Universal GravitationCircular OrbitsCentral ForceInverse Square DistanceMass DependenceEqual and OppositeGravitational ConstantUniversal GravitationUniversal GravitationCircular OrbitsCircular OrbitsThe moon moves in a nearly circular path around the The moon moves in a nearly circular path around the Earth.Earth.•The path is called an The path is called an orbitorbit•The period is about 28 daysThe period is about 28 daysThe Earth and planets move in nearly circular paths The Earth and planets move in nearly circular paths around the sun.around the sun.The moon and planets have a centripetal The moon and planets have a centripetal acceleration.acceleration.•A centripetal force - the law of actionA centripetal force - the law of actionCentral ForceCentral ForceThere is no normal or There is no normal or tension force affecting the tension force affecting the planets.planets.Like falling bodies that Like falling bodies that accelerate, the moon accelerate, the moon accelerates toward the earth.accelerates toward the earth.Gravity is a Gravity is a centralcentral force. force.Moon centripetal accelerationEarthorbital velocityInverse Square DistanceInverse Square DistanceThe Earth’s radius is about The Earth’s radius is about rrEE = 6400 km. = 6400 km.The centripetal acceleration The centripetal acceleration is a constant.is a constant.•gg = 9.8 m/s = 9.8 m/s22..The distance from the Earth The distance from the Earth to the Moon is about to the Moon is about 380,000 km = 60 380,000 km = 60 rrEE . .The centripetal acceleration The centripetal acceleration of the moon is known from of the moon is known from the period.the period.•aa = = vv22 / / rr = (4 = (422 / / TT22) ) rr•aa = 0.0027 m/s = 0.0027 m/s2 2 = = g g / 3600/ 3600If a falling object and the moon are acted on by the same force, If a falling object and the moon are acted on by the same force, the force gets weaker as the square of the distance.the force gets weaker as the square of the distance.This is an This is an inverse squareinverse square law: law: aa = = CC / / rr22..Mass DependenceMass DependenceNewton’s law of action applies Newton’s law of action applies to orbits.to orbits.•Centripetal acceleration times Centripetal acceleration times mass is the force of gravitymass is the force of gravity•FFEMEM = = mmMM a = ma = mMM CC / / rr22Moon EarthaFEMEqual and OppositeEqual and OppositeNewton’s law of reaction also Newton’s law of reaction also applies to the forces.applies to the forces.•The forces are equal and The forces are equal and opposite opposite •FFMEME = F = FEMEM•mmEE KK / / rr22 = m = mMM CC / / rr22Moon EarthFMEFEMGravitational ConstantGravitational ConstantTo make these equations agree Newton made the To make these equations agree Newton made the equation depend on the two masses.equation depend on the two masses.•FFEMEM = G m = G mEE mmMM / / rr22Other planets also obey the same law.Other planets also obey the same law.The gravitational force is universal.The gravitational force is universal.•F = G mF = G m11 mm22 / / rr22The gravitational constant, The gravitational constant, GG = 6.67 x 10 = 6.67 x 10-11-11 Nm
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