Question

Venus has an orbital period of 224.7 days and a rotational period of 243.02 days.  NASA would like to place a satellite around Venus which always remains in the same position over the Venusian surface.  

(a) (10 points) What should the altitude above the Venusian surface be (KILOMETERS)?

B. What should the speed of this satellite be (m/s)?

Answer 1

Rotational period of of Venus, T = 243.02 day 2 days = 20996928 See Since the satellite to be remain in the same position overe Venesian Sureface, the orbital period of satellite will also be T. a) It m be the mass of Satellite and M be the mass of Venus then gravitational atten. ction between satellite and Venus is respon. fore centrifugal force. Sible FG Fe GM m mol p2 p

w² GM r U- speed of satellite r= Radius of orbit If T is the time period, G = Gravitational Constant them, 212 T 2 4772 Tr GM p Т - 2 GMT 7 T2 47 3 GM or gp 3 472 P T= 20996928 See and Putting Mass of Venus, M = 4.867x1024 kg 616748103 "x 4.96781024 (20996929) 3 у? 2 471 m go 9 1.536 x 10 6 1.536X; 0 km Now realius of Nenus, R = 6051.8 km the attitude of satellite above Venus Surface will be his R-3 so = 1.536 x 10 605108 th 1529948.2 km = 1.5299 8106 km

b) Again 18 4 2 т у. T 9 27x1536x10 2099 6928 19 я 459. 64 m/s