Solution of Pb 91This problem is pretty hard,
. It require
s knowledge
about of Path Equation. However, we can derive it
, using basic conservation law
s.
From the conservation
s of angular momentum and energy.

. ......1

. ......2
Substitute

from 1 to 2 we get,


......3
And then devided by

,

We must find

from the definition


Let

,

and,

Then the equation turns to be,

.
then integrate this equation,


We set when

,

Then we get

.
Then
Ccalculate B and A

then

And we get


then

, If you plot
this equation, in polar coordinate
s, you will see that it
's will come
s form from infinity,
to move
s around the star one turn
s and then go
back to infinity (but in the opposite direction). And the minimum distance is obviously

, when

ps. If you see something incorrect please tell me even if it just a grammatically incorrect.
pps. Sorry that I type in english. I just want to practice.
