A planet A moves along an elliptical orbit around the Sun. At the moment when it was at the distance r 0 from the Sun its velocity was equal to v 0 and the angle between the radius vector r 0 and the velocity vector v 0 was equal to α . Find the maximum and minimum distance that will separate this planet from the Sun during its orbital motion. (Mass of Sun = M S )
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
r m = 
[1 ± 
],
where η = r 0 v 0 2 /GM S .
Sol.
at max and min. distance, Velocity will be perpendicular to the radius vector, Applying angular
momentum conservation about the sun, between initial position and the position of max or minimum
distance.
MV 0 r 0 sin α = MVr ..........(1)
applying energy conservation:
MV o 2 + 
= 
mv 2 + 
from equ (1) and (2) get
r = 
where 
have + sign will give r max and - sign will give r min .
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