Calculate Area of Ellipse in Keplerian Orbit

[cptolemy]

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 don't know if I'm explaning this right...Hope so.

Kind regards,

CPtolemy

 

[Mark44]

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 don't 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]

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]

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 $\pi ab$.

 

[martiandawn]

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.