Slingshot method problem?

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I trying to figure the hyperbola curve for a object heading towards Jupiter like a satellite [voyager] how would you graph the equation in polar cord.

i know the speed of the object at time zero is 40m/s at a distance of 5000,000 kilometers from Jupiter center

i know newton second law f=m*a which would be for both masses * acceleration of the object equal the force


What i am having problems with graphing the equation in polar cord of the satellite passing Jupiter slingshot method ? how would i do this? i know it calculus please help

thanks Steve If this problem been solved in the past where is the problem in a text book or something? and where can i find it

also would this deal with Newtonian physics or astro physics ? which one
 

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