Calculate Area of Ellipse in Keplerian Orbit

In summary, calculating the area swaped in a Keplerian orbit can be done using the equation dt = 2/h dA, where h is the specific angular momentum and dA is the area swept out by the orbiting body. This is consistent with Kepler's second law and can be found in Fundamentals of Astrodynamics by Bate, Mueller and White.
  • #1
cptolemy
48
1
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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  • #2
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.
 
  • #3
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
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
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.
 

1. How do you calculate the area of an ellipse in Keplerian orbit?

The formula for calculating the area of an ellipse in Keplerian orbit is A = π * a * b, where a and b are the semi-major and semi-minor axes of the ellipse, respectively. This formula is known as the "area law" in Kepler's laws of planetary motion.

2. What is the significance of calculating the area of an ellipse in Keplerian orbit?

The area of an ellipse in Keplerian orbit represents the amount of space swept out by an orbiting object over a specific period of time. This is an important concept in understanding the dynamics of celestial bodies in our solar system and beyond.

3. How does the area of an ellipse in Keplerian orbit relate to the orbital speed of an object?

The area of an ellipse in Keplerian orbit is directly proportional to the orbital speed of an object. This means that as the orbital speed increases, the area swept out by the object also increases, and vice versa.

4. Can the area of an ellipse in Keplerian orbit change over time?

Yes, the area of an ellipse in Keplerian orbit can change over time as the orbiting object moves through its elliptical path. This is due to the fact that the orbital speed and distance from the center of the ellipse are constantly changing.

5. Are there any real-world applications of calculating the area of an ellipse in Keplerian orbit?

Yes, calculating the area of an ellipse in Keplerian orbit has many practical applications in fields such as astronomy, astrodynamics, and aerospace engineering. It is used to accurately predict the motion of objects in space, plan satellite orbits, and even design spacecraft trajectories for space missions.

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