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Area for an ellipseby cptolemy
Tags: ellipse 
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#1
Aug2314, 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 


#2
Aug2314, 12:52 PM

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P: 21,397

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. 


#3
Aug2314, 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 


#4
Aug2314, 03:24 PM

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PF Gold
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]. 


#5
Aug2414, 01:54 PM

P: 9

In Fundamentals of Astrodynamics by Bate, Mueller and White, ISBN 0486600610, 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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