8.23*** A particle of mass m moves with angular momentum & in the field of a fixed force center with k λ F(r) =- + r2 where k and λ are positive. (a) Write down the transformed radial equation (8.41) and prove that the orbit has the form C r(Ø) = = 1+ € cos(Bo) 324 Chapter 8 Two-Body Central-Force Problems where c, B, 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 k λ F(r) =- + r2 where k and λ are positive. (a) Write down the transformed radial equation (8.41) and prove that the orbit has the form C r(Ø) = = 1+ € cos(Bo) 324 Chapter 8 Two-Body Central-Force Problems where c, B, 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?
Question
Transcribed Image Text:8.23*** A particle of mass m moves with angular momentum & in the field of a fixed force center with
k λ
F(r) =- +
r2
where k and λ are positive. (a) Write down the transformed radial equation (8.41) and prove that the
orbit has the form
C
r(Ø) =
=
1+ € cos(Bo)
324
Chapter 8 Two-Body Central-Force Problems
where c, B, 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?
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