8.23*** A particle of mass m moves with angular momentum & in the field of a fixed force center withk14/12324F(r)r(p) =+where k and are positive. (a) Write down the transformed radial equation (8.41) and prove that theorbit has the form=بدالC1 + € cos(Bo)Chapter 8 Two-Body Central-Force Problemswhere c, ß, and € are positive constants. (b) Find c and ß in terms of the given parameters, and describethe orbit for the case that 0 << < 1. (c) For what values of ß is the orbit closed? What happens to yourresults as λ → 0?

Given8.23*** A particle of mass m moves with angular momentum l in the field of a fixed force center…

8.23 *** A particle of mass m moves with angular momentum & in the field of a fixed force center with = - = /2+1/1/3 k r3 324 F(r) = -- where k and λ are positive. (a) Write down the transformed radial equation (8.41) and prove that the orbit has the form r(ø) = C 1 + € cos(Bo) Chapter 8 Two-Body Central-Force Problems where c, ß, and € are positive constants. (b) Find c and ß in terms of the given parameters, and describe the orbit for the case that 0 < € < 1. (c) For what values of ß is the orbit closed? What happens to your results as λ → 0?

8.23 *** A particle of mass m moves with angular momentum & in the field of a fixed force center with = - = /2+1/1/3 k r3 324 F(r) = -- where k and λ are positive. (a) Write down the transformed radial equation (8.41) and prove that the orbit has the form r(ø) = C 1 + € cos(Bo) Chapter 8 Two-Body Central-Force Problems where c, ß, and € are positive constants. (b) Find c and ß in terms of the given parameters, and describe the orbit for the case that 0 < € < 1. (c) For what values of ß is the orbit closed? What happens to your results as λ → 0?