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in yuri gagarin's first manned 

Solution,
Time period of orbit of the space flight can be determined using Kepler's 3rd law:
T squared equals fraction numerator 4 pi squared over denominator G M end fraction a cubed W h e r e comma T space i s space t h e space t i m e space p e r i o d space o f space o r b i t space o f space t h e space s p a c e space f l i g h t G space i s space t h e space g r a v i t a t i o n a l space c o n s tan t space equals space 6.67 cross times 10 to the power of negative 11 end exponent fraction numerator N m squared over denominator k g squared end fraction M space i s space t h e space m a s s space o f space t h e space e a r t h equals 6 cross times 10 to the power of 24 k g a equals s e m i minus m a j o r space a x i s M a j o r space a x i s comma space 2 a equals 181 plus 2 cross times 6400 plus 327 equals 13308 space k m T h u s comma a equals 13308 over 2 equals 6654 space k m S o comma T squared equals fraction numerator 4 cross times 3.14 squared cross times 6654 cubed cross times 10 to the power of 9 over denominator space 6.67 cross times 10 to the power of negative 11 end exponent cross times 6 cross times 10 to the power of 24 end fraction S o comma T equals 5388 s I t space i s space c l o s e space t o space o p t i o n space left parenthesis A right parenthesis. space S o comma space o p t i o n space left parenthesis A right parenthesis space i s space C O R R E C T. space o p t i o n space left parenthesis B right parenthesis space i s space n o t space c o r r e c t. T h e space s p e e d space w i l l space b e space m a x i m u m space w h e n t h e space s p a c e space c r a f t space i s space i n space t h e space p e r i g e e space a n d space i s space g i v e n space b y space t h e space r e l a t i o n colon v subscript P equals square root of fraction numerator G M over denominator R subscript P end fraction open parentheses 1 plus fraction numerator 1 over denominator R subscript P divided by R subscript a end fraction close parentheses end root w h e r e. R subscript P equals 181 plus 6400 space equals space 6581 space k m R subscript a equals 327 plus 6400 equals 6727 space k m P u t t i n g space t h e space v a l u e s space o f space G comma space M comma space R subscript P space a n d space R subscript a space a n d space s o l v i n g comma space w e space g e t v subscript P equals 15.7 space k m divided by s S o comma space O p t i o n space left parenthesis C right parenthesis space i s space n o t space c o r r e c t. S i n c e comma s e m i minus m a j o r space a x i s comma space a equals 6654 space k m comma space o p t i o n space left parenthesis D right parenthesis space i s space C O R R E C T. space

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