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Do Now Think!

Explore the life of an aging astronomer who must decide whether to share 30 years of valuable data with a rival scientist or take it to the grave. Delve into the historical context of Tycho Brahe and Johannes Kepler's groundbreaking work on planetary motion, specifically focusing on Kepler's First Law of Planetary Motion: The Ellipse Law.

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Do Now Think!

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  1. Do Now Think! You are an astronomer who has collected data on the motions of the solar system for 30 years. Your life goal has been to understand and explain the motions of the planets, but so far you have been unable to achieve your goal. You are now old, sick, and coming to the end of your life. Your rival, a scientist who is extremely smart, wants to use your data to complete your work. *Will you let him take your 30 years of data or will you take it with you to the grave?

  2. Historical Overview

  3. Page 3 Tycho Brahe (1546-1601) • Wealthy Danish nobleman with a gold nose • Best naked observer ever!!! • Observed and recorded 25 years worth of celestial motions • Designed and constructed the most precise astronomical measurement instruments to study the sky • Supported Helio- centric model

  4. Johannes Kepler- 1571-1630 • Johannes Kepler was a mathematician/astronomer • Meets the best astronomer of the time: Tycho Brahe & they decide to work together • Kepler became Tycho’s assistant • Mathematically experimented with circle orbits of planets Page 3

  5. Origin of Kepler’s 3 Laws • Why might Tycho Brahe have hesitated to hire Kepler? • Why do you suppose he appointed Kepler his scientific heir?

  6. Origin of Kepler’s 3 Laws • After Tycho's death, Kepler worked with Tycho's records and began to study planetary motion • Most extensive study was motion of Mars • Mathematically discovered that Mars orbits the Sun in an ellipse, with Sun at one focus

  7. Page 3 Kepler’s Laws of Planetary Motion

  8. Page 3 Kepler’s 1st Law Titled the: Ellipse Law States each planet moves around the Sun in an ellipse with the Sun located at one focus Planet Focus Focus Sun Sun

  9. Ellipse: A closed curve around two fixed points, called foci; shaped like an oval or flattened circle Foci: Two fixed points within the ellipse Think of the ellipse as a smiley face with the two eyes being the foci Page 3 Kepler’s 1st Law: Definitions Focus Focus

  10. Page 3 Kepler’s 1st Law Label the parts of the Ellipse: Orbit: The path of an object revolving around another object; such as the Earth around the sun. Major Axis: The longest diameter (axis) of an ellipse, running through the center and foci. Planet Focus Focus Sun Sun D= Origin Minor Axis

  11. Page 4 Kepler’s 1st Law: Definitions • Eccentricity: is a numerical value used to describe the degree of flatness or “ovalness” of an ellipse • How out of round the shape is • *Eccentricity of a perfect circle= 0 Comet Straight line= 1 Circle= 0

  12. Page 4 Eccentricities of Ellipses 1) 2) 3) e = 0.1 e = 0.2 e = 0.02 5) 4) e = 0.4 e = 0.6

  13. Page 4 Eccentricity of an Ellipse • Where to look: • Look at your Earth Science Reference Table (ESRT) • Page 1 • Under Equations

  14. Page 4 Calculating eccentricity of an ellipse: When the distance between foci get larger what happens to the ellipse? length of major axis (e) eccentricity = (d)distance between foci (L)length of major axis Formula:

  15. Page 4 Rules for Calculating Eccentricity of an Ellipse • Drop the units • Round to the thousandth place • Answer must be a number between 0-1

  16. Page 4 Example #1 • If the distance between the foci is 5.7 cm and the major axis is 20.2 cm, calculate the eccentricity. (round to nearest thousandth) Eccentricity= Distance between foci length of the major axis = .282 5.7 cm 20.2 cm

  17. Page 5 Using Eccentricity Formula Mars has two moons; Phobos and Deimos. The distance between the foci for Phobos is 281 km. The major axis is 18,800 km. Determine the eccentricity of Phobos’s orbit. (round to the nearest thousandth) eccentricity = distance between foci length of major axis eccentricity= 281 km 18,800 km eccentricity= 0.015

  18. Page 5 Example#2 • If the distance between the foci is 281 km and the major axis is 18,800 km, calculate the eccentricity. (round to nearest thousandth) Eccentricity= Distance between foci length of the major axis = .015 281km 18,800

  19. Page 5 Example#3 • If the distance between the foci is 234 km and the major axis is 46,918 km, calculate the eccentricity. (round to nearest thousandth) Eccentricity= Distance between foci length of the major axis = .005 234km 46,918

  20. Calculating eccentricity Worksheet Page 4 .417 .585 .468 .263

  21. Page 5 As the distance between foci increases, the shape of the ellipse becomes more elliptical or oval d. Relationship:

  22. Page 5 Which planet has the least perfectly circular orbit? Mercury

  23. Page 5 Which planet has the most perfectly circular orbit? Venus

  24. Kepler’s 1st Law Summary The Ellipse Law Simply states the orbits of the planets are ellipses and the Sun is located at one focus Eccentricity is a numerical value given to describe the ovalness of an ellipse

  25. Kepler’s 1st Law Summary • Eccentricity: is a numerical value used to describe the “ovalness” of an ellipse • How out of round the shape is • *Eccentricity of a perfect circle= 0 Comet Straight line= 1 Circle= 0

