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.
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
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].
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.