Notes & Reminders

1. Notes & Reminders Homework #1 is due today. Quiz #1 will be the last 15 minutes of class on Tuesday, September 10 (mostly qualitative understanding, but any math problem will not require calculators). - will cover material through today’s lecture

2. Transits Transit of Venus: June 8, 2004 • On rare occasions, an inner planet will be perfectly aligned with Sun during inferior conjunction, causing a transit across Sun’s surface. • Venus transits in 8 year pairs separated by 113 years  last was June 5-6, 2012, not again until 2117/2125.

3. When and why do we have leap years? • The length of a tropical year is about 365.25 days (but not quite – 11 minutes less). • In order to keep the calendar year synchronized with the seasons, we must add one day every 4 years (February 29). • For precise synchronization, years divisible by 100 (e.g., 1900) are not leap years unless they are divisible by 400 (e.g., 2000).

4. How do we locate objects on the celestial sphere? • Each point in the sky corresponds to a particular location on the celestial sphere. • Analogous to latitude and longitude on Earth

5. Celestial Coordinates • Right ascension: like longitude on celestial sphere (measured in hours with respect to spring equinox) • Declination: like latitude on celestial sphere (measured in degrees above celestial equator)

6. Celestial Coordinates of Vega • Right ascension: Vega’s RA of 18h36m15s (out of 24h) places it most of the way around celestial sphere from spring equinox. • Declination: Vega’s dec of +3847’01’’ puts it almost 39 north of celestial equator (negative dec would be south of equator).

7. How do stars move through the local sky? • A star’s path depends on your latitude and the star’s declination. • The RA-Declination coordinate system moves with the sky over the course of a night as the Earth rotates!

8. Star Paths at North Pole • At the North Pole stars remain at same altitude as Earth rotates. • Star’s altitude above horizon equals its declination (you’ll never see stars rise/set!).

9. Star Paths at Equator • At the equator, all stars remain above horizon for exactly 12 hours each day. • Celestial equator passes overhead. See every star!

10. Star Paths in Northern Hemisphere • In north, stars with dec > (90 minus your latitude) are circumpolar (i.e., never set). • Celestial equator is in south part of sky.

11. Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

12. Basic Types of Energy • Kinetic (motion) • Radiative (light) • Potential (stored) Unit of Energy = Joule (or erg) 1 Joule = 1 kg m2/s2 = 1 Newton meter 1 erg = 1 g cm2/s2 = 1 dyne cm = 10-7 J

13. Kinetic Energy • Energy of motion (macroscopic objects) • Thermal energy (atomic and molecular motion)

14. Kinetic Energy of Motion Energy = ½ * m * v2 where m = mass v = velocity Any time an object is moving, it has kinetic energy.

15. Thermal Energy:the collective kinetic energy of many particles(for example, in a rock, in air, in water) Thermal energy is a form of kinetic energy. Thermal energy is related to temperature but it is NOT the same. Temperature is the average kinetic energy of the many particles in a substance – a measure of how fast the molecules of a substance are moving (Maxwellian velocity distribution). Velocity of moving (vibrating) molecules is dependent on their temperature.

16. Temperature Scales Kelvin scale is the preferred measure of temperature in astronomy. Kelvin = Celsius + 273 degrees Absolute zero: temperature at which all molecular motion ceases

17. Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends both on temperatureAND density. Example: Which would you rather put your hand in?

18. Don’t Confuse Temperature and Thermal Energy The Sun possesses a low-density corona with a temperature of 1 million degrees Kelvin. But the heat in the corona is not enough to warm up a cup of coffee  too few particles per volume! High temperature does not automatically imply high kinetic (thermal) energy! (Think hot air vs. hot water).

19. Radiative Energy Energy in the form of light or other form of electromagnetic radiation (more on this in Chapter 5) .

20. Potential Energy • Gravitational • Chemical • Elastic • 4) Mass-energy

21. Gravitational Potential Energy • On Earth, depends on: • object’s mass (m) • strength of gravity (g) • distance object could potentially fall • In astronomy, two objects at infinite distance are defined to have zero gravitational potential energy, and as they approach one another their gravitational potential energy becomes increasingly negative.

22. Gravitational Potential Energy • In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts. • A contracting cloud converts gravitational potential energy to thermal energy. Gravitational potential energy a large negative value Gravitational potential energy nearly zero (slightly negative)

23. Chemical Potential Energy • Energy in an unlit match is stored chemical potential energy. • Energy in food (breaking apart chemical bonds of starches, carbohydrates, etc.)

24. Elastic Potential Energy Coiled spring Stretched rubber band Stretched archer’s bow Bent diving board (just after diver lands on it)

25. Mass-Energy E = mc2 • A small amount of mass can release a great deal of energy • Concentrated energy can spontaneously turn into particles (for example, in particle accelerators) Amount of energy in a 1 kg rock could power all cars in the United States for a week. 0.1 kg of material

26. Conservation of Energy • Energy can be neither created nor destroyed. • It can change form or be exchanged between objects. • The total energy content of the Universe was determined in the Big Bang and remains the same today.

