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Re: Area of ellipse between major axis and ray through focus, given angle

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  • Subject: [mg71939] Re: Area of ellipse between major axis and ray through focus, given angle
  • From: rip pelletier <bitbucket at>
  • Date: Tue, 5 Dec 2006 06:04:37 -0500 (EST)
  • References: <ek96ij$fd5$>

In article <ek96ij$fd5$1 at>,
 "Kelly Jones" <kelly.terry.jones at> wrote:

> Given:
> 1) an ellipse with eccentricity "ec", one focus on the origin, and
> the major axis along the x-axis
> 2) a ray through the origin at angle theta to the x-axis
> Question:
> What Mathematica function gives the relation/inverse relation between
> the angle theta and the area of the ellipse between the x-axis and the ray?

two books which i find very useful for doing orbital mechanics are:

prussing & conway, "orbital mechanics", 1993, oxford.    

bate, mueller & white, "fundamentals of astrodynamics", 1971, dover.

kepler's equation for position-on-orbit is pretty and simple; and a 
geometric proof of it leads to a a pretty and simple solution for the 
area. the key is to define an auxiliary angle called the eccentric 
anomaly, for which see mathworld.

especially, note the last sentence, which tells you how to get the area: 
"M can also be interpreted as the area of the shaded region in the above 


NB eddress is r i p 1 AT c o m c a s t DOT n e t

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