哈工大天文学概论——银河.pptVIP

Newtonian Gravity an explanation for planetary motions Newton’s 3 Laws of Motion starting-point Necessary ingredient to calculate motions Exact description of forces involved How to quantify gravity ? Galileo’s Law of Falling Bodies Newton, the Apple and the Moon ! Galileo’s Mechanics Experiments Prior to work with telescope, Galileo performed fundamental research on motion. Explored the rate of falling bodies by dropping different weights, or sliding them down inclined planes. Law of Falling Bodies: In the absence of air, heavy objects and light objects fall at the same, constant rate of acceleration. The Idea of Universal Mutual Gravitation Newton, in his Principia, formulated the Law of Universal Mutual Gravitation: Gravity is an Attractive force: Works to bring massive objects closer together. Gravity is a Universal force: Works everywhere in the Universe. Gravity is a Mutual force: Works between pairs of massive objects. Towards an exact description Force of gravity between any two objects depends only upon: The masses of the two objects: More massive objects feel a stronger force. The distance between them: Objects closer together feel a stronger force. It does not depend at all on the shapes, colors, or compositions of the two objects. Towards an exact description Newton’s Idea : Force depends linearly on masses of objects Twice as much mass ? twice the force Half as much mass ? half the force Newton’s Laws then guarantee Galileo’s observation of Falling Bodies What is the dependence on distance ? Comparing an apple to the moon Newton’s fascinating thought process : Assumptions : Fall of an apple and path of moon governed by the same principle ? Gravitational attraction (only !) Gravity independent of shape of Earth Careful numerical analysis leads to deeper understanding of gravity What Newton knew about apples Falling apples on Earth : Constant acceleration near surface of Earth : a=9.8 meters/second2 Radius of Earth : 6378 km = 6378,000 meters (Erat