# Opening for today… Kepler’s Laws of Planetary Motion Objective: Students will explain planetary motion using gravitational laws.

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Opening for today…

Kepler’s Laws of Planetary Motion Objective: Students will explain planetary motion using gravitational laws.

Background What is “Planetary Motion”? What makes up planetary motion? 365 days refers to…? 24 hours refers to…? Refers to how planets, like the Earth, move through space. All planets orbit a central star, this orbit is called it’s revolution. The Earth’s period (time duration) for 1orbit, or revolution, around the Sun. 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 Period 2 = 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 Eccentricity? Is a circle an ellipse? Ellipse length Ellipse height 2 focal points, called foci (plural) Refers to “flatness” of an ellipse. Value between 0 and 1. Circle has eccentricity of 0. Major axis 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’s speed around the Sun constant or varies? Earth’s distance from the Sun constant or varies? Earth, and all planets, but in an ellipse pattern. 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: P 2 =a 3 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 P 2 = ? 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 P 2 = ? 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 a 3 = 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: P 2 =a 3 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? P 2 =1.88 2 =3.53 P 2 =a 3 therefore a 3 =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)All planets move in the shape of an ellipse around the sun. 2)A line drawn from the planet to the sun sweeps out equal areas over equal time. 3)The square of a planet’s period of revolution is proportional to the cube of the planet’s mean distance.

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