Calculate Area of Ellipse in Keplerian Orbit

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Discussion Overview

The discussion revolves around calculating the area swept out by a body in a Keplerian orbit, specifically focusing on the area defined by an angle measured from the focus of the ellipse where the Sun is located. Participants seek to clarify terminology and explore the mathematical relationships involved in this calculation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • CPtolemy initially expresses uncertainty about how to calculate the area swept out in a Keplerian orbit, using the term "swaped" instead of "swept."
  • Some participants clarify that the area of interest is the area "swept out" by the planet's motion within the elliptical orbit.
  • One participant mentions that the area of an ellipse can be calculated using the formula \(\pi ab\), where \(a\) and \(b\) are the lengths of the major and minor axes, respectively.
  • Another participant references a specific equation from a textbook related to the relationship between time and area swept out, involving specific angular momentum and flight path angle.

Areas of Agreement / Disagreement

There is no consensus on the exact method for calculating the swept area, as participants provide different perspectives and formulas without resolving the discussion.

Contextual Notes

Participants have not fully defined the parameters necessary for calculating the swept area, such as the specific angle or the values of the semi-major and semi-minor axes. The discussion also reflects some uncertainty in terminology.

Who May Find This Useful

This discussion may be useful for individuals interested in orbital mechanics, particularly those exploring the mathematical aspects of Keplerian orbits and area calculations related to celestial bodies.

cptolemy
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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
 
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cptolemy said:
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.
 
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.
 

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