Transcript Slide 1

Geometry of Orbits – Kepler’s 2nd Law & Newton’s Gravity
The Law of Equal Area in Equal Time
To understand Kepler’s second law you need to have some understanding of
Newton’s Law of Gravity.
Visit the following website: Newton’s Law of Gravity
http://www.westhamptonbeach.k12.ny.us/Teachers/Cohen/sciweb/earthscience/a
stro_new/newtongrav.html
You will visit a special website (see below). Read it through. It is not long but try to gain
an understanding of the important components of the gravity equation:
•
The relationship between gravity and the Masses of objects.
•
The relationship between gravity and the Distance between objects.
When you are through reading the information on the website answer the following
questions:
1. Describe what happens to gravitational force when you increase or decrease the
mass of one of the objects?
2.
Determine
thetorelationship
Thought
by many
be one of between mass and gravity described in #1 above.
3.
Describe
what happens
to gravitational force when you increase or decrease the
the most
influential
scientists
distance between the two objects?
in our entire history.
4. Determine the relationship between mass and gravity described in #3 above
Geometry of Orbits
designed by Johann Kepler early 1600’s
Kepler’s Law #2. Equal Area in Equal Time:
An imaginary line joining a planet and the Sun sweeps out equal areas in
equal intervals of time (Why?)
Watch and listen carefully to this movie. Can you determine when the planet
is traveling faster (closer or further from the Sun) in its orbit and when is it
traveling slower (closer or further from the Sun)?
1. Why would the planet travel faster in one part of its orbit?
2. Why does it travel slower in the other part?
3. Does this variation in speed determine how much area it covers in the
orbit?
• Look at this image and animation. Determine at
which position the earth would be traveling
faster and at which position it would be traveling
slower. of Orbits
Geometry
• Why
doesOrbit
the earth change its orbital speed?
Earth’s
Elliptical
• During which season are we closer to the Sun?
Does this make any sense? (Actually the
change in distance is so slight compared to the
great distance between the Earth and the Sun
that there is only a slight variation in temperature
from Perihelion to Aphelion). Remember, the
eccentricity of the earth is very slight 0.0017!
Geometry of Orbits – Kepler’s 3rd law
The Harmonic Law
•
The ratio of the squares of the periods (of revolution) for two planets is
equal to the ratio of the cubes of their semimajor axes.
•
Click on the button for “Kepler’s 3rd Law” demo.
Kepler 3rd Law Demo
Where:
• P = the period of revolution of the planet
• R = the radius of the ellipse (semimajor axis)
•
So!! What does this all mean?? Watch the animation again if you don’t understand.
•
Once you understand everything in these PowerPoint presentations you can try some of the questions in your
Earth Science Review Book, file: “Earth and its Moon” page 680 questions #4 – 7, page 683 #17, 18, and page 684
#20.