1. What is Ellipse Eccentricity?

Eccentricity (e) is a parameter that determines how much an ellipse deviates from being circular. It ranges from 0 (perfect circle) to values approaching 1 (highly elongated ellipse).

2. How Does the Calculator Work?

The calculator uses the ellipse eccentricity formula:

Where:

• \( a \) — Semi-major axis (longest radius)
• \( b \) — Semi-minor axis (shortest radius)
• \( e \) — Eccentricity (unitless)

Explanation: The formula calculates how "flat" or elongated the ellipse is compared to a perfect circle.

3. Importance of Eccentricity Calculation

Details: Eccentricity is crucial in astronomy (planetary orbits), engineering (elliptical designs), and mathematics (conic sections analysis).

4. Using the Calculator

Tips: Enter both semi-major axis (a) and semi-minor axis (b) values in the same units. Ensure a > b > 0 for valid ellipse parameters.

5. Frequently Asked Questions (FAQ)

Q1: What does eccentricity = 0 mean?
A: An eccentricity of 0 indicates a perfect circle where a = b.

Q2: Can eccentricity be greater than 1?
A: For ellipses, eccentricity ranges from 0 to 1. Values greater than 1 indicate hyperbolic orbits.

Q3: How is eccentricity used in astronomy?
A: It describes the shape of planetary orbits around the sun (Earth's orbit has e ≈ 0.0167).

Q4: What's the relationship between foci and eccentricity?
A: Higher eccentricity means the foci are farther apart, creating a more elongated ellipse.

Q5: Are there other ways to calculate eccentricity?
A: Yes, eccentricity can also be calculated using focal distance and semi-major axis: e = c/a where c is the distance from center to focus.