Download Kepler Notes

Opening for today…
Kepler’s Laws
of Planetary Motion
• Objective: Students will explain planetary
motion using gravitational laws.
Background
•What is “Planetary Motion”?
•Refers to how planets, like the
Earth, move through space.
•What makes up planetary
motion?
•All planets orbit a central star,
this orbit is called it’s
revolution.
•365 days refers to…?
•The Earth’s period (time
duration) for 1orbit, or
revolution, around the Sun.
•24 hours refers to…?
•The period for 1 rotation of the
Earth.
Kepler the Man
Who is Johannes Kepler?
What did he discover?
His 3 Laws of Planetary Motion
German theological student,
mathematician, science fiction writer.
Using mentor’s observations, and own
study of Mars, discovers elliptical
orbits.
Law #1 Planets move in an elliptical
orbit
Law #2 Planets move faster when they
are closer to the Sun, slower when
farther away.
Law #3 Period2 = semimajor axis 3
(Period - the planets period of
revolution)
Kepler’s Three Laws of
Planetary Motion
1) Planets orbit the Sun in ellipse pattern
2) A line drawn from any planet to the Sun
sweeps out equal areas over equal time.
3) Very complex, but in short, the square of a
planets period is proportional to the cube of
its average distance from the Sun.
(the period squared = semimajor axis cubed)
Demonstration of Law #1
Notes: What in the world is an ellipse???
Goal: Take notes over introductory concepts on planetary motion and elliptical
orbits
• An ellipse is a close curve in which the sum of the
points (foci) inside the ellipse is always the same.
Facts About Law #1
• Ellipse properties
•2 focal points, called foci (plural)
• Eccentricity?
•Refers to “flatness” of an ellipse.
Value between 0 and 1.
• Is a circle an ellipse?
•Circle has eccentricity of 0.
• Ellipse length
•Major axis
• Ellipse height
•Minor axis
Demonstration of Law #2
Notes: Planets move faster when???
Goal: Take notes over introductory concepts on planetary motion and elliptical
orbits
• Suppose that it takes the planet the same amount of time to go
between positions C and D as it did for the planet to go
between positions A and B. Then the planet must move faster
when it is closer to the sun and slower when it is farther away.
Facts About Law #2
• Earth’s orbit around the sun
Circle or Ellipse?
•Earth, and all planets, but in an
ellipse pattern.
• Earth’s speed around the Sun
constant or varies?
• Earth’s distance from the
Sun constant or varies?
•The speed is not constant.
•Distance varies slightly.
Brief Tutorial
• Period of ANY planet is calculated in years.
• The semi-major axis is a planets average
distance from the SUN.
• P=period of revolution
• A=average distance measured in AU
Notes: Period, axis; Can we say LOST???
Hang in there…we will get through this!
Goal: Take notes over introductory concepts on planetary motion and elliptical
orbits
• Let’s do a little practice problem:
• P2=a3
• P is the period of revolution and a is the
semimajor axis of the orbiting planet
• If Mars period of revolution is 1.88 years
what is its semimajor axis?
• First, we cube 1.88 years for the P2 = ?
• 3.53 sound about right???
Notes: Period, axis; Can we say LOST???
Hang in there…we will get through this!
Goal: Take notes over introductory concepts on planetary motion and elliptical
orbits
• Let’s do a little practice problem:
• First, we cube 1.88 years for the P2 = ?
• 3.53 sound about right???
• Now, we take this value, 3.53, and we
equate it to the cube of the semi-major
axis. So a3 = 3.53
• To find the AU, we have to take the
CUBE root of 3.53….
• 1.52 AU sound about right? Check page
Notes: Period, axis; Can we say LOST???
Hang in there…we will get through this!
Goal: Take notes over introductory concepts on planetary motion and elliptical
orbits
• Let’s do a little practice problem:
• P2=a3
• P is the period of revolution and a is the semimajor axis of
the orbiting planet
• If Mars period of revolution is 1.88 years what is its
semimajor axis?
• P2=1.882=3.53
• P2=a3 therefore a3=3.53
• So a = 3√3.53 =1.523
• Now you try one. What is the semimajor axis of Mercury
if its period of revolution is 88 days?
Vocabulary to Remember
• Orbit
• Ellipse
• Eccentricity
• Period
• How a planet moves
around a central star.
• Circle that is
somewhat flattened.
• Value from 0 to 1,
circle is 0.
• How much time an
orbit takes.
Let’s Look At The Lab!
Write in the purpose for this lab:
Students will explain planetary motion using
gravitational laws.
Write in Kepler’s 3 Laws:
1)
2)
3)
All planets move in the shape of an ellipse around the
sun.
A line drawn from the planet to the sun sweeps out equal
areas over equal time.
The square of a planet’s period of revolution is
proportional to the cube of the planet’s mean distance.