2 Circular OrbitsThe moon moves in a nearly circular path around the Earth.The path is called an orbitThe period is about 28 daysThe 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
3 Central ForceThere 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 velocitycentripetal accelerationMoonEarth
4 Inverse Square Distance The Earth’s radius is about rE = 6400 km.The centripetal acceleration is a constant.g = 9.8 m/s2.The distance from the Earth to the Moon is about 380,000 km = 60 rE .The centripetal acceleration of the moon is known from the period.a = v2 / r = (4p2 / T2) ra = m/s2 = g / 3600If 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.
5 Mass Dependence Newton’s law of action applies to orbits. Centripetal acceleration times mass is the force of gravityFEM = mM a = mM C / r2MoonFEMaEarth
6 Equal and OppositeNewton’s law of reaction also applies to the forces.The forces are equal and oppositeFME = FEMmE K / r2 = mM C / r2FEMMoonFMEEarth
7 Gravitational Constant To make these equations agree Newton made the equation depend on the two masses.FEM = G mE mM / r2Other planets also obey the same law.The gravitational force is universal.F = G m1 m2 / r2The gravitational constant, G = 6.67 x Nm2/kg2.next