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Do Now Think!

As an aging astronomer, you must decide whether to pass on your valuable data to a rival scientist or take it to the grave with you. Explore the origins of Kepler's laws and the eccentricities of planetary orbits.

kennethjackson
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Do Now Think!

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  1. Do Now Think! Read this & be ready to discuss it 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. 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

  3. 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

  4. 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?

  5. 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

  6. Page 3 Kepler’s Laws of Planetary Motion

  7. 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

  8. Ellipse is: a closed curve around two fixed points, called foci; shaped like an oval or flattened circle Foci are: 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

  9. 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

  10. 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

  11. 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

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

  13. 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:

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

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

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

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

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

  23. 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

  24. 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

  25. 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

  26. 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

  27. Page 6 Kepler’s 2nd Law • Essentially what Kepler discovered was the planets change speed during their orbit around the Sun Interactive Animation #1- excellent Interactive Animation #2 Glencoe video explains the law Animation of all 3 Laws

  28. 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)

  29. 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

  30. Increasing speed Page 6 HINT: Study one know the other by default Perihelion Aphelion Closest to the Sun Furthest from the Sun Decreasing speed Jan. 4th July 4th Max. speed Min speed Max. Gravitational Attraction Min. Gravity LARGEST SMALLEST diameter

  31. 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 Essentially Kepler is saying: The further a planet is to the sun, the longer it takes to revolve around the Sun Try Kepler’s Third Law Calculator

  32. 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?

  33. 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) Animation- Review of all 3 Laws

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

  35. 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 Page 7 Major achievements: • 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

  36. 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

  37. 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

  38. 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.

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

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

  41. 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)! v Different cases of acceleration: • 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)

  42. 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

  43. The Universal Law of Gravity • Any two bodies are attracting each other through gravitation • The force is proportional to the product of their masses • And inversely proportional to the square of their distance: Mm F = - G r2 (G is the Universal constant of gravity.)

  44. Understanding Orbital Motion The universal law of gravity allows us to understand orbital motion of planets and moons What are 2 factors that affect the amount of gravity (gravitational force) between two object? Mass of both objects & the distance between them

  45. Kepler’s Third Law Explained by Newton Balancing the force (called “centripetal force”) necessary to keep an object in circular motion with the gravitational force expression equivalent to Kepler’s third law, Py2 = aAU3 Neil Degrasse Tyson talking about Newton 1:57- funny

  46. Understanding Orbital Motion The universal law of gravity allows us to understand orbital motion of planets and moons: Example: • Earth and moon attract each other through gravitation. Dv • Since Earth is much more massive than the moon, the moon’s effect on Earth is small. v v’ • Earth’s gravitational force constantly accelerates the moon towards Earth. Moon F • This acceleration is constantly changing the moon’s direction of motion, holding it on its almost circular orbit. Earth

  47. Center of Mass (SLIDESHOW MODE ONLY)

  48. Orbital Motion (2) In order to stay on a closed orbit, an object has to be within a certain range of velocities: Too slow => Object falls back down to Earth Too fast => Object escapes Earth’s gravity

  49. Orbital Motion (3) Geosynchronous Orbits

  50. Newton’s Cannon (SLIDESHOW MODE ONLY)

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