6 Spitzer shows Andromeda much larger than previously thought Spitzer shows Andromeda much larger than previously thought. Eventually our galaxy will collide with Andromeda in about 5 – 10 billion years.
8 Hole in Universe billions of light years. August 24, 2007 Hole in Universe billions of light years. August 24, WMAP shows a cold spot and their radio wave data show the hole is nearly devoid of matter.
16 13.2 Measuring the Gravitational Constant G = 6.67 x Nm2/kg2
17 13.3 Freefall Acceleration and the Gravitational Force ProblemUsing Newton’s framework (Newton’s Laws) and the Universal Law of Gravity, find an expression for g (acceleration of gravity) at the surface of the Earth given ME, RE, and G.
18 13.4 Kepler’s Laws and the Motion of Planets K1: Planet orbits about Sun are ellipses.
20 K2: Planets sweep out equal areas in equal times as the orbit the Sun. K3: The square of the planet’s period is proportional to the cube of the planet’s semimajor axis (a). The semimajor axis is roughly the average distance of the planet from the Sun.Squeak Demo
21 Show how to obtain the Universal Law from Kepler’s Third Law. T2 = KSa3Do P (p. 413)
23 This question is asking about the dependence of the force of Earth’s gravity on mass. The force of the Earth on a mass m is directly proportional to m. F = mg = ma so a = g a constant Common misconception - The student indicates that the gravitational force is the same magnitude for all objects near the earth. Correct answer
24 Common misconceptions - Objects in water have a smaller gravitational force by Earth because the water pushes up (e.g., the scale reading underwater is interpreted as a measure of the gravitational force) or Earth's pull on an object is a magnetic force or Earth's gravitational force of an object is proportional to the water pressure acting down on it. Correct answer
25 Common misconceptions - The student thinks the distance between objects does not affect the size of the gravitational force or the student does not understand the factors that affect the strength of the gravitational force. Correct answer
26 13.5 The Gravitational Field ^rmTM^k“Point” MassUniform Field near Earth’s SurfaceGravity Fields – Two Cases
29 13.7 Energy Considerations in Planetary and Satellite Motion E = K + U is conserved because gravity is a conservative force (work is independent of the path).For a circular orbit:K = GMm/2r U = -GMm/r E = -GMm/2rNote: K 0 K = |E| K = |U|/2
30 13.7 Energy Considerations in Planetary and Satellite Motion Do 13.32, and 13.51
32 Force Law(s): Universal Law of Gravity Thinking MapReflect: How can this be used? Is it reasonable?Simplifications: Earth uniform and perfect sphere, neglect air resistanceInput Parameters: G, ME, RENewton’s Laws: Calculate the acceleration of gravity at the Earth’s surfaceWhat do I need to know?Output: gGeneralizations: What is g(r)? Other planets?Mathematics: algebraForce Law(s): Universal Law of Gravity