1/5/2017

Lesson Objectives • Describe Kepler's three laws of planetary motion. • Solve problems using Kepler's laws. • Explain the effects of Earth, the moon, and the Sun on each other.

Earth-Moon-Sun System Section 6-2

Kepler’s First Law

Johannes Kepler

• The orbits of planets are ellipses with the Sun at one focus

• 1571-1630 • Built on Nicolaus Copernicus’s heliocentric model of the solar system • Analyzed twenty years of data collected by Tycho Brahe • Developed three laws of planetary motion

Ellipses

Elliptical Orbit Vocabulary

Co-vertex Minor Axis Vertex

Major Axis Focus

Center

Focus

Vertex

• Perihelion: The point on an object’s orbit closest to the star • Aphelion: The point on an object’s orbit furthest from the star • Semi-major Axis (): Half of the longer axis – Half the distance from perihelion to aphelion – Average distance an object is from the star it orbits

Co-vertex

1

1/5/2017

Kepler’s Second Law

Kepler’s Second Law

• The speed of a planet varies, such that it sweeps out equal areas in equal time frames.

Kepler’s Second Law

Kepler’s Third Law

• Distance from sun changes, since elliptical • Gravitational force changes, since  = • Tangential speed changes, since  =

  

 

• The square of the orbital period, , is directly proportional to the cube of the average distance from the Sun, . ∝  • Comparing two objects orbiting the same central body:

   =  

Newton’s Version of Kepler’s 3rd Law

You-Try #1 • Use the data provided to determine the time it takes Mars to orbit the Sun. • Earth’s orbital period = 1.00 years • Earth’s average distance from the Sun = 1.00 AU • Mars’s average distance from the Sun = 1.52 AU

= • • • •

4  

= orbital period  = universal gravitational constant  = mass of the central body = semi-major axis of the orbit (the average distance between the orbiting object and the central body)

2

1/5/2017

Rearranging =

   

You-Try #2

4  

   = 4

• Saturn’s moon Mimas has an orbital period of 82,800 s at a distance of 1.87 × 10" m from Saturn. Determine Saturn’s mass.

Simplified Kepler’s 3rd Law

You-Try #3

 =



∙ $%& = • = orbital period, measured in Earth years • $%& = mass of the star, measured in solar masses, '⊙

• Determine the orbital period of Venus, measured in Earth years. The semi-major axis of Venus’s orbit is 1.08 × 10-- m = 0.723 AU.

– 1 '⊙ = 1.989 × 10+ kg = mass of the sun

• = semi-major axis of the orbit, measured in astronomical units, AU. • An astronomical unit (AU) is the average distance from the Earth to the Sun, 1.496 × 10-- m.

You-Try #4 • Saturn orbits the Sun at an average distance of 1.43 × 10- m. Determine Saturn’s orbital period, measured in Earth years.

You-Try #5 • An exoplanet is observed orbiting a 5.7 solar mass star at an average distance of 3.2 AU. What is the orbital period of this exoplanet?

3

1/5/2017

You-Try #6 • What is the orbital period of the moon around Earth? Earth’s mass is 5.97 × 10  kg. The semi-major axis of the moon’s orbit is 3.83 × 10" m. Convert your answer to days.

Earth and Moon • Moon’s orbit around Earth is nearly circular. • Has equal rotational and orbital periods due to tidal locking. • This is why the same side of the moon is always facing Earth.

You-Try #7 • What is the moon’s rotational period? The radius of the moon is 1.76 × 104 m. The rotational tangential speed of the moon is 4.63 m/s. Convert your answer to days.

Tides • The Moon pulls the closer side of the Earth more strongly than the far side of the Earth. • This stretches out the Earth’s oceans. • As Earth rotates, the stretching changes, leading to ocean tides. • The sun has a similar, but smaller, effect.

Unit 6 Assignments • Read textbook chapter 14 (pages 199-209) – Page 209 #1-8, 11-17

• 6-1 Practice Problems • 6-2 Practice Problems

4

062 PowerPoint - Earth-Moon-Sun System - 6.pdf

Page 1 of 4. 1/5/2017. 1. Earth-Moon-Sun System. Section 6-2. Lesson Objectives. • Describe Kepler's three laws of planetary. motion. • Solve problems using ...

