Physics 125 Solar System Astronomy

Transcription

1 Physics 125 Solar System Astronomy James Buckley Lecture 7 The Physics behind Astronomy

2 Reading Quiz 4 -What conservation law explains why an ice skater spins faster when she pulls in her arms? -From the NYT article, what is one possible reason for the difference in appearance of the near and far side of the moon? (Just a sentence about the root cause would suffice)

3 Physics

4 Vectors Scalars are quantities like temperature or mass (just a magnitude no direction) Vectors are quantities like velocity, acceleration, displacement (they have both a magnitude and direction) We denote a vector in an equation by putting a little arrow over top of the quantity, or we draw an arrow with a length and direction. ~v There are some special vectors called unit vectors that have a magnitude of 1 and a direction. They are like pure direction! Some examples include the unit vectors along the x and y axes: ˆx, ŷ A UNIT wearing his hat!

5 Apples and Oranges What is one apple + 3 oranges? You can t add apples and oranges. and you can t add different vectors (e.g., what is a velocity of 6 m/sec + an acceleration of 35 m/sec2) and you can t add vectors and scalars (e.g., what is a velocity of 6 mph in the x-direction + 55 degrees celcius?) But you can add like vectors, and here is how...

6 Adding Vectors You add vectors like you add dogs, head to tail

7 Relative Velocities 100 mph 60 mph A train heads northeast at 100 mph. A baseball pitcher throws a ball off the train in the northwest direction at 60 mph. What velocity does the ball appear to make with respect to the ground? Solve graphically (no math!)

8 Vectors N Relative length of velocity vectors are proportional to the speed - say 1 inch per 50 mph Resultant vector comes from putting the tail of each vector in the sum to the head of the last vector. The sum of vectors goes from the tail of the first to head of the last. ~v ball = 60 mph (NW) W ~v total = ~v train + ~v ball ~v total S ~v train = 100 mph (NE) E Relative directions in your drawing are the same as the relative directions on the ground - just lable the directions, or define an x and y axis A train heads northeast at 100 mph. A baseball pitcher throws a ball off the train in the northwest direction at 60 mph. What velocity does the ball appear to make with respect to the ground? Solve graphically (no math!)

9 Multiplying Vectors ~A B cos ~B You can multiply two vectors to get a scalar by finding the length of one vector projected on the other and taking the product of the two - this is called the scalar product ~A ~B = AB cos( )

10 Multiplying Vectors ~A ~ B B sin ~A ~B You can multiply two vectors to get a vector by multiplying the length of one vector perpendicular to another vector, then defining the direction as the direction that a screw would propagate as you turned the first vector A into the second B. or using the right hand rule ~A ~ B = AB sin( )

11 Newton s First Law and Momentum An object at rest remains at rest, an object in motion remains in motion unless acted upon by a uniform force. Momentum defined as the product of mass times velocity is conserved. p = mv Momentum is a vector, with a magnitude and direction ~p = m ~v The force required to stop a moving object is proportional to the momentum. Force time = change in momentum

12 Angular Momentum! ~L = mvrˆn v m r ( ~ L = m ~r ~v) Angular momentum is the product of mass times distance from the axis of rotation times the angular velocity. What direction does it point? Can you find a special direction that is constant throughout the motion? What does it take to stop a spinning object. Is it harder with more mass? Is it harder if it is spinning faster? Is it harder if the mass is more spread out? (Yes)

13 Torque Torque = Force Distance Just like it takes a big Force to bring an object with a large momentum to rest, It takes a big Torque to bring a spinning object with a large angular momentum to rest. Here s how it works - someone slams a door on you - it is better to push near the hinge or near the edge of the door? To stop the angular momentum you need a big torque - the product of force and distance

14 Torque as a Vector Force is a vector - it is pretty clear what direction to assign to a force. If you push in the positive x-direction, the force goes in that direction. Imagine a force acting at a distance on a door. What is the direction of the torque? How does it compare with the angular momentum? ~L ~T ~r ( ~ T = ~r ~ F ) ~F Torque time = change in angular momentum

15 Summarizing Force time = change in momentum ~F t = ~p ~F = ~p t ~F t = m ~v ~F = m ~v t ~F = m~a Torque time = change in angular momentum ~T t = L ~ ~T = ~ L t

16 Energy Energy is what makes matter do stuff Energy can take the form of Kinetic energy (the energy of motion) K = 1 2 mv2 or Potential energy, for example a mass m held at some height z above a surface, then dropped: U = mgz Or the potential energy of a spring, that is compressed by a distance x F = kx U = 1 2 kx2 Thermal energy (or heat) is in the form of random motion. The Temperature is equal to the average kinetic energy with a constant of proportionality known as Boltzmann s constant

17 Conservation of Energy We can define any quantity we want, but conserved quantities are useful Momentum, Angular Momentum and Energy are all conserved - making them very useful in understanding a range of physical phenomena

18 Energy Chemical bonds are kind of like compressed springs. For example, plants convert solar energy to little compressed-spring-like molecules. We eat these, add oxygen, and get some of that potential energy back out. Bonds in nuclei are also like compressed springs for nuclei more massive than iron - wanting to split apart. Or for light nuclei it is kind of like putting things in a potential well (deeper hole) reducing potential energy when protons and neutrons are combined to form Helium. E=mc 2 - so do compressed springs weigh more?!

19 Discussion Question: A compressed spring (A) weighs more than an uncompressed spring, (B) less than an uncompressed spring (C) the same as an uncompressed spring and with the same inertia, (D) weighs the same but has a larger inertial mass?

