This document discusses Johannes Kepler's three laws of planetary motion and how they were developed based on data collected by Tycho Brahe. It also explains key terms like ellipses, eccentricity, and barycenter. Kepler's first law states that planets orbit in ellipses with the Sun at one focus. The second law describes how a line connecting a planet to the Sun sweeps out equal areas in equal times. Kepler's third law relates the orbital periods of planets to the semi-major axes of their orbits. Finally, it introduces Isaac Newton and his law of universal gravitation.

1. Think About It…
How would Earth be different
if its orbit was more oval
than circular?

2. Earth’s Orbit and
Kepler’s Laws
How do Kepler’s laws describe
Earth’s orbit?

3. Johannes Kepler (1571-1630)
 Kepler based his three laws of planetary
motion on the earlier foundations provided
by Copernicus
 Kepler was the assistant to Tycho Brahe
 Brahe afraid that Kepler would surpass
him assigned him the daunting task of
solving Mars orbit. This Martian data was
the key piece needed to solve the motion
of all the planets

4. Kepler’s Laws…
Johannes Kepler,
working with data
painstakingly
collected by Tycho
Brahe (from 1576-
1601) without the aid
of a telescope,
developed three laws
which described the
motion of the planets
across the sky.
Unless otherwise noted, the info on the slides on Kepler’s laws was taken from the
following website: http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html
http://www.nmspacemuseum.org/halloffame/images.php?image_id=131

5. II. A-1.Kepler’s First Law…
• The Law of Orbits or Law of Ellipses: All planets
move in elliptical orbits, with the sun at one
focus.
• An ellipse is an oval shape that is centered on
two points (called foci) instead of a single point.

6. What is an ellipse?
• An ellipse has two foci.
• An ellipse has two axes.
– The long one is called the major axis
• Half of it is called a semi-major axis
– The short one is called the minor axis.

7. HANDS-ON ACTIVITY!!
• Planetary Orbits:

8. Orbital Period
• The orbital period of a planet is the length
of time it takes for it to travel a complete
orbit around the sun. (a year!)

9. Orbit Eccentricity…
 The eccentricity of an ellipse can be defined as the ratio
of the distance between the foci to the major axis of the
ellipse. The more eccentric an orbit, the more of an oval
it is.
 The eccentricity is zero for a circle.
 Pluto (no longer considered a planet by astronomers)
has a large eccentricity.
http://solarsystem.nasa.gov/multimedia/display.cfm?IM_ID=175

10. Examples of Ellipse Eccentricity
Planetary orbit
eccentricities
Mercury .206
Venus .0068
Earth .0167
Mars .0934
Jupiter .0485
Saturn .0556
Uranus .0472
Neptune .0086
Pluto .25

11. Kepler’s Second Law…
• The Law of Areas: A line that connects a planet to
the sun sweeps out equal areas in equal times.
http://www.mathacademy.com/pr/prime/articles/kepler/index.asp

12. • Planets move fastest when they are at
their closest point to the Sun (called
perihelion) and slowest when they are at
their farthest point from the Sun (called
aphelion).

13. Kepler’s Third Law…
• The Law of Periods: The square of the period of any planet
is proportional to the cube of the semimajor axis of its orbit.
• This law arises from the law of gravitation. Newton first
formulated the law of gravitation from Kepler's 3rd law.

14. .
• What does this mean? This means that if
you know how much time a planet's orbit
around the Sun takes, you can easily
know it's average distance from the Sun,
or vice-versa!
• The closer a planet is to the Sun, the less
time it takes for the planet’s orbit.

15. • Kepler's Third Law is written like
this: P2=a3
• P=the orbital period in Earth years
• A= the length of the semimajor
axis (average distance from the
Sun) in Astronomical Units.

16. Barycenter and Earth’s Orbit…
• The law of universal
gravitation states…
– that every pair of
bodies in the universe
attract each other with
a force that is…
• proportional to the
product of their masses
and
• inversely proportional to
the square of the
distance between them.

17. Barycenter and Earth’s Orbit…
• A planet, such as Earth, actually orbits…
– a point between it and the Sun called the
center of mass
– This center of mass is called the barycenter.
http://www.barewalls.com/pv-605547_Barycenter-Diagram.html

18. Barycenter
• This is the point
between 2 objects
where they balance
each other.
• It is the center mass
where two or more
celestial bodies orbit
each other.
• The sun although the
center of the universe
is not stationary, it
moves as other
planet’s gravity “tug”
on it. But it never
strays too far from the
solar system’s
barycenter.

19. • The Effect of the Moon
• The moon has a noticeable effect on the
earth in the form of tides, but it also affects
the motion and orbit of the earth. The
moon does not orbit the center of the
earth, rather, they both revolve around the
center of their masses called the
barycenter. This is illustrated in the
following animation.

20. Barycenter and Earth’s Orbit…

21. Isaac Newton
• 1666, England (45 years
after Kepler).

22. 9/27/2023
Newton’s Law of
Universal Gravitation
• The apple was attracted
to the Earth
• All objects in the Universe
were attracted to each
other in the same way the
apple was attracted to the
Earth

23. 9/27/2023
Newton’s Law of
Universal Gravitation
• Every particle in the Universe attracts every
other particle with a force that is directly
proportional to the product of the masses and
inversely proportional to the square of the
distance between them.
2
2
1
r
m
m
G
F 

24. 9/27/2023
Universal Gravitation
• G is the constant of universal gravitation
• G = 6.673 x 10-11 N m² /kg²
• This is an example of an inverse square law
• Determined experimentally
2
2
1
r
m
m
G
F 

25. 9/27/2023
Universal Gravitation
• The force that mass 1 exerts
on mass 2 is equal and
opposite to the force mass 2
exerts on mass 1
• The forces form a Newton’s
third law action-reaction
 The gravitational force exerted by a uniform
sphere on a particle outside the sphere is the
same as the force exerted if the entire mass of the
sphere were concentrated on its center