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ASTR 2010 Cosmology

ASTR 2010 Cosmology. Week 4: Lecture 9: Gravity and orbits: The 4 Forces of Nature. Announcements Should have Read Ch 4 : “The Universe Through Motion & Gravity” Meet in Fiske dome on Wednesday (not here !!!) Today:

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ASTR 2010 Cosmology

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  1. ASTR 2010 Cosmology Week 4: Lecture 9: Gravity and orbits: The 4 Forces of Nature

  2. Announcements • Should have Read Ch 4: • “The Universe Through Motion & Gravity” • Meet in Fiske dome on Wednesday • (not here !!!) • Today: • Newton: “Laws” of Motion • Gravity • Kepler’s “laws” of planetary orbits • Stable objects & systems: • balance of opposing forces

  3. Stable Systems Balance of opposing forces Planets:Gravity v.s. stiffness of solid matter Solar System:Gravity vs. orbit motion Stars:Gravity v.s. pressureof hot gas (sustained by nuclear fusion) Galaxies:Gravity v.s. rotation (spirals) Gravityrandom motions (ellipticals) Atoms:Electromagnetism v.s. wave-nature of electrons Nucleii:Nuclear forces v.s. wave nature of quarks 4 “forces”: Gravityinverse square (weak) Electro-magnetism“ “ (strong) Strong nuclear forceshort-range (10-13 cm) Weak Nuclear forceshort-range (10-15 cm)

  4. Orbits

  5. M51 - the “Whirlpool Galaxy” Distance: 23 million light years Speed: + 600 km /sec gravity v.s. orbital motion of stars

  6. M13 (Globular star cluster of ~ 10 Gyr old stars) M13 in Hercules: (~ 10 billion year old swarm of stars) gravity v.s. random motion of stars

  7. M 87 (Giant Elliptical galaxy) gravity v.s. random motion of stars

  8. Perseus Cluster of Galaxies: Distance: 230 million l.y. Speed: + 5200 km /sec NGC 1275

  9. Structure of (Ordinary) Matter: Balance of opposing forces Electro-magnetism wave nature of electrons Strong nuclear force vs. quarks waves Weak nuclear force “up” v.s. “down” quarks

  10. Strong Nuclear Force Fusion of hydrogen (H) Into Helium (He) • 4 1H => 4He + 26.7 MeV • - Occurs at T ~ 1.5 x 107 K • - Main energy source of stars ! • 0.007% of the mass converts • to energy via • E = mc2 E = 0.007 M(He)c2 ~ 4 x10-5 erg / He

  11. Weak Nuclear Force • Decay of free neutrons: mn ~ 1.67 x 10-24 g • ….in ~10 minutes ! Down quark => up quark

  12. Outline: Gravity and Orbits - Laws of Motion (Newton’s mechanics) position, velocity, acceleration mass, inertia, force, centrifugal force - The inverse square law: Newton’s law of gravity falling apples, and the moon - Escape speed velocity needed to escape - Orbits balance between gravity and centrifugal force - Kepler’s Laws of planetary motions

  13. Motion - Velocity (or speed): V =[change in position] / [ time interval] Example: Car moving. Covers 100 meters in 60 seconds 10 m = 104 cm V = 104 / 60 = 166 cm/sec = 1.67 m/sec = 65 ft/sec = 44.7 mi/hr - Acceleration: a =[change in velocity] / [time interval] Example: Drop a rock in Earth’s gravity …. Speed increases by 980 cm/sec every second (until air resistance sets in) a = 980 cm s-2 (= 32 ft sec-2)

  14. Mass, inertia, force, centrifugal force - Mass, M: a measure of the amount of material Example: Mo = Mass of the Sun = 2 x 1033 grams Mearth = Mass of the Earth = 6 x 1027 grams Weight = the downward force a given mass exerts in the Earth’s gravitational field: Note: The acceleration of gravity at the Earth’s surface is a = 980 cm s-2 This is used so often we call it little ‘g’ g = 980 cm s-2 acceleration at Earth’s surface - Force = [mass] x [acceleration] F = ma Weight = m g

  15. Forces • Acceleration in presence of a force, F • a = F / m • - The four (known) fundamental Forces: • Gravity (planets, stars, galaxies, …) • FG = - GmM / r2 • Electro-magnetism (atoms, molecules) • FEM = - q1q2 / r2 + q1 VxB / c • Strong nuclear force (binds atomic nuclei) • Weak nuclear force (radioactive decay, binds electrons to protons) Isaac Newton

  16. Gravity Falling objects on Earth most motions in astronomy F = G Mm / r2inverse square law! Force pulls together objects with MASS (mass has TWO roles - inertia AND creating gravity) Force is weaker when the distance between them is greater Force is stronger when the distance between them is greater This formulation of FORCE predicts motions of planets accurately!

