A satellite is launched tangentially from a height h above earth's surface as shown. I. Find v_(min) so that it just touches the earth's surface II. If h = R and satellite is launched tangentially with speed = sqrt((3GM)/(5R)) find the maximum distance of satellite from earth's centre .

A satellite is launched tangentially from a height h above earth's sur

1.	A satellite is launched tangentially from a height h above earth's surface as shown. I. Find v_(min) so that it just touches the earth's surface II. If h = R and satellite is launched tangentially with speed = sqrt((3GM)/(5R)) find the maximum distance of satellite from earth's centre .
Answer» SOLUTION :(I) Satellite just Grazes surface of earth when `2a = 2R+h` `a = (R+(h)/(2))` Total energy `(E )= -(GMm)/(2a)=-(GMm)/((2R+h))` `(1)/(2)mV_(0 min)^(2)-(GMm)/(R+h)=-(GMm)/(2R+h)` `V_(0 min)^(2) = 2GMm[(1)/(R+h)-(1)/(2R+h)]` `= (2GMR)/((R+h)(2R+h)) = (2GMR)/(r(R+r))` `V_(0 min) =sqrt((2GMR)/(r(R+r)))` where `r = h+R` (II) To find maximum distance from CENTRE. `E = - (GMm)/(2a) = (1)/(2)mv_(0)^(2) - (GMm)/(2R)` `= (1)/(2)m. (3GM)/(5R)-(GMm)/(2R)` `-(1)/(2a)=(3)/(10R)-(1)/(2R) = -(2)/(10R)` `2a = 5R =` Major axis Required distance = 3R