Path Independence We move a baseball from point A to point G along a path consisting of three radial lengths and three circular arcs (centered on Earth). We are interested in the total work W done by Earth’s gravitational force F on the ball as it moves from A to G. We discussed such a result in a […]
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Potential Energy and Force We derived the potential energy function U(r) from the force function F(r). We should be able to go the other way-that is, to start from the potential energy function and derive the force function. This is Newton’s law of gravitation . The minus sign indicates that the force on mass m points radially inward, […]
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Escape Speed If you fire a projectile upward, usually it will slow, stop momentarily, and return to Earth. There is, however, a certain minimum initial speed that will cause it to move upward forever, theoretically coming to rest only at infinity. This initial speed is called the (Earth) escape speed. The escape speed does not depend on the […]
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Planets and Satellites: Kepler’s Laws The motions of the planets, as they seemingly wander against the background of the stars, have been a puzzle since the dawn of history. The motion of Mars, was particularly baffling. Johannes Kepler (1571-1630), after a lifetime of study, worked out the empirical laws that govern these motions. 1 THE LAW OF ORBITS: All […]
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