Eccentric & Mean Anomaly: Difference & Drawing

In summary, the difference between the Eccentric Anomaly and Mean Anomaly is that the former is represented by the angle E in the drawing, while the latter is a mathematical construct denoted by M. The True Anomaly (f) and Eccentric Anomaly (E) do not change at a constant rate, so the Mean Anomaly is obtained by averaging E over the entire orbit to create an angle that increases at a constant rate. This concept is similar to the Mean Solar Day, where the average length of a day is used to create a day that is always the same length. It is not possible to visually represent the Mean Anomaly on the drawing.
  • #1
Philosophaie
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What is the difference between the drawing of the Eccentric Anomaly and the Mean Anomaly.
http://www.philosophaie.com/EA.png
One has a circle radius "a" inscribed an ellipse with a focus "F". The True Anomaly makes "f" makes an angle to point "P" then a perpendicular is drawn to a point on the circle where a line is drawn to the center.

What is this angle Mean or Eccentric? How do you draw the other Anomaly?
 
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  • #2
Is Mean Anomaly from point "P" on the ellipse to the center?
 
  • #3
The mean anomaly is a mathematical construct. Neither the True anomaly (f in the drawing) nor the Eccentric anomaly (E in the drawing) change at a constant rate, because the planet goes more slowly when it is far away from the Sun than when it is close to the sun. So the Mean Anomaly is obtained by taking E and averaging it over the whole orbit so that M is always increasing at a constant rate. It is similar in concept to the "Mean Solar Day", where we take the average length of the day over the whole year and create a day that is always the same length, even though the actual length of the day changes slightly as we go through the year. Since it is a construct, I don't know of a way to picture it on the drawing.
 

1. What is the difference between eccentric anomaly and mean anomaly?

Eccentric anomaly and mean anomaly are both measurements used in orbital mechanics to describe the position of a celestial object in its orbit. The main difference between them is the way they are calculated. Eccentric anomaly is calculated using the eccentricity of the orbit and the true anomaly, while mean anomaly is calculated using the eccentricity and the time since the object passed through its perihelion (closest point to the sun).

2. How are eccentric and mean anomaly related?

Eccentric and mean anomaly are related through Kepler's equation, which describes the relationship between the position and time of a celestial object in an elliptical orbit. Mean anomaly is used to calculate eccentric anomaly, which in turn is used to calculate the true anomaly and determine the position of the object in its orbit.

3. Can eccentric and mean anomaly be negative?

Yes, both eccentric and mean anomaly can be negative. Eccentric anomaly is a measure of the angular distance from the center of the orbit, so it can be positive or negative depending on the position of the object. Mean anomaly is also a measure of angular distance, but it is relative to the time since the object passed through its perihelion, so it can also be negative.

4. How do you draw eccentric and mean anomaly on an orbit diagram?

To draw eccentric and mean anomaly on an orbit diagram, you first need to calculate their values using the eccentricity of the orbit and the true anomaly. Then, you can plot these values on the diagram, with eccentric anomaly on the x-axis and mean anomaly on the y-axis. This will create a curve known as Kepler's ellipse, which represents the orbital path of the object.

5. Why are eccentric and mean anomaly important in orbital mechanics?

Eccentric and mean anomaly are important in orbital mechanics because they help us understand and predict the position of celestial objects in their orbits. These measurements are used in Kepler's laws of planetary motion, which are fundamental principles in understanding the motion of objects in space. Eccentric and mean anomaly also play a crucial role in satellite and spacecraft operations, as they are used to determine the timing and trajectory of maneuvers and orbits.

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