Question

A geosynchronous satellite is placed above the equator and orbiting around the earth to facilitate communication around the world. (You may consider that the mass of the satellite is m, mass of the earth is M(6x1024 kg), center-to-center distance between the satellite and the earth is r, radius of the earth is R(6.4×106 m), and the universal gravitational constant G = 6.67x10-11 N.m2/kg2.) Satellite Earth Applying newton's 2nd law, write an equation describing the circular motion of the satellite. (4 points) Write an expression for v in terms of T and r. (4 points) Using the expression for v, simplify the equation you obtained in part f to get an expression for the radius r of the satellite's orbit and calculate r. (4 points)

Answer 1

solution A GMm = mit ATY 2T8 3 27 T = Tr. → Ve SIT v = 2101 3- Vom = 2tr 23/22 I ſam > r3= T2 GM aralIG But T = 24 hours = 86400 seconds so r=[(86400 ) 3 6067X10² x 60x102471 4x (3:14) 2_ = 17406496 X108 x 40.02.X/0!3] [757504613x1021) = 4.2312x107 m r= 4,2312 8107 m 452, 452 39, 4384