A geostationary satellite above the equator is orbiting around the earth at a fixed distance r_1 from the center of the earth. A second satellite is orbiting in the equatorial plane in the opposite direction to the earth's rotation, at a distance r_2 from the center of the earth, such that r_1=1.21

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A geostationary satellite above the equator is orbiting around the earth at a fixed distance r_1 from the center of the earth. A second satellite is orbiting in the equatorial plane in the opposite direction to the earth's rotation, at a distance r_2 from the center of the earth, such that r_1=1.21 r_2. The time period of the second satellite as measured from the geostationary satellite is 24 p hours. The value of p is

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Correct answer: A. A

T r ^ 3 / 2 T _2 ~T _1 = ( r _2 r _1 )^ 3 / 2 _2 _1 = ( r_1 r_2 )^ 3 / 2 =(1.21)^ 3 / 2 aligned & _2= _1(1.331) ...(i)\ & ( _2+ _1 ) t_0=2 ...(ii) aligned t_0= 2 _2+ _1 = 2 ( 4 3 +1 ) _1 = 6 7 _1 t _0= 6 2 ( ~T _ GSS ) (7) t _0= 3 24 hours 7 = 24 p hours p = 7 3 =2.33

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