Kepler's equation relates the eccentric anomaly to the mean anomaly for a body on an…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Mechanics & Dynamical Systems · Gravitation and central-force motion

Computational Physics, Ch Where a function vanishes, and what lies between the points

Problem

Kepler's equation relates the eccentric anomaly

E

to the mean anomaly

M

for a body on an elliptical orbit of eccentricity

e

E - e\sin E = M.

Both angles are in radians. (a) Write this as a root problem

f(E) = 0

. (b) For Mars,

e = 0.0934

. At a certain time

M = 2.50\,\mathrm{rad}

. Using the physical bound

|E-M|\le e

, state a bracket for

E

and check it by evaluating

f

at both ends. (c) For a comet with

e = 0.85

, at a time when

M = 0.65\,\mathrm{rad}

, state and check a bracket in the same way.

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