1. Orion Nebula

2. Homework #1 is due tomorrow, Thursday, September 15, 5:00 pm Homework #2 will be posted shortly A number of out-of-class activities will be posted to the class website later this week.

3. Kepler's Laws 1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus. 2. The Law of Areas: Planets move faster in their orbit the closer they are to the Sun. 3. The Law of Periods: Planets on larger orbits take longer to complete an orbit than planets smaller orbits.

4. Kepler’s First Law Each planet’s orbit around the Sun is an ellipse, with the Sun at one focus. x 2 /a 2 + y 2 /b 2 = 1 Eccentricity e 2 = 1 - b 2 /a 2 Semiminor axis = b Semimajor axis = a The circle is a special form of an ellipse

5. Orbits of inner planets perihelion (green dot) aphelion (red dot) Orbits change color when they pass through the ecliptic plane Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Orbits of outer planets perihelion (green dot) aphelion (red dot)

6. Kepler’s Second Law ● A planet moves along its orbit with a speed that changes in such a way that a line from the planet to the Sun sweeps out equal areas in equal intervals of time. ● Consequence: planets move faster when they are closer to the sun and, conversely, planets spend more time in the more distant parts of their orbits A good animation demonstrating this law can be found at: www.physics.sjsu.edu/tomley/Kepler12.html

7. Comet orbits: highly eccentric, spend most of their time in the outer parts of their orbits

8. Kepler’s Third Law The ratio of the cube of a planet’s average distance from the Sun “a” to the square of its orbital period “P” is the same for each planet. Consequence: Planets with larger orbits have longer orbital periods. a 3 / P 2 = constant The constant is the same for all planets A good animation demonstrating this law can be found at: www.physics.sjsu.edu/tomley/Kepler3.html

9. a 3 / P 2 = constant Earth: a = 1 AU, P = 1 year So, if we measure the size of a planet’s orbit in AU and its orbital period in Earth years, then constant in the 3rd Law is 1 AU 3 yr -2 Jupiter: a = 5.203 AU, P = 11.86 years

10. Kepler’s First Law of planetary motion states that A)an imaginary line joining the Sun and planet sweeps out equal areas in equal times B)the further a planet is from the Sun, the faster it moves in its orbit C)the orbits of planets are ellipses D)the further a planet is from the Sun, the slower it moves in its orbit

11. Kepler’s First Law of planetary motion states that A)an imaginary line joining the Sun and planet sweeps out equal areas in equal times B)the further a planet is from the Sun, the faster it moves in its orbit C)the orbits of planets are ellipses D)the further a planet is from the Sun, the slower it moves in its orbit

12. Kepler’s Second Law of planetary motion states that A)as a planet orbits the Sun, it moves faster the closer it is to the Sun B)a planet on a larger orbit orbitsthe Sun more slowly than a planet with a smaller orbit C)the orbits of planets are ellipses

13. Kepler’s Second Law of planetary motion states that A)as a planet orbits the Sun, it moves faster the closer it is to the Sun

14. Kepler’s Third Law of planetary motion states that A)the further a planet is from the Sun, the faster it moves in its orbit B)an imaginary line joining the Sun and planet sweeps out equal areas in equal times C)the further a planet is from the Sun, the longer it takes to complete a full orbit D)the orbits of planets are ellipses

15. Kepler’s Third Law of planetary motion states that A)the further a planet is from the Sun, the faster it moves in its orbit B)an imaginary line joining the Sun and planet sweeps out equal areas in equal times C)the further a planet is from the Sun, the longer it takes to complete a full orbit D)the orbits of planets are ellipses

16. Which of the following is a contradiction of Kepler's Laws of planetary motion? A planet in a highly eccentric orbit spends most of its time in the outer parts of its orbit. A planet orbiting in a circular orbit. An inferior planet having a shorter orbital period than the Earth's orbital period. Planets have their smallest velocity when they are nearest the sun.

17. Which of the following is a contradiction of Kepler's Laws of planetary motion? A planet in a highly eccentric orbit spends most of its time in the outer parts of its orbit. A planet orbiting in a circular orbit. An inferior planet having a shorter orbital period than the Earth's orbital period. Planets have their smallest velocity when they are nearest the sun.

18. GeocentricHeliocentric Two models of the Universe

19. A hallmark of science is that theories are testable

20. Which model more accurately depicts nature?  Both make predictions for the apparent motions of the Sun, planets and stars.  The Heliocentric model, with modifications incorporating Kepler’s Laws, gives more accurate predictions  But, the Geocentric model might be made more accurate through appropriate modifications.  Need additional predictions that clearly differentiate between the two models. (need tests)

21. Contemporary with Kepler was Galileo Galilei (1564-1642) the “founder of experimental science” ● First person known to point a telescope at the sky ● He wanted to connect the physics understood on earth with objects in the heaven

22.  Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body) (Some of) Galileo’s Observations

23.  Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)  Sunspots (sun not “perfect”) (Some of) Galileo’s Observations

24.  Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)  Sunspots (sun not “perfect”)  Rotation of sun (Some of) Galileo’s Observations

25.  Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)  Sunspots (sun not “perfect”)  Rotation of sun  Moons of Jupiter (Heavenly bodies existed which did not orbit the earth) (Some of) Galileo’s Observations

26.  Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)  Sunspots (sun not “perfect”)  Rotation of sun  Moons of Jupiter (Heavenly bodies existed which did not orbit the earth)  Phases of Venus: the two models of the Universe made two very different predictions. (Some of) Galileo’s Observations

27. Phases of Venus

28. Galileo’s observation of the phases of Venus was the final evidence that buried the geocentric model. Geocentric Heliocentric No gibbous or full phases!All phases are seen! Galileo observed all phases!

