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Transcript
Satellites Universal Gravitational Constant Force due to Gravity Centripetal Force Mass of the earth Fg = mg Mass of the earth Fg = mg Fg = Gmme r2 Mass of the earth Fg = mg Fg = Gmme r2 mg = G mme r2 Mass of the earth Fg = mg Fg = Gmme r2 mg = G mme r2 g = G me r2 Mass of the earth Fg = mg Fg = Gmme r2 mg = G mme r2 g = G me r2 gr2 = me G 9.8m/s2(6.38e6m)2=me 6.67e-11N m2/kg2 Mass of the earth Fg = mg Fg = Gmme r2 mg = G mme r2 g = G me r2 gr2 = me G 9.8m/s2(6.38e6m)2=me 6.67e-11N m2/kg2 Mass of the earth Fg = mg Fg = Gmme r2 mg = G mme r2 g = G me r2 gr2 = me G 9.8m/s2(6.38e6m)2=me 6.67e-11N m2/kg2 5.98e24= me Velocity of the moon with respect to the earth Fc= mv2 r Velocity of the moon with respect to the earth Fc= mv2 r Fg = Gmme r2 Velocity of the moon with respect to the earth Fc= mv2 r Fg = Gmme r2 mv2 = G mme r r2 Velocity of the moon with respect to the earth Fc= mv2 r Fg = Gmme r2 mv2 = G mme r r2 v2 = G m e r r2 Velocity of the moon with respect to the earth Fc= mv2 r Fg = Gmme r2 mv2 = G mme r r2 v2 = G m e r r2 v2 = G m e r Velocity of the moon with respect to the earth Fc= mv2 r Fg = Gmme r2 mv2 = G mme r r2 v2 = G m e r r2 v2 = G m e r v= 6.67e-11(5.98e24kg) 3.84e8m Velocity of the moon with respect to the earth Fc= mv2 r Fg = Gmme r2 mv2 = G mme r r2 v2 = G m e r r2 v2 = G m e r v= 6.67e-11(5.98e24kg) 3.84e8m v=1019m/s Geostationary Satellites Geostationary Satellities Rotate around the earth in 24hr Geostationary Satellities Rotate around the earth in 24hr Therefore t= Geostationary Satellities Rotate around the earth in 24hr Therefore t=24hr(60min)(60sec)=86400s Geostationary Satellities Rotate around the earth in 24hr Therefore t=24hr(60min)(60sec)=86400s v= 2 P r t Geostationary Satellities Rotate around the earth in 24hr Therefore t=24hr(60min)(60sec)=86400s v= 2 P r t Fg=Fc Geostationary Satellite v=2 P r t Geostationary Satellite v=2 P r t v=2 P r 86400s Geostationary Satellite v=2 P r t v=2 P r 86400s Fc= mv2 r Geostationary Satellite v=2 P r t v=2 P r 86400s Fc= mv2 r Fg = Gmme r2 Geostationary Satellite v=2 P r t v=2 P r 86400s Fc= mv2 r Fg = Gmme r2 mv2 = G mme r r2 Geostationary Satellite mv2 = G mme r r2 v2 = G r me r2 v2 = G me r (2 P r )2 = G me (86400)2 r 4 P2 r2 =G (86400)2 me r 4 P2 r3 = Gme (86400)2 r3 = (86400s)2 G(5.98e24kg) 4 P2 G=6.67x10-11Nm2/kg2 r = r =4.22e7m Geostationary Satellite mv2 = G mme r r2 v2 = G r me r2 v2 = G me r (2 P r )2 = G me (86400)2 r 4 P2 r2 =G (86400)2 me r 4 P2 r3 = Gme (86400)2 r3 = (86400s)2 G(5.98e24kg) 4 P2 G=6.67x10-11Nm2/kg2 r = r =4.22e7m Geostationary Satellite mv2 = G mme r r2 v2 = G r me r2 v2 = G me r (2 P r )2 = G me (86400)2 r 4 P2 r2 =G (86400)2 me r 4 P2 r3 = Gme (86400)2 r3 = (86400s)2 G(5.98e24kg) 4 P2 G=6.67x10-11Nm2/kg2 r = r =4.22e7m Geostationary Satellite mv2 = G mme r r2 v2 = G r me r2 v2 = G me r (2 P r )2 = G me (86400)2 r 4 P2 r2 =G (86400)2 me r 4 P2 r3 = Gme (86400)2 r3 = (86400s)2 G(5.98e24kg) 4 P2 G=6.67x10-11Nm2/kg2 r = r =4.22e7m Geostationary Satellite mv2 = G mme r r2 v2 = G r me r2 v2 = G me r (2 P r )2 = G me (86400)2 r 4 P2 r2 =G (86400)2 me r 4 P2 r3 = Gme (86400)2 r3 = (86400s)2 G(5.98e24kg) 4 P2 G=6.67x10-11Nm2/kg2 r = r =4.22e7m Geostationary Satellite mv2 = G mme r r2 v2 = G r me r2 v2 = G me r (2 P r )2 = G me (86400)2 r 4 P2 r2 =G (86400)2 me r 4 P2 r3 = Gme (86400)2 r3 = (86400s)2 G(5.98e24kg) 4 P2 G=6.67x10-11Nm2/kg2 r = r =4.22e7m Geostationary Satellite mv2 = G mme r r2 v2 = G r me r2 v2 = G me r (2 P r )2 = G me (86400)2 r 4 P2 r2 =G (86400)2 me r 4 P2 r3 = Gme (86400)2 r3 = (86400s)2 G(5.98e24kg) 4 P2 G=6.67x10-11Nm2/kg2 r = r =4.22e7m Geostationary Satellite mv2 = G mme r r2 v2 = G r me r2 v2 = G me r (2 P r )2 = G me (86400)2 r 4 P2 r2 =G (86400)2 me r 4 P2 r3 = Gme (86400)2 r3 = (86400s)2 G(5.98e24kg) 4 P2 G=6.67x10-11Nm2/kg2 r = r =4.22e7m Geostationary Satellite mv2 = G mme r r2 v2 = G r me r2 v2 = G me r (2 P r )2 = G me (86400)2 r 4 P2 r2 =G (86400)2 me r 4 P2 r3 = Gme (86400)2 r3 = (86400s)2 G(5.98e24kg) 4 P2 G=6.67x10-11Nm2/kg2 r = r =4.22e7m Geostationary Satellite r3 = (86400s)2 G(5.98e24kg) 4 P2 3 r = (86400s)2 (6.67e-11Nm2/kg2)(5.98e24kg) 4 P2 Geostationary Satellite 3 r =(86400s)2 (6.67e11Nm2/kg2 (5.98e24kg) 4 P2 r =4.22e7m Geostationary Satellite velocity with respect to the earth V= 2pr = 2 p ( 4.22e7m) 86400s 86400s v=3069m/s Geostationary Satellite velocity with respect to the earth V= 2pr = 2 p ( 4.22e7m) 86400s 86400s v=3069m/s Geostationary Satellite velocity with respect to the earth V= 2pr = 2 p ( 4.22e7m) 86400s 86400s v=3069m/s Velocity of the earth with respect to the sun Fc= mev2 r Velocity of the earth with respect to the sun Fc= mev2 r Fg = Gmems r2 Velocity of the earth with respect to the sun Fc= mev2 r Fg = Gmems r2 mev2 = G m e ms r r2 Velocity of the earth with respect to the sun Fc= mev2 r Fg = Gmems r2 mev2 = G m e ms r r2 v2 = G m s r r2 Velocity of the earth with respect to the sun Fc= mev2 r v2 = G m s r r2 Fg = Gmems r2 v2 = G m s r mev2 = G m e ms r r2 Velocity of the earth with respect to the sun Fc= mev2 r v2 = G m s r r2 Fg = Gmems r2 v2 = G m s r mev2 = G m e ms r r2 v= 6.67e-11(1.99e30kg) 1.51e11m Velocity of the earth with respect to the sun Fc= mev2 r v2 = G m s r r2 Fg = Gmems r2 v2 = G m s r mev2 = G m e ms r r2 v= 6.67e-11(1.99e30kg) 1.51e11m v=29648 m/s Velocity of the moon with respect to the sun Fc= mmv2 r v2 = G m s r r2 Fg = Gmmms r2 v2 = G m s r mmv2 = G m m ms r r2 v= 6.67e-11(1.99e30kg) 1.51e11m v=29648 m/s Velocity of the Geostationary Satellite with respect to the sun Fc= mgv2 r v2 = G m s r r2 Fg = Gmgms r2 v2 = G m s r m g v2 = G m g m s r r2 v= 6.67e-11(1.99e30kg) 1.51e11m v=29648 m/s Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the velocity of the stars? What is the mass of the stars? Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the velocity of the stars? What is the mass of the stars? 8x1010m Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the velocity of the stars? What is the mass of the stars? 