Classical Scattering: Understanding Hyperbolic Orbits

[Amith2006]

I have spent lot of time trying to understand scattering from Goldstein but in vain. The general equation of an orbit is,

1/r = K[1 + e*cos(θ - θ')] where e=eccentricity
I refer to a sentence in goldstein which says, if θ'=pi then θ = 0 corresponds to the periapsis. What is θ' in the case of hyperbolic orbit? As far as the general equation is concerned, θ' is one of the turning angles of the orbit but in scattering there is only one turning angle which corresponds to the periapsis.
Then the equation becomes,
1/r = K[1 - e*cos(θ)]
Please help.

 

[gtoguy97]

In the case of a hyperbolic orbit, θ' is the angle between the initial position of the particle and the periapsis. This angle is typically measured from the position of the particle at the time of the closest approach (periapsis) to the central body. In the equation you provided, θ represents the angle between the current position of the particle and the periapsis.