Eccentricity Of Ellipse Given Area, Linear Eccentricity And Semi Minor Axis Calculator

Formula Used:

\[ e = \frac{\pi \times b \times c}{A} \]

Semi Minor Axis of Ellipse (b):

Linear Eccentricity of Ellipse (c):

Area of Ellipse (A):

m²

Eccentricity of Ellipse (e):

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1. What is the Eccentricity of an Ellipse?

The eccentricity of an ellipse is a measure of how much the ellipse deviates from being circular. It is defined as the ratio of the distance between the foci to the length of the major axis. For an ellipse, eccentricity ranges between 0 (a circle) and 1 (a parabola).

2. How Does the Calculator Work?

The calculator uses the formula:

\[ e = \frac{\pi \times b \times c}{A} \]

Where:

\( e \) — Eccentricity of the ellipse
\( b \) — Semi minor axis of the ellipse (m)
\( c \) — Linear eccentricity of the ellipse (m)
\( A \) — Area of the ellipse (m²)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the eccentricity of an ellipse using its semi minor axis, linear eccentricity, and area.

3. Importance of Eccentricity Calculation

Details: Eccentricity is a fundamental property of ellipses used in various fields including astronomy, physics, and engineering. It helps describe orbital paths, optical properties, and mechanical systems.

4. Using the Calculator

Tips: Enter the semi minor axis and linear eccentricity in meters, and the area in square meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of possible values for eccentricity?
A: For ellipses, eccentricity ranges from 0 (perfect circle) to values less than 1. A value of 1 represents a parabola, and greater than 1 represents a hyperbola.

Q2: How is eccentricity related to the shape of an ellipse?
A: Lower eccentricity values indicate a more circular shape, while higher values (closer to 1) indicate a more elongated ellipse.

Q3: Can eccentricity be negative?
A: No, eccentricity is always a non-negative value. For ellipses, it ranges between 0 and 1.

Q4: What are some practical applications of eccentricity?
A: Eccentricity is used in astronomy to describe planetary orbits, in optics for elliptical mirrors, and in mechanical engineering for cam designs and gear systems.

Q5: How accurate is this calculation method?
A: This formula provides exact results for perfect ellipses when accurate measurements of semi minor axis, linear eccentricity, and area are provided.