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Area for an ellipse

by cptolemy
Tags: ellipse
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cptolemy
#1
Aug23-14, 12:47 PM
P: 7
Hello everybody,

I'm trying to know, in a keplerian orbit, how to calculate the area of a swaped area; since the Sun is at one of the focus, I wish to calculate given an angle measured from focus to the orbiting body, the area swaped.
I dont know if I'm explaning this right...Hope so.

Kind regards,

CPtolemy
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Mark44
#2
Aug23-14, 12:52 PM
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P: 21,397
Quote Quote by cptolemy View Post
Hello everybody,

I'm trying to know, in a keplerian orbit, how to calculate the area of a swaped area; since the Sun is at one of the focus, I wish to calculate given an angle measured from focus to the orbiting body, the area swaped.
I dont know if I'm explaning this right...Hope so.

Kind regards,

CPtolemy
swaped = ? What is this word?

Calculating the area of an ellipse is pretty straightforward. There are several formulas if you know the equation of the ellipse. See http://en.wikipedia.org/wiki/Ellipse#Area.
cptolemy
#3
Aug23-14, 01:17 PM
P: 7
Hi,

I mean swept. Sorry for my english... :(

I don't want to know the entire area of the ellipse - just the swept area by the body.

Regards,

CPtolemy

HallsofIvy
#4
Aug23-14, 03:24 PM
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P: 39,682
Area for an ellipse

I think he meant the area "swept out" by the planets motion- the area inside the elliptic orbit.

cptolemy, the area of an ellipse with major and minor axes of lengths a and b is [itex]\pi ab[/itex].
martiandawn
#5
Aug24-14, 01:54 PM
P: 9
In Fundamentals of Astrodynamics by Bate, Mueller and White, ISBN 0-486-60061-0, I can see the following equation:

dt = 2/h dA

h is the specific angular momentum, given by h = r v sin(γ), where γ is the flight path angle, i.e. the angle between the r and v vectors. This is consistent with Kepler's second law as h is a constant for a given orbit.


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