geocentric” model,
which means Earth centered
Problem with this model though: doesn’t
explain all aspects of planetary motion
EX: normal direction for motion of planets
is toward the East as observed from
Earth; sometimes though a planet will
appear to move the opposite direction
across the sky in what is called retrograde
motion
Example of retrograde motion
Mars retrograde motion
 The search for an explanation for this
retrograde motion motivated early
astronomers to keep searching for a
better model of our solar system
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Heliocentric Model
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1543 Polish scientist Nicolaus Copernicus
suggested Sun was center of solar system
First time a sun-centered or “heliocentric”
model was proposed
In a heliocentric model, the inner planets
move faster in their orbits than the outer
planets do; as Earth bypasses a slower
moving outer planet it appears the outer
planet temporarily moves backward in the
sky
Retrograde Motion in Heliocentric
Model
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Heliocentric retrograde motion
Kepler’s First Law
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Ideas of Copernicus not originally
accepted by scientific community, but
within a century other astronomers found
evidence to support the heliocentric model
Using accurate data of planetary
observations, Kepler demonstrated each
planet orbits the Sun in a shape called an
ellipse instead of a circle
This is Kepler’s First Law
Kepler
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The orbits of planets are not circles
but oval-shaped curves called
ellipses!
Kepler
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Ellipse is oval shape centered
on two points instead of a
single point, like a circle
The two points are called the
foci (singular focus)
Each planet’s ellipse is a
different shape and size, and
the Sun is always at one focus
The major axis is the line that
runs through both foci and is
the maximum diameter of the
ellipse
Half the length of a major
axis is called the semi-major
axis
Kepler
The semi-major axis is the average
distance between the Sun and the
planet
 For the Sun and the Earth, it is 1.496
x 108 km, or 1 astronomical unit
(AU)
 Average distance between Sun and
each planet are measured in
astronomical units
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Kepler’s Laws
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A planet in a elliptical orbit is not at a
constant distance from the Sun
When planet is at closest distance to the
Sun in its orbit, it is at perihelion
When a planet is at farthest distance away
from the Sun in its orbit, it is at aphelion
The shape of a planet’s elliptical orbit is
defined by eccentricity (ratio of distance
between foci to the length of the major
axis)
Kepler’s Laws
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Eccentricity values range from 0-1
0 is a perfect circle
Nearly 1 is a very elongated oval
1 is equal to a parabola
Most planets have orbits not very
eccentric and are close to being circles
Orbital period – time required for a planet
or body to travel a complete elliptical orbit
around the Sun
Kepler’s Laws
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Planetary Motion
Gravity and Orbits
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Newton realized any two bodies attract each other with
a force that depends on their masses and the distance
between the two bodies
This relationship is called the law of universal
gravitation
The greater the distance between two bodies, the less
the force between them is
The smaller the distance between two bodies, the
greater the force between them is
Barycenter
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Newton also determined each planet
orbits a point between it and the Sun
called the barycenter
The barycenter is the balance point
between two orbiting bodies (where all
the mass of an object is concentrated)
This is similar to the pivot point on a
see-saw
If one of two bodies orbiting each other
is more massive than the other, the
center of mass is closer to the more
massive body
If two bodies are similar in mass, their
center of mass is near the middle
position between them
For any planet and the Sun, the center
of mass is just above the surface of the
Sun (or within the Sun) because the Sun
is more massive than any planet
Barycenter
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Barycenter is closer to the end of the broom
The Earth does not revolve around the Sun,
but rather the barycenter!