Question

there are 2 formulas for escape vel,in what condition should we use the first formula and where should we use the second?

Answer 1

ι нσρє уσυ нєℓρ !!!

 

when satellite is at earth surface then

total energy = PE + KE

PE = -GMm/R     , (KE)i = ?                       (M is mass of earth )

TE = (KE)i - GMm/R           .....1                  (R is radius of earth)

 

when satellite escapes from earths gravitational field then it reaches to infinity ...

total energy finally = TE = KE + PE

PE = GMm/r          ( r is infinity )

PE = 0 , (KE)f = ?

TE = (KE)f  +  0 = (KE)f   .............2

 

since energy is conserved so eq 1 equals eq 2

-GMm/R + (KE)i = (KE)f

   (KE)i  = GMm/R +  (KE)f        .................3

from this eq we can see that if (KE)f is 0 then (KE) intial is minimum 

value of energy should be given to satellite so that it escapes out...

now , (KE)i = mv2/2 ,  (KE)f = 0 , putting these values in eq 3 we get

v = (2GM/R)1/2

this is the required result...