AST101- chp 4.docx

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Astronomy & Astrophysics
Michael Reid

AST101 4.4 The Universal Law of Gravitation * In astronomy the most important force is gravity because it governs virtually all large-scale motion in the universe * What determines the strength of gravity? - Universal Law of Gravitation o (3) statements that summarize this law: o every mass attracts every other mass through the force called gravity o the strength of the gravitational force attracting any two objects is directly proportional to the product of their masses o the strength of gravity between two objects decrease with the square of the distance between their centers. That is, the gravitational force follows an inverse square law with distance - All three statements can be combined into a single equation(4.5):  where fg is the force of gravitational attraction, M1 and M2 are the masses of the two objects, and d is the distance between their centers How does Newton’s law of gravity extend Kepler’s laws? - Newton proved Kepler’s law by showing that the laws are consequences of the laws in motion and the universal law of gravitation - (4) ways in which Newton extended Kepler’s laws: o Planets are not the only objects with elliptical orbits: showed that any object going around another object will obey Kepler’s first two laws o Ellipses are not the only possible orbital paths: Kepler was right about ellipses being the only possible shapes for bound orbits – orbits in which an object goes round another object over and over again (term comes from the idea that gravity creates a bond that holds the objects together)  Newton discovered objects can also follow unbound orbits- paths that bring an object close to another object just once o Objects orbit their center of mass: Newton showed that two objects attracted by gravity actually both orbit around their center of mass- the point at which the two objects would balance if they were somehow connected o Orbital characteristics tell us the masses of distant objects: Newton creates a version of Kepler’s third law which allows us to measure orbital period and distance in any units we wish (rather than only in years an AU) and shows that the relationship between the orbital period and the average distance depends on the masses of orbiting objects Newton’s version of Kepler’s third law (4.3) - Where M1 and M2 are the masses of the two objects, p is their orbital period, and a is the distance between their centers. 4.5 Orbits, Tides, and the Acceleration of Gravity * Newton’s law of universal gravitation explains Kepler’s laws of planetary motion * How do gravity and energy together allow us to understand orbits? - Role of Energy in orbits: o Orbital Energy: a planet’s total sum of its kinetic and gravitational potential energies always stays the same  This fact is a consequence of the law of conservation of energy o Gravitational Encounters:
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