  17. Mass, inertia, force, centrifugal force - Inertia, M: a measure of the resistance to a force In a vacuum (space) object in motion stay in motion those at rest, stay at rest (unless there is a force). - CentrifugalForce - actually a consequence of inertia When tethered to a string, a rock is forced by the string to move in a circle … but inertia wants to make it move in a straight line. The resulting force on the string is: Fcent = [mass] x [ Velocity2] / [ radius ] Fcent = mV2 / r Example: m = 100 kg, radius r = 100 cm, velocity = 100 cm/sec F = 100 1002 / 100= 104 (g cm sec-2)

  18. ASTR 2010 Cosmology Week 4: Lecture 10: Gravity and orbits: The 4 Forces of Nature

  19. Announcements • H2 #2 due • 2-nd SBO Observing session, Monday 22 Sept. • First Midterm: Monday, 28 Sept. in class. • (not Wed. as I stated before). • Today: • Newton: “Laws” of Motion • Gravity • Kepler’s “laws” of planetary orbits

  20. Clicker Question A yellow star speeds past you as you float motionless in space. At the instant the star passes your line of sight at a right anlge to its motion, what happens to the light as seen by you? The light is redshifted. The light is blueshifted The light is neither redshifted nor blueshifted. The light momentarily dies out. The light increases greatly in brightness.

  21. Clicker Question 2] A hot gas viewed through a prism would exhibit: An emission-line spectrum. A blackbody spectrum.  An absorption-line spectrum on top of a continuum spectrum A continuous spectrum. Only an absorption spectrum.

  22. Orbits: Balance of opposing forces Gravity <=> Centrifugal force G M m / R2 = m V2orbit / R Solve for Vorbit: Vorbit = (GM / R)1/2 Newton’s constant: G = 6.67 x 10-8 c.g.s. M m Vorbit

  23. Escape speed • Velocity needed to escape from a gravitating body • Kinetic Energy =(1/2) mV2 • Gravitational potential Energy = G M m / r • G = 6.67 x 10-8 • Newton’s gravitational constant • Drop a mass m from infinitely far away • onto an object of mass M, and radius r, • object m will have kinetic energyE(m) = GMm / r • Thus,1/2 m V2 = G M m / r • On, impact, the speed of object m will be (solve for V): • V = (2 GM / r)1/2

  24. Escape speed • Conversely • If you want to leave the surface of Earth, you have • to launch with speed • Vescape = (2 GM / r)1/2 • Escape speed: Note Vescape is independent of m! • (it cancelled out) • Example: Earth, M = 5.97 x 1027 grams • Earth’s Radius, r= 6371 km =6.4 x 108 cm • G = 6.67x10-8 • Vescape= (2 x [6.67x10-8]x[6.0 x 1027] / [6.4 x 108])1/2 • = 1.1x106 cm/sec = 11 km/s

  25. Orbits • Centrifugal force = Gravitational force • Fcent = FG • mV2 / r = - GmM / r2 • On a roughly circular orbit … • Vorbit = (GM / r)1/2 • Note. This is square-root of 2 smaller than escape speed from mass M ! • Example: Earth’s orbit around Sun Msun = 2 x 1033 grams • Earth - Sun distance, r = 1 A.U. = 1.5 x 1013 cm • G = 6.67x10-8 • Vorbit= ([6.67x10-8]x[2.0 x 1033] / [1.5 x 1013])1/2 • = 3.0x106 cm/sec = 30 km/s

  26. ASTR 2010 Cosmology Week 4: Lecture 11 (21 Sept. 2012) Tools: spectra, atoms, black-bodies Structure of matter

  27. Johannes Kepler - 1610

  28. Kepler’s Laws • Bound orbits are elliptical (circles are special cases) • The central mass is at one focus of the ellipse • ( = the center for a circle) • Equal areas • swept out in equal time • [Orbit period (orbit time)]2proportional to [semi major axis]3 • P2 = Constant a3

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