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Chapter 4


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University of Toronto Mississauga

AST 101H5F Solar System Astronomy University of Toronto Mississauga Summary of Chapter 4 Understanding Motion, Energy and Gravity th Essential Cosmic Evolution, 6 Edition The key points from Chapter 4 1. Definitions of terms relating to motion: (a) speed = change of location in some time interval, m/s or km/h (b) velocity = change of location and direction in some time interval, m/s 2 (c) acceleration = change of velocity in some time interval, (m/s)/s = m/s (d) momentum = mass × velocity 2. Momentum changes because of a net force Example: as it orbits around Earth, the Moon is constantly changing the direction of its motion = changing velocity, which is caused by the force of Earth’s gravity 3. Net force is the result of summing all the separate forces affecting an object Example: the Moon’s orbit is affected by Earth’s gravity + Sun’s gravity + Jupiter’s gravity + ... 4. Mass = total amount of matter in an object, expressed in kilograms (kg) 5. Weight = force of gravity on a mass, expressed in Newtons Example: a mass of 50 kg on Earth, where the acceleration of gravity is about 10 m/s , has a weight of 50 kg × 10 m/s = 500 Newtons 6. Newton’s three laws of motion • If there is no net force, the momentum does not change • If there is a net force, the momentum does change Because changing momentum is usually a changing velocity = acceleration, this is usually written F = ma. • Forces come in equal but opposite pairs, force = reaction force AST 101H5F Chapter 4 2 M1M 2 7. Newton’s universal law of gravity: G = G d2 • F depends directly on each mass G • F depends inversely on the square of the separation G • G is a universal constant • F extends forever, until the separation in infinite G • F is never canceled out because all masses are positive quantities G • FG is extremely important in astronomy because of the huge masses and huge separations 8. Newton’s version of Kepler’s first law • Four types of orbits are possible: circular, elliptical, parabolic and hyperbolic. • To have a circular orbit there must be a perfect balance of motion by gravity → extremely unlikely • Many combinations of motion and gravity produce elliptical orbits → very likely • Objects on parabolic and hyperbolic orbits never return, so we never see them 9. Newton’s version of Kepler’s third law: p = 4π2 a3 G(M 1M 2 • We measure p and a • G, π
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