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AP Unit I F 4,5

AP Unit I F 4,5. Newton’s Law of Gravity and Orbits. 4. Newton’s Law of Gravity. Students should know Newton’s Law of Universal Gravitation, so they can a) Determine the force that one spherically symmetrical mass exerts on another.

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AP Unit I F 4,5

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  1. AP Unit I F 4,5 Newton’s Law of Gravity and Orbits

  2. 4. Newton’s Law of Gravity • Students should know Newton’s Law of Universal Gravitation, so they can • a) Determine the force that one spherically symmetrical mass exerts on another. • b) Determine the strength of the gravitational filed at a specified point outside a spherically symmetrical mass.

  3. 5. Orbits of planets and satellites • Students should understand the motion of an object in orbit under the influence of gravitational force, so they can: • a) For a circular orbit: • (1) Recognize that the motion does not depend on the object’s mass; describe qualitatively how the velocity, period of revolution, and centripetal acceleration depend on the radius of the orbit; and derive expressions for the velocity and period of revolution in such an orbit.

  4. Newton’s Law of Universal Gravitation Ref. 7.7 • F = G (m 1 m2)/ r2 • G = 6.673 x 10 –11 N m2/kg2 m1 m2 r

  5. Strength of Gravitational Field (g) • g = F/m = (GMpm /R2)/m = G Mp/R2 Calculate gravitational field for Earth. Mp = 5.979 x 1024 kg Rp = 6.3713 x 106 m R m Mp

  6. Circular Orbits • Fg = Fc • G m1 m2/r2 = m2 v2/r • G m1/r = v2 • v = (G m1/r) v r m2 m1

  7. Period (T) of the satellite orbit Since v = 2πr/ T T = 2πr/v = 2πr/(G m1/r) = 2πrr/(G m1) T =2π (r3 /Gm1)

  8. Kepler’s Third Law for Circular orbits Ref. 7.9 • For planet mass Mp orbiting sun mass Ms at a distance R with speed v • Fgravitational = F centripetal • G Ms Mp/ r2 = Mp v2/r • Since v = 2πr/T • G Ms Mp/ r2 = Mp (2πr/T)2/r • T2 = (4π2/G Ms) r3 = Ks r3 • Therefore the ratio of the square of the periods of any two planets is proportional to ratio of their mean distances from the sun. • (T 1/ T2 )2 = ( r1/r2)3

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