Problem

By expanding e sin ψ in a Fourier series in ωt, show that Kepler’s equation has the formal...

By expanding e sin ψ in a Fourier series in ωt, show that Kepler’s equation has the formal solution

where Jn is the Bessel function of order n. For small argument, the Bessel function can be approximated in a power series of the argument. Accordingly, from this result derive the first few terms in the expansion of ψ in powers of e.

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Solutions For Problems in Chapter 3