Gravity

Classical Mechanics Physics Thermodynamics Electromagnetism Modern 1600 to 1900 Classical Physics Mechanics Thermodynamics Electromagnetism 1940 Modern Relativity Large speeds (108 m/s). Quantum Mechanics Very small scales (10-10 m). present Current Particle Physics Cosmology

From the marriage of Particle Physics and Cosmology in the early 1970s a picture of the universe began to emerge. WMAP has contributed some of the most accurate data to date.

Carina Nebula in our Galaxy

Andromeda Galaxy – a “close neighbor”

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.

Hole in Universe billions of light years. August 24, 2007 Hole in Universe billions of light years. August 24, 2007. WMAP shows a cold spot and their radio wave data show the hole is nearly devoid of matter.

13.1 Newton’s Universal Law of Gravity

Do 13-6

Caveats to Universal Law Does 1/r2 hold to very small scales (~1 mm)? Is G(t)? 3 Body Problem General Relativity

Concept Question 13.1 A. B. C. D. E.

13.2 Measuring the Gravitational Constant G = 6.67 x 10-11 Nm2/kg2

13.3 Freefall Acceleration and the Gravitational Force Problem Using 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.

13.4 Kepler’s Laws and the Motion of Planets K1: Planet orbits about Sun are ellipses.

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

Show how to obtain the Universal Law from Kepler’s Third Law. T2 = KSa3 Do P13.15 (p. 413)

Concept Question 13.2 A. B. C. D. E.

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

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

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

13.5 The Gravitational Field ^ r mT M ^ k “Point” Mass Uniform Field near Earth’s Surface Gravity Fields – Two Cases

13.6 Gravitational Potential Energy

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/2r Note: K  0 K = |E| K = |U|/2

13.7 Energy Considerations in Planetary and Satellite Motion Do 13.32, 13.34 and 13.51

Concept Question 13.3 total energy A. B. C. D. E.

Force Law(s): Universal Law of Gravity Thinking Map Reflect: How can this be used? Is it reasonable? Simplifications: Earth uniform and perfect sphere, neglect air resistance Input Parameters: G, ME, RE Newton’s Laws: Calculate the acceleration of gravity at the Earth’s surface What do I need to know? Output: g Generalizations: What is g(r)? Other planets? Mathematics: algebra Force Law(s): Universal Law of Gravity