29. With Galileo’s observations, the revolution begun by Copernicus was nearly complete…  The structure of the universe had been totally changed.  The motions of the planets were understood, at least from a geometrical perspective.  Earth was no longer a “special” place in the universe.  However, there were no physical underpinnings for the model – it was an empirical model, i.e., derived from observations  The crowning achievement was yet to come - discovering the laws of nature that naturally lead to the newly determined structure.

30. Sir Isaac Newton (1642-1727) Derived the relationships between motion and forces (Laws of Motion) Invented calculus Connected gravity and planetary forces

31. Universal Law of Gravitation Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.

32. This force is always attractive and it applies to ALL objects possessing mass!

33. ● Extending Kepler’s Law #1, Newton found that ellipses were not the only orbital paths. Orbital Paths from Law of Gravitation ● All orbits are “conic sections” – ellipse (bound) – parabola (unbound) – hyperbola (unbound)

35. The Center of Mass In Kepler's Laws, the Sun is fixed at a point in space (a focus of an ellipse) and the planet revolves around it. Why is the Sun privileged? Kepler had mystical ideas about the Sun, endowing it with almost god-like qualities that justified its special place. Newton demonstrated that the the Sun does not occupy a privileged position and in the process he modified Kepler's 3rd Law.

36. The center of mass is familiar to anyone who has ever played on a see-saw. The fulcrum point at which the see-saw will exactly balance two people sitting on either end is the center of mass for the two persons. m 1 d 1 = m 2 d 2

37.  Newton realized that in the planet-Sun system the planet does not orbit around a stationary Sun (a planet exerts as much gravitational force on the Sun as the Sun does on a planet).  Instead, Newton proposed that both the planet and the Sun orbited around the common center of mass for the planet-Sun system.  This led Newton to modify Kepler's 3rd Law. Recall Kepler’s 3rd law:P 2 / a 3 = constant F g = Gm 1 m 2 /d 2

38. P 2 = 4  2 a 3 / G (m 1 + m 2 ) G is known as the universal gravitational constant. Newton’s Version of Kepler’s Third Law If you can measure the orbital period of two objects (P) and the distance between them (a), Then you can calculate the sum of the masses of both objects (m 1 + m 2 )

39. Forces and Motion

40. A body in motion remains in motion and a body a rest remains at rest unless acted upon by an outside force. F = ma (= rate of change of momentum) For every applied force, a force of equal size but opposite direction arises. Newton's Laws of Motion

41. Scalars and Vectors Scalar: a quantity described solely by its size (and units) Vector: a quantity described by its size AND direction

42. speed – rate at which an object moves [e.g., m/s]. A scalar quantity. velocity – an object’s speed AND direction, [e.g.,10 m/s east]. A vector quantity. acceleration – a change in an object’s velocity, i.e., a change in speed OR direction [m/s 2 ]. A vector quantity.

43. Momentum (p) – the mass of an object times its velocity (p=mv) Force (f) – anything that can cause a change in an object’s momentum As long as the object’s mass does not change, a force causes a change in velocity, or an acceleration (a) Force, momentum, and acceleration are all vectors

44. Newton’s First Law of Motion A body in motion remains in motion and a body at rest remains at rest unless acted upon by an outside force. If the net force acting on an object is zero, then there is no change in the object’s motion. OR

45. The change in a body’s velocity due to an applied force is in the same direction as the force, and is proportional to the force, but is inversely proportional to the body’s mass. F = ma Or F = rate of change of momentum Newton’s Second Law of Motion

46. Because force is a vector, forces only affect motion in the direction of the force. Motion perpendicular to the force is unchanged.

47. A planet is always changing its direction of motion. Newton’s second law therefore states that a force must be acting on the planet. Gravity provides this force. Gravity & Orbits

48. F = ma can be rewritten to show that for a given force, the acceleration is inversely proportional to the mass: a = F / m

49. Do not confuse mass and density Mass = amount of matter Density = amount of matter per volume Higher density means more matter packed into same volume

50. Law of Conservation of Momentum If the net force acting on an object is zero, then the total momentum of a system remains constant. Momentum: p = mv

51. Newton’s Third Law of Motion “For every applied force, a force of equal size but opposite direction arises” or For every action there is an equal and opposite reaction

53. Each attracts the other by the same size force, but in opposite directions