27. Conservation of Energy At top of arc, ball has lots of gravitational potential energy and little kinetic energy. Just before the ball hits the table, it has less gravitational potential energy, but more kinetic energy (it is moving faster). Conservation of energy tells us that sum of kinetic energy + gravitational potential energy of ball is the same at all times.

28. Conservation of Energy Near the Sun, planet has less gravitational potential energy and more kinetic energy (it is moving faster), than when planet is far away from the Sun (but potential energy + kinetic energy always a constant).

29. How do we describe motion? Precise definitions to describe motion: • Speed: Rate at which object moves • Example: 10 meters/second • Velocity: Speed and direction • Example: 10 meters/second, due east • Acceleration: Any change in velocity - units of speed/time2 (example: meters/secondper second) Speeding up and slowing down is an acceleration. Turning in your car is an acceleration because your direction is changing (even if your speed is constant).

30. Force and acceleration • Force = mass x acceleration • Accelerations are caused by forces • Everynet force will lead to an acceleration (change in velocity) • That’s why you feel a force on your body when you speed up, slow down, or turn a corner – you are changing your velocity, and a change in velocity is an acceleration.

31. For each of the following is there a net force on the object? • A car coming to a stop • A bus speeding up • An elevator moving at constant speed • A bicycle going around a curve • A moon orbiting Jupiter

32. For each of the following is there a net force on the object? • A car coming to a stop: Y • A bus speeding up: Y • An elevator moving at constant speed: N • A bicycle going around a curve: Y • A moon orbiting Jupiter: Y

33. Momentum • Linear momentum = mass* velocity - a force is needed to change momentum, which changes the velocity, which means an acceleration • Angular momentum = mass * velocity * radius - rotational momentum of spinning/revolving objects - a top spinning in place has no linear momentum, but it does have angular momentum - Earth has both two forms of angular momentum (spinning on its axis and motion around the Sun) We will talk about angular momentum throughout this course – understand it.

34. Why do objects move at constant velocity if no net force acts on them? Objects continue at constant velocity because of conservation of momentum. • The total momentum of interacting objects cannot change unless an external force is acting on them • Total gray ball + yellow ball momentum is conserved – it can be exchanged, but not destroyed (without an external force).

35. Conservation of Angular Momentum Angular momentum = mass * velocity * radius • The angular momentum of an object cannot change unless an external twisting force is acting on it. • Earth experiences no twisting force as it orbits the Sun, so its rotation and orbit will continue indefinitely. • Conservation of angular momentum is important for solar system formation, star formation, black hole accretion, etc., etc.

36. Angular momentum conservation also explains why objects rotate faster as they shrink in radius. • Mass * velocity * radius = constant • If radius (arm length) goes up, velocity must go down to conserve angular momentum • If radius (arm length) goes down, velocity must go up to conserve angular momentum • Angular momentum cannot be created or destroyed, only transferred between objects. Important concept!

37. Kepler’s 2nd Law is Simply a Restatement of the Conservation of Momentum Conservation of angular momentum: Mass * velocity * radius = constant m * v * r = constant If r goes down, v must go up If r goes up, v must go down (think of an ice skater pulling in her arms)

38. How did Newton change our view of the universe? • Realized the same physical laws that operate on Earth also operate in the heavens • one universe • Discovered laws of motion and gravity • Much more: experiments with light, first reflecting telescope, calculus… Sir Isaac Newton (1642–1727)

39. Not bad! • 1665: develops calculus (for gravitation, tides) • 1667: laws of optics • 1670ish: laws of gravitation This would be like one person discovering bacteria, penicillin, and DNA in the same 5-year period.

40. What are Newton’s three laws of motion? Newton’s first law of motion: An object moves at constant velocity unless a net force acts to change its speed or direction.

41. Newton’s second law of motion: Force = mass  acceleration The unit of force is the Newton or dyne: 1 Newton = 1 kg m/s2 (MKS) 1 dyne = 1 g cm/s2 (cgs) For circular motion: Fcentripetal = mv2/r

42. Newton’s third law of motion: For every force, there is always an equal and opposite reaction force. Note: Rocket exhaust pushing against the ground does not propel rockets! Conservation of momentum does.

43. The Acceleration of Gravity • All falling objects accelerate at the same rate (not counting friction of air resistance). • On Earth, g ≈ 9.8 m/s2: speed increases 10 m/s with each second of falling.

44. Newton’s Second Law and Gravity The Universal Law of Gravitation: • Every mass attracts every other mass. • Attraction is directly proportional to the product of their masses. • Attraction is inversely proportional to the square of the distance between their centers. G = Gravitational constant of Nature

45. g vs. G g: local acceleration due to gravity = 980 cm/s2 (9.8 m/s2) on surface of Earth (1/6th on surface of the Moon; 2.4x higher on surface of Jupiter) G: universal constant of Nature = 6.67 x 10-8 cm3/(g s2) or 6.67 x 10-11 m3/(kg s2) determined experimentally, same value everywhere in the Universe Mind your units! (always use cm – g – second or m – kg – second )!

46. Why do all objects fall at the same rate? g = • The gravitational acceleration of an object like a rock does not depend on its mass because Mrock in the equation for acceleration cancels Mrock in the equation for gravitational force.