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An earth satellite is revolving in a cir...

An earth satellite is revolving in a circular orbit of radius a withh a velocity `v_(0)`. A gun in the satellite is directly aimed toward earth. A bullet is fired from the gun with muzzle velocity `(v_(0))/2`. Find the ratio of distance of farthest and closest approach of bullet from centre of earth. (Assume that mass of the satellite is very-very large with respect to the mass of the bullet)

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The correct Answer is:
3
`v_(0)=sqrt((GM)/a)`
`mv_(0)a=mvr`
`1/2m(v_(0)^(2)+(v_(0)^(2))/4)-(GMm)/a=1/2mv^(2)-(GMm)/r`
Solving `(r_(max))/(r_(min))=(2a)/(2a//3)=3`
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