139KB Sizes 0 Downloads 342 Views

Recommend Documents

This is a Test of the Powerpoint System
Immediate goal. > To build computer systems that can process text and speech more intelligently computer language language. Understanding. Generation ...

The Planets & Our Solar System PowerPoint PDF.pdf
The Planets & Our Solar System PowerPoint PDF.pdf. The Planets & Our Solar System PowerPoint PDF.pdf. Open. Extract. Open with. Sign In. Main menu.

Bus # 062.pdf
Page 1 of 4. DRIVER. NAME: JACQUIE DUNCAN 62. STOP # TIME FRIDAY STOP ADDRESS. START 6:50 1612 N. 700 E. (DBG). 1 7:08 24995 W. ROCK CRK RD. 2 7:13 24991 W. ROCK CRK RD. 3 7:17 23959 W. ROCK CREEK RD. 4 7:22 11183 W. 3470 S. W. RIVER RD. 5 7:23 3473

BCS-062.pdf
SHTTP works by negotiating encryption scheme types used between client and server. Page 3 of 3. BCS-062.pdf. BCS-062.pdf. Open. Extract. Open with.

powerpoint template -
Four SICA project meeting. Imperial College, London, 24 May 2013. Florin Grigorescu MD, PhD ... Consortium. Taragona. Cantazaro. Rome. Bologna. Bucharest.

מצגת של PowerPoint - Editorial Express
Overconfidence. Introduction. Example. Results. Variants. Evolution. Model. People report 80 .... Principal wants agents with the most accurate private signals to.

PowerPoint bemutató - Tárki
Dec 15, 2012 - Data archives. Scientific analytic papers. Survey instruments. Administrative data collection. Other forms of data collection. Outline: the structure of the .... Form of access (web access, file transfer, remote statistical analysis ..

062-066 vol 9.pdf
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. 062-066 vol 9.Missing:

PowerPoint bemutató - Tárki
Dec 15, 2012 - (Tarki Social Research Institute, Budapest) with contributions by .... Project websites ... content, frequency, etc. so that all will understand the.

Circular 062-15 - Bourse de Montréal
Jun 3, 2015 - self-certification process as determined by the Derivatives Act (R.S.Q., chapter I-14.01). Process for Changes to the Rules. The Bourse is ...

מצגת של PowerPoint
information → a few overconfident agents survive. ▫. Second-best outcome; compensates another bias (e.g., excess risk aversion): Wang (91), Blume & Easly ...

Presentación de PowerPoint
Job Description: GRADIANT, Galician Research and Development Center in Advanced Telecommunications, leader in the generation and transfer of ICT knowledge in Galicia, needs to incorporate a ... Work with a qualified team with flexible schedules. •

PowerPoint Sunusu -
Flexible Production. • Specialization of labor. • Keynesian Institutions are failed. • Labor unions are getting out of picture. • Social security system declined.

016 PowerPoint Slides.pdf
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. 016 PowerPoint ...

PowerPoint bemutató - Tárki
Dec 15, 2012 - (Tarki Social Research Institute, Budapest) with contributions ... Social monitoring and social reporting. Scientific community .... Project websites ...

PowerPoint Handout
During the PPT activity, take notes on Romanticism from the screen so that during our class ... Romantic Period, take notes on the pieces of art and poetry.

17-03-062. Corrigendum to unnumbered20170317090608.pdf ...
LEARNING AREAS NAME OF TRAINERS DESIGNATION scHooL/ oFrIcE. Agriculture/ Industrial. Arts. MTi Nueve De Febrero ES. Araling Panlipunan Ceasar A. Nachor BPS SDO. Edukasyon. Pagpapakatao. SA Merlina Pandaan MTI Jose Fabella MS. English Ramon R. Belardo

Circular 062-15 - Bourse de Montréal
Jun 3, 2015 - Toll-free within Canada and the U.S.A.: 1 800 361-5353 ... The Bourse is authorized to carry on business as an exchange and is recognized as ...