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An artificial satellite is moving in a c...

An artificial satellite is moving in a circular orbit around the earth with a speed of equal to half the magnitude of escape velocity from earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on the earth. Find the speed with which it hits the surface of earth. Given, M=mass of earth & R =Radius of earth

Text Solution

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The correct Answer is:
(i). 6400 km
(ii). 7.9 km/s
(i). Orbital velocity
`v_(2)=sqrt((GM)/(r))=(1)/(2)sqrt((2GM)/(R))`
`impliesr=2R=R+himpliesh=R=6400km`
(ii) COME : `-(GMm)/(2R)+0=-(GMm)/(R)+(1)/(2)mv^(2)`
`impliesv=sqrt((GM)/(R))=sqrt(gR)=7.9184m//s`
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