  26. Kepler’s 1st Law How did Kepler's first law of planetary motion alter the Copernican Heliocentric (Sun centered) model? • It changed the perfect circles to ellipses • It placed the Sun at one focus of each orbit instead of the center of the Solar System

  27. Page 6 Kepler’s 2nd Law • Titled: Equal Time, Equal Area States as a planet revolves around the Sun a straight line joining the center of the planet and the center of the Sun, the planets sweeps out equal areas in space in equal intervals of time Eccentricity Website

  28. Page 6 Kepler’s 2nd Law • Essentially what Kepler discovered was the planets change speed during their orbit around the Sun Interactive Animation #2- excellent model Glencoe- Good 2nd Law Explanation Excellent Summary of all 3 Laws-Another Good interactive 2nd law

  29. Page 6 When does a planet move slowest in its orbit? When closest to Sun (perihelion) When furthest from Sun Video When does a planet move fastest in its orbit? (aphelion)

  30. Page 6 Kepler’s 2nd Law • What does Kepler's second law indicate about the orbital speed of a planet? • A planet moves at its fastest when it is closest (perihelion) to the Sun

  31. Increasing speed Page 6 Perihelion Aphelion Jan. 4th July 4th Decreasing speed Max. speed Min speed Max. Gravitational Attraction Min. Gravity MAX Apparent Diameter Min diameter HINT: Study one know the other by default Page 17

  32. Page 7 Kepler’s 3rd Law • Titled The Harmonic Law States a planet’s orbital period (P) squared is proportional to its average distance from the sun (au) cubed: Period= The orbit of a planet; 1 revolution (Py = period in years; aAU = distance in AU) Py2 = aAU3 What does it mean? The further a planet is to the sun, the longer it takes to revolve around the Sun Try Kepler’s Third Law Calculator

  33. Origin of Kepler’s 3 Laws • For 70,000 years Astronomers couldn’t explain the motions of the solar system until Kelper’s 3 Laws • How do you think the church reacted and felt when this discovery was purposed? • If you were a person living in the time these ideas were purposed would you believe Kepler? Why?

  34. Re-Cap What are Kepler’s 3 Laws of Planetary Motion? • The Ellipse Law: Each planet moves around the Sun in an ellipse with the Sun at one focus • Equal areas in space in equal intervals of time (Planets change speed in orbit: Closer to sun= faster) • Period squared (2)= Distance cubed (3) (faster period of revolution when closer to sun) Brahe/Kepler Rap

  35. Historical Overview

  36. Galileo Galilei (1564 – 1642) • Invented the modern view of science: Transition from a faith-based “science” to an observation-based science. • Greatly improved on the newly invented telescope technology. (But Galileo did NOT invent the telescope!) • Was the first to meticulously report telescope observations of the sky to support the Copernican Model of the Universe.

  37. Major Discoveries of Galileo (2) • Surface structures on the moon; first estimates of the height of mountains on the moon

  38. Major Discoveries of Galileo • Moons of Jupiter • (4 Galilean moons) (What he really saw) • Rings of Saturn (What he really saw)

  39. Major Discoveries of Galileo (3) • Sun spots (proving that the sun is not perfect!)

  40. Major Discoveries of Galileo (4) • Phases of Venus (including “full Venus”), proving that Venus orbits the sun, not the Earth!

  41. Historical Overview

  42. Page 7 A New Era of Science Mathematics as a tool for understanding physics

  43. Isaac Newton (1643 - 1727) • Building on the results of Galileo and Kepler • Adding physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler Major achievements: Page 7 • Invented Calculus as a necessary tool to solve mathematical problems related to motion • Discovered the three laws of motion • Discovered the universal law of mutual gravitation

  44. Page 7 Newton’s Laws of Gravity 1. All objects possess gravity and will pull all other objects with a certain gravitational force 2. The mass of an object determines the amount of gravitational force that an object possess. greater mass= greater gravitational force

  45. Page 7 Newton’s Laws of Gravity 3. The gravitational force between 2 objects changes as the distance between them changes As distance ↑, gravitational force ↓ Show Peter has own gravity clip from desktop Neil deGrasse Tyson on Newton 1:47

  46. Newton’s Laws of Motion #1 • A body continues at rest or in uniform motion in a straight line unless acted upon by an outside force. An astronaut floating in space will continue to float forever in a straight line unless some external force is accelerating him/her.

  47. Newton’s Laws of Motion (2) • The accelerationa of a body is inversely proportional to its massm, directly proportional to the net forceF, and in the same direction as the net force. a = F/m F = m a

  48. Acceleration of Gravity Acceleration of gravity is independent of the mass (weight) of the falling object! Iron ball Wood ball

  49. Velocity and Acceleration Acceleration (a) is the change of a body’s velocity (v) with time (t): a a = Dv/Dt Velocity and acceleration are directed quantities (vectors)! Different cases of acceleration: v • Acceleration in the conventional sense (i.e. increasing speed) • Deceleration (i.e. decreasing speed) • Change of the direction of motion (e.g., in circular motion) Feather vs. Hammer on the Moon

  50. Newton’s Laws of Motion (3) • To every action, there is an opposite and equal reaction. M = 70 kg V = ? The same force that is accelerating the boy forward, is accelerating the skateboard backward. m = 1 kg v = 7 m/s

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