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Announcements

Announcements. CAPA Set #7 due Friday at 10 pm This week in Section  Assignment 4: Circular Motion & Gravity Finish reading all sections of Chapter 5, start Chapter 6 in Friday’s lecture this week Reminder  Exam #2 on Tuesday, October 11

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Announcements

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  1. Announcements • CAPA Set #7 due Friday at 10 pm • This week in Section  • Assignment 4: Circular Motion & Gravity • Finish reading all sections of Chapter 5, start Chapter 6 in • Friday’s lecture this week • Reminder  Exam #2 on Tuesday, October 11 • See course web link (“exam info”) for details • Reminder about office hours … • Nagle (Monday 2-3 in office, Wednesday 1:45-3:45 pm help room) • Kinney (Thursday 4-5 pm help room) • Uzdensky (Tuesday 11am-noon help room)

  2. Lab Make-Up Procedure • You must complete at least 5 of the 6 labs to receive a passing grade in this course. • If you missed a lab, you can make it up during one of two Review/Lab make-up weeks: • October 24-28 (labs 1-3) • December 5-9 (labs 4-6) • Even if you don’t need to make up a lab, you still mustattend your section those weeks for the Review Recitation. • To make up a lab, contact your TA ahead of time. You will need to arrange attending twice: (1) for lab make-up and (2) for the review recitation. You can attend any other section (in addition to your regular section), if you have that section’s TA permission in advance. Contact: Professor Uzdensky if there are any questions.

  3. Earth at the Center of Everything Geocentrism - Epicyles - Equant - Deferent Claudius Ptolemaeus (Ptolemy) 90 – 168 AD

  4. Heliocentrism (Sun at the Center) Nicolaus Copernicus 1473-1543 Johannes Kepler 1571-1630 Tycho Brahe 1546-1601 De revolutionibusorbiumcoelestium (On the Revolutions of the Celestial Spheres) Heliocentrism Three Laws astronomical observations Epitome astronomia Copernicanae (Epitome of Copernican Astronomy)

  5. Kepler’s Laws of Planetary Motion Law #1: The orbit of each planet is an ellipse, with the Sun at one focus.

  6. Elliptical Geometry The sum of the distances from any point P on the ellipse to those two foci is constant and equal to the major diameter ( PF1 + PF2 = 2a ).

  7. Kepler’s Laws of Planetary Motion Law#2: An imaginary line drawn from each planet to the Sun sweeps out equal areas in equal times.

  8. Room Frequency BA Clicker Question Notice how a planet with an elliptical orbit moves closer to and further away from the Sun. The point of closest approach to the Sun is called perihelion. The furthest point is called aphelion. At which position is the asteroid moving at the largest magnitude velocity? Far left (aphelion) Far right (perihelion) Top Bottom Same velocity magnitude everywhere

  9. Kepler’s Laws of Planetary Motion Law #3: The ratio of the square of a planet’s orbital period is proportional to the cube of its mean distance from the Sun.

  10. What is the relationship betweenvelocity and orbit Radius? Consider F=ma in the radial direction: +inward Force of Gravity Only Rs Condition for Circular Motion Re h elevation Rs = Re + h

  11. Room Frequency BA Clicker Question Satellite 1 is in circular orbit about the Earth and is moving with tangential speed v1. Satellite 2 is also in orbit but with speed v2 > v1. Satellite 2’s orbit radius is: Bigger than Satellite 1’s Smaller than Satellite 1’s Unclear from the information given. Rs Re h elevation Rs = Re + h

  12. Room Frequency BA Clicker Question Satellite 1 is in circular orbit about the Earth with radius R1. Satellite 2 is also in circular orbit with a radius R2 and a speed twice that of Satellite 1. What is true about the radii? R1 = 2 x R2 R1 = ½ x R2 R1 = 4 x R2 R1 = ¼ x R2 Unclear from the information given. Rs Re h elevation Rs = Re + h

  13. Room Frequency BA Clicker Question Eliminate velocity in place of period (T) Period T Rs Which of the following correctly presents the relationship between Rsand T? Re h elevation Rs = Re + h

  14. Recall Kepler’s Empirical Value

  15. Knowledge of a planet’s period (easy to measure) allows us to determine it orbital radius. Where is Mars? Mars is 1.52 times as far away as the earth is from the sun.

  16. Exoplanets Upsilon Andromedae is a binary star located about 44 light-years away from the Earth. The primary star is a yellow-white dwarf star that is younger than the Sun. There is a second star that is a red dwarf in a wide orbit. As of 2010, four confirmed extrasolar planets have been discovered. (b)  (0.0595)3/(4.61)2=9.9x10-6 AU3/days2 (c)  (0.832)3/(241.3)2=9.9x10-6 AU3/days2 (d)  (2.53)3/(1278.1)2=9.9x10-6 AU3/days2 (e)  (5.24)3/(3848.8)2=9.7x10-6 AU3/days2

  17. Discovery of accelerating universe! Need a large scale repulsion force (not gravity). No one knows what it is – just called Dark Energy!

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