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Universal Gravitation Circular Orbits The moon moves in a nearly circular path around the Earth. • The path is called an orbit • The period is about 28 days The Earth and planets move in nearly circular paths around the sun. The moon and planets have a centripetal acceleration. • A centripetal force - the law of action Central Force There is no normal or tension force affecting the planets. Like falling bodies that accelerate, the moon accelerates toward the earth. Gravity is a central force. orbital velocity centripetal acceleration Moon Earth Inverse Square Distance The Earth’s radius is about rE = 6400 km. The distance from the Earth to the Moon is about 380,000 km = 60 rE . The centripetal acceleration is a constant. The centripetal acceleration of the moon is known from the period. • g = 9.8 m/s2. • a = v2 / r = (4p2 / T2) r • a = 0.0027 m/s2 = g / 3600 If a falling object and the moon are acted on by the same force, the force gets weaker as the square of the distance. This is an inverse square law: a = C / r2. Mass Dependence Newton’s law of action applies to orbits. • Centripetal acceleration times mass is the force of gravity FEM • FEM = mM a = mM C / r2 Moon a Earth Equal and Opposite Newton’s law of reaction also applies to the forces. • The forces are equal and opposite • FME = FEM • mE K / r2 = mM C / r2 FME Earth FEM Moon Gravitational Constant To make these equations agree Newton made the equation depend on the two masses. • FEM = G mE mM / r2 Other planets also obey the same law. The gravitational force is universal. • F = G m1 m2 / r2 The gravitational constant, G = 6.67 x 10-11 Nm2/kg2. next