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Chapter 4

AST101-Chapter 4.txt

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Department
Astronomy
Course
AST101H5
Professor
John Lester
Semester
Fall

Description
Chapter 4: Understanding Motion, Energy and Gravity (the "experience " we need How do we describe motion? 1. Speed = change in position or location in some amount of time = m/s 2. Examples: 1. walking speed = 1 m/ 2. running speed = 10 m/s 3. driving speed = 27.8 m/s = 100 km/h 4. Earth's orbit speed = 30 km/s = 108,000 km/h 3. Velocity = this is NOT the same as speed = change in (location + direction) in some amount of time. 4. units are m/s - same as speed - confusing 5. Example: driving 100km/h west is NOT the same velocity as driving 100km/h n orth, although the speeds are the same 6. Acceleration = change in velocity in some amount of time = (m/s)/s = m/s2. 7. Increasing speed is an acceleration. 8. Decreasing speed is a deceleration = acceleration with a negative sign. 9. Changing direction of motion at a constant speed is also an acceleration. 10. Example of Acceleration: 1. Dropping a motionless object, v = 0 m/s @ 0 s 2. v = 10 m/s @ 1 s -> a = (10m/s - 0m/s)/s = 10 m/s2. 3. v = 20 m/s @ 2 s -> a = (20m/s - 10m/s)/s = 10 m/s2. 11. Momentum = velocity x mass 1. - Note: momentum has direction because velocity has direction. 2. changing velocity -> changing momentum. 3. changing mass also changes momentum. 4. Momentum cannot change on it own. 5. Force is needed to change momentum. 6. Net (=total) force changes momentum. What is Mass? 1. Mass = all the matter (molecules and atoms) in an object. That is a HUGE nu mb of molecules and atoms. 1. Example: person = 1028 molecules + atoms = 10,000,000,000,000,000,000,000 ,000,000. 2. We cannot count that number of molecules and atoms, so represent mass wit h a simple number = kilogram. What is Weight? 1. Weight = force of gravity pulling on the mass of an object. Weight is NOT t he same as mass. 2. It is wrong to use kg for the unit for both mass and weight (unit = Newton) . 3. Example: 1. an astronaut's mass is the same on the Moon and on Earth. 2. but the astronaut's weight is different on the Moon because the Moon's gr avity is different. Newton's Law of Motion 1. 1st Law: If there is no net force, an object's momentum does not change. 2. 2nd Law: A net force changes an object's momentum (usually changing its vel ocity = acceleration) 1. Equation: net force = mass x acceleration (f = ma) 3. 3rd Law: Forces come in opposite pairs, force = reaction force. Newton's Law of Gravitational Force 1. Gravity is a UNIVERSAL force between all objects having mass. 2. Force of gravity depends on all masses. 3. Force of gravity depends on separation. 1. greater separation -> weaker force 2. weakens as 1/(separation)2 = "inverse square" law. 3. but force of gravity never goes to zero, 4. Fg = G M1M2/ d2, G = 6.67 x 10-11. Gravity is important for astronomy 1. Astronomical objects have: 1. huge masses -> huge force of gravity 2. huge separations -> weak force of gravity 3. small separations -> huge force of gravity 2. Mass is a positive quantity -> gravity cannot cancel out. 3. Gravity never stops, even at the largest distances. 4. Electric force cancels out: + and - charges. 5. Magnetic force cancels out: North and South poles. Date: Sept 26, 2013 Kepler's Law, Again 1. Kepler studied Tycho's observations to discover that planets have elliptica l orbits. 2. Newton used his general laws of motion and gravity to show why a orbits are elliptical -> a much deeper understanding. 3. Kepler observed p2 = a3. 4. Newton derived, p2 = [(4)(pi)2 / G(M1+M2)] a3 5. Very important equation in astronomy, 1. observing p and a -> derive M1 + M2 2. if M is small, like a tiny moon, we can ignore it and learn the value of M1 3. -> Best way of measuring mass in astronomy. Cosmic Calculation, Mass of Eris - Calculation done in notebook Conservation Laws 1. "Conserved" means cannot be destroyed. 2. Examples: 1. mass = matter 2. momentum = mass x velocity 3. angular momentum = mass x velocity x radius = regular momentum x orbit si ze 3. Conserving angular momentum explains how Kepler's 2nd Law works. 4. Angular momentum is conserved as Earth orbits the Sun. Tides 1. Recall Fgravity depends on 1/(separation)2. 2. Different parts of Earth are different distances from the Moon -> the Moon' s gravitational pull to be: 1. strongest on the near side of Earth. 2. average on the centre of Earth. 3. weakest on the far side of Earth. 3. Difference i
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