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Topic: ellipse, mean distance from point on perimeter to a focus ?
Replies: 8   Last Post: Feb 12, 2010 5:56 PM

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Achava Nakhash, the Loving Snake

Posts: 931
Registered: 12/6/04
Re: ellipse, mean distance from point on perimeter to a focus ?
Posted: Feb 10, 2010 3:12 PM
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On Feb 10, 11:03 am, G Patel <> wrote:
> Is the mean distance from a point on perimeter to a focus equal to the
> semi major axis length?

When the books give us the "average distance of a planet from the sun"
they are giving us the length of the semi-major axis. So in that
sense, yes. In other senses, you need to specify what you are
measuring this with respect to. Average in time? Average in space,
for which the natural definition is the integral of the distance with
respect to the arclength divided by the length of the perimeter, or
something else? I don't actually know the answers to any of these,
but certain integrals to investigate come to mind immediately. Have
you tried to do anything with this?


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