20 Tidal Locking Near Side (we always see this face from Earth) Near Side (we always see this face from Earth) Moon is tidally locked to the Earth, we always see the same side (left) never the far side (right). How did this come to be? If the moon were not tidally locked, it would be compressed one way, then the next. All of this crunching dissipates energy and the moon is only happy when it is locked in place!

21 Summary Read Sections 4.4 and 4.5 Think about it: Say their is a planet in another solar system around a smaller sun. Is it more or less likely to become tidally locked? If it is tidally locked, how might this affect the evolution of life?

22 Units of distance 1 a.u. = 93 million miles = km A light year is defined as the distance that light travels in one years time or 1ly sec m/sec = km = 63, 000 a.u. A parsec is defined as the distance at which 1 a.u. would subtend one second of arc. A star at distance d (measured in parsecs) will be observed to have a parallax angle of θ (in arcsecs) given by the formula: ( ) θ 1 arcsec = d 1 1 parsec 1 p.c. = 3.26 ly Physics Lecture 3 p. 12/12

23 Kepler s laws Kepler s First Law: A planet orbits the Sun in an ellipse with the sun at one focus of the ellipse. r + r =2a Kepler s Second Law: A line connecting a planet to the Sun sweeps out equal areas in equal time intervals. Kepler s Third Law: P 2 = a 3 Physics Lecture 3 p. 7/12

24 Parallax distance S un Earth! Mercury

25 Distance to Planets Parallax distance S un Earth! Mercury Venus transit, APOD July 20, 2004 Relative scales of the solar system Planet Period (years) Approx. Radius (a.u.) Earth Mercury Venus Mars Jupiter Venus transit, Crow Observatory, June 5, 2012

26 List # 1 2 Map of nearby stars 3 Future and past 4 See also 5 References 6 External links Nearest Stars System Designation Star Star # Stellar class Apparent magnitude (m V ) Absolute magnitude (M V ) Epoch J Right ascension [2] Declination [2] Solar System Sun G2V [2]!26.74 [2] 4.85 [2] variable: the Sun travels along the ecliptic Alpha Centauri (Rigil Kentaurus; Toliman) Proxima Centauri (V645 Centauri) # Centauri A (HD ) # Centauri B (HD ) EZ Aquarii B 16 M? List of nearest stars and parallax [2] [2] EZ Aquarii C 16 M? (from Wikipedia) [2] [2] Parallax [2][3] Arcseconds(±err) Distance [4] Light-years (±err) Additional references 1 M5.5Ve [2] [2] 14 h 29 m 43.0 s!62 40! 46" (0 29)" [5][6] (16) [7] 2 G2V [2] 0.01 [2] 4.38 [2] 14 h 39 m 36.5 s!60 50! 02" 2 K1V [2] 1.34 [2] 5.71 [2] 14 h 39 m 35.1 s!60 50! 14" (1 17)" [5][8] (68) 2 Barnard's Star (BD a) 4 M4.0Ve 9.53 [2] [2] 17 h 57 m 48.5 s ! 36" (1 00)" [5][6] (109) 3 Wolf 359 (CN Leonis) 5 M6.0V [2] [2] [2] 10 h 56 m 29.2 s ! 53" (2 10)" [5] (390) 4 Lalande (BD ) 6 M2.0V [2] 7.47 [2] [2] 11 h 03 m 20.2 s ! 12" (0 70)" [5][6] (148) 5 Sirius (# Canis Majoris) 6 Luyten Sirius A 7 A1V [2]!1.46 [2] 1.42 [2] 06 h 45 m 08.9 s!16 42! 58" (1 28)" [5][6] (289) Sirius B 7 DA2 [2] 8.44 [2] [2] Luyten A (BL Ceti) Luyten B (UV Ceti) 9 M5.5Ve [2] [2] 01 h 39 m 01.3 s!17 57! 01" (2 70)" [5] (631) 10 M6.0Ve [2] [2] 7 Ross 154 (V1216 Sagittarii) 11 M3.5Ve [2] [2] 18 h 49 m 49.4 s!23 50! 10" (1 78)" [5][6] (512) 8 Ross 248 (HH Andromedae) 12 M5.5Ve [2] [2] 23 h 41 m 54.7 s ! 30" (1 10)" [5] (36) 9 Epsilon Eridani (BD!09 697) 13 K2V [2] 3.73 [2] 6.19 [2] 03 h 32 m 55.8 s!09 27! 30" (0 79)" [5][6] (27) 10 Lacaille 9352 (CD! ) 14 M1.5Ve 7.34 [2] 9.75 [2] 23 h 05 m 52.0 s!35 51! 11" (0 87)" [5][6] (31) 11 Ross 128 (FI Virginis) 15 M4.0Vn [2] [2] 11 h 47 m 44.4 s ! 16" (1 35)" [5][6] (49) EZ Aquarii (GJ 866, Luyten 789-6) Procyon (# Canis Minoris) EZ Aquarii A 16 M5.0Ve [2] [2] 22 h 38 m 33.4 s!15 18! 07" (4 40)" [5] (171) Procyon A 19 List of nearest stars - Wikipedia, the free encyclopedia has 8 planets has two proposed planets F5V- IV [2] 0.38 [2] 2.66 [2] 07 h 39 m 18.1 s ! 30" (0 81)" [5][6] (32) [2] [2] [2]

27 Tropics of Cancer and Capricorn Sun is directly overhead on the Summer Solstice along a line of geographic latitude known as the tropic of cancer. Further north, it may never reach this altitude angle.

28 Celestial Sphere Template

29 Earth Template