A cosmic body A moves towards the Sun with velocity v 0 (when far from the Sun) and aiming parameter λ , the direction of the vector v 0 relative to the center of the Sun as shown in the figure. Find the minimum distance by which this body will get to the Sun. (Mass of Sun = M S )
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
r min = (GM S / v 0 2 ) [ 
– 1]
Sol. Applying angular momentum conservation:
mv 0 λ = mvd
v 0 λ = vd .......... (i)
Initial energy = 
mv 0 2 + 0
Final energy = 
mv 2 – 
Applying energy conservation,
mv 0 2 = 
mv 2 – 
v 0 2 = v 2 – 
.......... (ii)
From equation (i) and (ii):
v 0 2 = 
– 
d 2 + 
d – λ 2 = 0
Solving this quadratic
d = – 
+ 
= 
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