4x1010m Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the velocity of the stars? v=2pr t Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the velocity of the stars? v=2pr t v= 2 p ( 4x1010m) = 633 m/s (12.6yrs(365d)(86400s) ( 1yr )( 1 day ) Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the velocity of the stars? v=2pr t v= 2 p ( 4x1010m) = 633 m/s (12.6yrs)(365d)(86400s) ( 1yr )( 1 day ) Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the velocity of the stars? v=2pr t v= 2 p ( 4x1010m) = 633 m/s (12.6yrs)(365d)(86400s) ( 1yr )( 1 day ) Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the velocity of the stars? v=2pr t v= 2 p ( 4x1010m) = 633 m/s (12.6yrs)(365d)(86400s) ( 1yr )( 1 day ) Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the velocity of the stars? v=2pr t v= 2 p ( 4x1010m) = 633 m/s (12.6yrs)(365d)(86400s) ( 1yr )( 1 day ) Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the velocity of the stars? v=2pr t v= 2 p ( 4x1010m) = 633 m/s (12.6yrs)(365d)(86400s) ( 1yr )( 1 day ) Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg Fg Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg Fg Fg causes the centripetal acceleration therefore Fg = Fc Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal acceleration therefore Fg = Fc Fg=Fc Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal accelertion therefore Fg = Fc Fg=Fc G mm = (8x1010m)2 Distance between centers m v2 4x1010m Distance to the center of rotation Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal accelertion therefore Fg = Fc Fg=Fc G mm = (8x1010m)2 Distance between centers m v2 4x1010m Distance to the center of rotation Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal accelertion therefore Fg = Fc Fg=Fc G mm = (8x1010m)2 Distance between centers m v2 4x1010m Distance to the center of rotation Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal accelertion therefore Fg = Fc Fg=Fc G mm = (8x1010m)2 Distance between centers m v2 4x1010m Distance to the center of rotation Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal accelertion therefore Fg = Fc Fg=Fc G mm = (8x1010m)2 Distance between centers m v2 4x1010m Distance to the center of rotation Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal accelertion therefore Fg = Fc Fg=Fc G mm = (8x1010m)2 m v2 4x1010m Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal accelertion therefore Fg = Fc Fg=Fc G mm = (8x1010m)2 m (633m/s)2 4x1010m Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal accelertion therefore Fg = Fc Fg=Fc Gm = (8x1010m)2 (633m/s)2 4x1010m Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal accelertion therefore Fg = Fc Fg=Fc mG = (633m/s)2 (8x1010m)2 4x1010m Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal accelertion therefore Fg = Fc Fg=Fc m = (633m/s)2 (8x1010m)2 G 4x1010m Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal accelertion therefore Fg = Fc Fg=Fc m = (633m/s)2 (8x1010m)2 6.67x10-11Nm2/kg2 4x1010m Bipolar Star System Two stars 8x1010m apart rotate about a point 4x1010 m from each other in a circular path in 12.6 years. The two stars have the same mass. What is the mass of the stars? Fg causes the centripetal accelertion therefore Fg = Fc Fg=Fc m = (633m/s)2 (8x1010m)2 6.67x10-11Nm2/kg2 4x1010m m = 9.61x1026kg
