1. What is Linear Eccentricity of Ellipse?

Linear Eccentricity of an Ellipse is the distance from the center to either focus of the ellipse. It is an important parameter that helps define the shape and properties of the ellipse.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( c \) — Linear Eccentricity (m)
• \( A \) — Area of Ellipse (m²)
• \( b \) — Semi Minor Axis (m)
• \( \pi \) — Archimedes' constant (≈3.14159)

Explanation: This formula derives the linear eccentricity from the area and semi-minor axis of the ellipse using geometric relationships.

3. Importance of Linear Eccentricity

Details: Linear eccentricity is crucial in understanding the elliptical shape, determining focal points, and calculating other ellipse parameters. It's used in various fields including astronomy, physics, and engineering.

4. Using the Calculator

Tips: Enter the area of ellipse in square meters and semi-minor axis in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between linear eccentricity and other ellipse parameters?
A: Linear eccentricity relates to semi-major axis (a) and semi-minor axis (b) through the formula: c² = a² - b².

Q2: Can linear eccentricity be greater than the semi-minor axis?
A: Yes, linear eccentricity can be greater than the semi-minor axis, but it's always less than the semi-major axis.

Q3: What are typical applications of this calculation?
A: This calculation is used in orbital mechanics, optical systems, architectural design, and any application involving elliptical shapes.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect ellipses. Accuracy depends on the precision of input values.

Q5: What if I have the semi-major axis instead of area?
A: If you have semi-major axis (a), you can calculate linear eccentricity directly using: c = √(a² - b²).