A satellite is revolving around the Earth in a circular orbit with radius of 2R, where R is radius of earth.If suddenly,its velocity becomes zero in the orbit due to collision with some inter-stellar object(like a satellite),find the time which it takes to hit surface of the earth. Ignore the effect of atmosphere and treat earth to be perfect sphere.
36Assume mass of the satellite to be 'm'
T.Ei = -G(m)(M)/2r + 0 and T.Ef = -G(m)(M)/R + 1/2mv2
Now, by conservation of energy..
T.Ei = T.Ef
=> v = √(Gm)
Now since satellite is a free-falling body
so, we can apply the eqns. of motion
√(Gm) = 0 + gt
=> t = √(GM/g2)
66One can use Kepler's law. The time period of a satellite orbiting at the same distance is
T = \sqrt{\dfrac{4\pi^2}{GM}(2R)^3} = 2\sqrt{2}\sqrt{\dfrac{4\pi^2}{gM}R^3}
The time to fall is then given by
\dfrac{T}{4\sqrt{2}}
1Actually Kaymant sir i wanted to ask u about this question.Your solution is fairly classical but it releies on the assumption that the sattellite moves in an extended flat ellipse but my question is that it cant be perefeclty accurate as you are approimating it and most importantly i dont understand how could one imagine an extended flat ellipse in this situation. for another solution u can use calculus at hieght hieght x above the centre accelration =GM/x^2
now use vdv=adx to get a function of v versus x and then write v as dx/dt and integrat eunder proper limits but i will have to accept that it has to much calcualtion
71Is it also necessary that the satellite revolves round the earth only once.. ? I mean is it swirling inwards towards the earth or what? Can you present us with a sketch of possible motion of the satellite?
1@ Vivek that is the assumption of the problem an exteded flat ellipse such that it approximates into striaght line motion ..i dont know but i have been never able to imagine it
