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Phys 1830: Lecture 14

Phys 1830: Lecture 14. The Vela Cloud. Today: Office Hours so come take up your test starting at 3pm. Appointment otherwise e.g. 2:45 pm Wednesday. J. English. Astroclub Wed 5:30pm Allen 330. Workshop is probably the Monday after Reading Week. Do not hand in greyscale images.

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Phys 1830: Lecture 14

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  1. Phys 1830: Lecture 14 The Vela Cloud Today: Office Hours so come take up your test starting at 3pm. Appointment otherwise e.g. 2:45 pm Wednesday. J. English Astroclub Wed 5:30pm Allen 330 Workshop is probably the Monday after Reading Week. Do not hand in greyscale images. • Previous Classes: • Angular Momentum • Newton’s Laws • This Class • Gravity • Tides • Coming up: • General Relativity

  2. Motion: • Angular Momentum • Newton’s Laws • Inertia • Acceleration • Equal and opposite reaction

  3. Gravity • Newton • Tidal Forces • Interacting Galaxies • Einstein • Gravitational Lensing

  4. Gravity • Gravity is a force that causes motion in the universe e.g. orbits, tides • Newton’s Law of Gravity • Einstein’s General Theory of Relativity • In both descriptions, gravity depends on mass.

  5. Question about the role of gravity: • If the Sun (and hence its mass) were suddenly to disappear the Earth would • Continue in its current orbit. • Suddenly change its orbital speed. • Fly off into space. • Stop spinning.

  6. 2.7 Newton’s Laws Gravity For two massive objects, gravitational force is proportional to the product of their masses divided by the square of the distance between them. Newtonian Gravity is always attractive.

  7. 2.7 Newton’s Laws Gravity The constant G is called the gravitational constant; it is measured experimentally and found to be: G = 6.67 x 10-11 m3/s2/kg • If we keep the distance the same (r = constant) • m F • 2 * m1 2 * F • 3 * m1 3 * F • The force felt on m1 due to m2 is equal to the force felt by m2 due to m1.

  8. Question 14 1) increases with distance. 2) depends upon the state of matter (solid, liquid, or gas). 3) can be attractive or repulsive. 4) increases with mass. Newton’s Law of Gravitystates that the force between two objects

  9. Question 14 1) increases with distance. 2) depends upon the state of matter (solid, liquid, or gas). 3) can be attractive or repulsive. 4) increases with mass. Newton’s Law of Gravitystates that the force between two objects The attractive force of gravity INCREASES with greater mass, and DECREASES QUICKLY with greater distance. The force doesn’t depend on the kind of matter.

  10. Question: • The mass of the Earth is a few millionths that of the Sun. Therefore • The gravitational force of the earth on the sun will be roughly 1/1,000,000 that of the gravitational force of the sun on the earth. • The gravitational force of the earth on the sun will be equal to the gravitational force of the sun on the earth.

  11. Gravity is inversely proportional to DISTANCE! The closer the objects the stronger the gravitational force. • r F 1  1 2  ¼ 3  1/9 etc.

  12. Tides: An example of the effect of gravity • The moon produces tides on Earth using the force of gravity.

  13. Tides • No iclicker: 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? • The red (closest) ball? • The blue (middle) ball? • The yellow (furthest) ball?

  14. Tides • No iclicker: Make note of your prediction. • Which ball moves the least? • The red (closest) ball? • The blue (middle) ball? • The yellow (furthest) ball?

  15. Tides: • Movie about the motion of the balls. • Note the perspective from someone sitting on the centre ball

  16. Tides • There is a difference in the gravitational force on each side of an object.

  17. Tides • To the centre ball it looks like the other 2 balls have moved in opposite directions. These 2 opposing forces are referred to as tidal forces. • Tidal forces cause the distortion of an object by the gravitational pull of another object. • Can occur when • Objects are close together (e.g. Earth and Moon) • An object is very massive (e.g. Jupiter and Io; the Sun and the Earth.)

  18. Tides • The moon also pulls on the Earth and the tides effect the water more that the land.

  19. Tides • Note that there are 2 tidal bulges at one time!

  20. Tidal Force Examples: The Asteroid Belt – the tidal force of Jupiter prevented planetesimals from coalescing into a planet.

  21. Tidal Force Examples: • The tidal force of Jupiter (and Europa) cause • - deformation of the interior of Io. • -> heat •  volcanism Galileo Project, NASA

  22. Tidal Force Examples: • Jupiter’s gravity attracts comets and other planetesimals. The tidal force can split comets into fragments. E.g. Comet Shoemaker –Levy NASA

  23. NASA

  24. Tidal Force Examples: Interacting Galaxies Image credit: J. English and colleagues.

  25. Tidal Force Examples: Interacting Galaxies • Interacting galaxies eventually merge together. • Minor Merger: • 2 galaxies • One’s mass is smaller than the other.

  26. Tidal Force Examples: Interacting Galaxies Hubble Heritage • Minor Merger: • Note the distortion of the smaller galaxy. It is extended on either side of the centre.

  27. Tidal Force Examples: Interacting Galaxies • Major merger: • 2 galaxies • They are approximately the same mass • Bridge between galaxies and a long tidal tail left behind.

  28. Tidal Force Examples: Interacting Galaxies B. Whitmore (STScI) HST on right • Antennae Galaxy. • Hot, young stars (blue) in the disks. • Long curved tails.

  29. Tidal Force Examples: Interacting Galaxies ACS S&E Team, HST • “Tadpole” galaxy: Tidal tail in a later stage. • Looking at many peculiar, tidally disturbed galaxies we can build up a picture of galaxy evolution.

  30. Tidal Force Examples: Interaction and Merger J. Barnes & J. Hibbard • Animation of computer simulation of interacting galaxies. • Each particle feels the force of gravity between it and every other particle.

  31. Tidal Force Examples: Groups of Galaxies Image credit: J. English • Galaxies residing in groups also feel tidal forces.

  32. Tidal Force Examples: Groups of Galaxies – velocity fields J. English • 2 tidal arms in the upper galaxy – major merger. • One long arm to the left in the left galaxy – minor merger. • Cloud is likely to be tidal debris.

  33. Tidal Force Examples: Clusters of Galaxies • Groups which have hundreds to thousands of galaxies are called clusters. • Gravitas - http://www.galaxydynamics.org/ J. Dubinski

  34. Motion in a Gravitational Field Can we predict the velocity at which a planet orbits a star? Does a falling heavy object speed up compared to a falling light object? How do we know that there is Dark Matter?

  35. Combining Forces of Motion and Gravity: Constant Acceleration and • Force on an object due to orbital motion is equal to the force on object due to gravity. • mass of the smaller object cancels out.

  36. Combining Forces of Motion and Gravity: Constant Acceleration • Consider 2 objects of different mass feeling the pull of gravity from M. • mass of these objects doesn’t matter. • Start 2 objects at same distance from centre of gravity  acceleration on them is constant. Think about this for the next class.

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