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Lecture 5 Phys 1810 MONDAY! 1.Tutorial/Office hour 3:00 pm Allen 514. Syllabus at http://www.physics.umanit oba.ca/~english/2014fallph ys1810/ (Google “Jayanne English teach”) along supplemental material. REVISE DATE IS Wed. Sept 15 (Do Honours rather than General Science 3yr degree) • Read BEFORE coming to class: – Electromagnetic Radiation 3.1 to 3.4 • Energy • Thermal Radiation Box 3-2 • Flux and Luminosity (L equation in Box 17-2) – Spectra 4.1, 4.2 • Kirkhhoff’s Laws – Radio Emission 18.4 – Doppler shift: 3.5, Box 3-3, 4.5 Examples of the Effects of Gravity: Tides Tides at the Bay of Fundy Effect of the Moon on Earth Gravity ( ) Tidal Forces: == Distortion of an object by the gravitational pull of another object. -- nearby (e.g. Earth & Moon) OR -- very massive (e.g. Earth & Sun) Tidal Force Examples: Asteroid Belt –tidal force of Jupiter prevented formation of planet between Mars & Jupiter. Tidal Force Examples: The tidal force of Jupiter (and Europa) cause - deformation of Io’s interior -> heat - volcanism Split apart Comet Shoemaker-Levy q Saturn raises tides on its moons. Gravity orbits of material in rings. Peculiar Galaxies Tidal Tail Tides summary Recall column • Make note of your prediction. • There is a difference in the gravitational force on each side of an object. Splitting the object into 3 parts, which is going to feel the most force? a) The red (closest) ball? b) The blue (middle) ball? c) The yellow (furthest) ball? summary Tides Recall column • Make note of your prediction. • Which ball moves the least? a) The red (closest) ball? b) The blue (middle) ball? c) The yellow (furthest) ball? summary Tides: Recall column • Movie about motion of the balls. • Note perspective from someone sitting on centre ball summary Tides Recall column • Difference in object. on each side of an Tides summary Recall column • On centre ball: appears other 2 balls have moved in opposite directions. These 2 opposing forces == tidal forces. • Tidal forces: cause distortion of an object by pull of another object. • Can occur when – Objects close (e.g. Earth & Moon) – 1 object is very massive (e.g. Jupiter & Io; Sun & Earth.) Tides summary Recall column • Moon pulls on Earth & tides effect water more than land. • Make a prediction about how Earth’s ocean is distributed due to moon. summary Tides Recall column • Note 2 tidal bulges at one time! Apply what we know: Recall column summary • If the Earth had no Moon, then the tides would occur twice a day but would not be as strong. (Think of the objects in the Solar System.) Tidal Locking: summary Tidal Drag Recall column Why does the moon always show the same face to us? Synchronous Orbit: P == Period Tidal Locking: What happens to Earth summary Tidal Drag Recall column Misalignment due to friction between ocean & crust crust drags ocean Moon pulls back on tidal bulge Earth’s spin slows down. 100’s of billions of yrs tidal locking Tidal Locking: summary Tidal Drag Recall column Moon’s tidal bulge formed when moon solidified & Earth’s tidal pull on moon’s bulge is larger tidal locking faster for moon. P == Period summary Tidal Locking: Recall column • Summary – Examples: Tidal forces cause 1) Synchronous Orbits 2) Fragmenting Comets 3) Structures in Interacting Galaxies Note: there is structure on each side of an individual galaxy – the bridge and the tail. 2.7 Newton’s Laws Gravity Kepler’s Laws of Planetary Motion from Newton’s perspective. Description of Ellipse Objects orbit a common centre of mass. Centre of mass == average position of all matter making up the 2 bodies. Equal mass 1 object more massive 1 object very massive Notice “wobble” of sun! large planets around stars are easier to detect because they cause star to “wobble”. • Kepler’s 1st Law : Kepler I • Orbit of a planet around the sun is an ellipse with the center of mass of the planet-sun system at one focus • Note: r = radius of circle = distance. O.k. since r == average distance, which equals semi-major axis a • Kepler II An imaginary line connecting the sun to any planet sweeps out equal areas of an ellipse in equal intervals of time. • • • Area of A, B, and C are the same. Note Arc of A, Arc of C and Arc of B v = distance/time and time remains constant. Therefore planet travels a different speeds when at different distances from the sun. • Kepler III The square of the planet’s orbital period (P) is proportional to the cube of its semi-major axis (a) divided by the combined mass in the system (Mtotal) Solar mass = 99.85% of Mtotal Note proportionality. If distance from sun increases so does time to go around sun. Relationship is NOT 1-to-1. Note P in earth years A in AU M in solar masses Example: Planet A and Planet B. Distance between star and B is twice that of A. Long does it take for B to orbit compared to A? Example: Planet A and Planet B. Distance between star and B is twice that of A. Long does it take for B to orbit compared to A? Compare planets’ velocities Keplerian Rotation Curve And since Works for: • Earth’s satellites • Jupiter’s moons • planets Plot Velocity Equation for planets the Solar System: summary Recall column a 1 25 36 64 100 v 1 1/5 1/6 1/8 1/10 Keperlian motion Keplerian rotation curve. Important when we study Dark Matter. summary Derive v using Newton’s Laws Recall column Notice how m of smaller object cancels out. So hammer and feather have same acceleration! For Earth’s gravity: accel = g Derive v using Newton’s Laws Recall column Kepler’s v is empirical with no reason for formula. Newton’s version provides reason – Forces in balance for an object to be in orbit. Since r = semi-major axes “a” and G & M are constant: summary • • • v to little, fall back v enough, go into orbit v to much, unbound ==escape Escape Velocity • Let’s weigh the sun! – Re-arrange the velocity equation and substitute. – Exercise – weigh the Earth using the moon.(Look relevant values in textbook.) Weighing the sun Recall column summary Weighing the sun Recall column Many ways to calculate co-efficients. How does this compare with the Earth’s mass? What else can we “weigh” with this equation? summary