1. What is Ellipse Eccentricity?

Eccentricity (e) is a parameter that determines how much an ellipse deviates from being circular. It's a unitless number between 0 (perfect circle) and 1 (parabola).

2. How Does the Calculator Work?

The calculator uses the eccentricity formula:

Where:

• \( a \) — Semi-major axis (longest radius)
• \( b \) — Semi-minor axis (shortest radius)
• \( e \) — Eccentricity (0 ≤ e < 1)

Explanation: The formula shows how the shape's flatness depends on the ratio between the axes. When a = b (circle), e = 0.

3. Importance of Eccentricity

Details: Eccentricity is crucial in astronomy (planetary orbits), engineering (arch design), and physics (particle motion in fields).

4. Using the Calculator

Tips: Enter both semi-axes in the same units. Semi-major axis (a) must be ≥ semi-minor axis (b). Values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What does eccentricity = 0 mean?
A: A perfect circle (both axes equal length).

Q2: Can eccentricity be 1 or greater?
A: For ellipses, 0 ≤ e < 1. e=1 is a parabola, e>1 is a hyperbola.

Q3: How is eccentricity used in astronomy?
A: It describes planetary orbits - Earth's e≈0.0167 (nearly circular), Halley's comet e≈0.967 (highly elliptical).

Q4: What's the relationship with flattening?
A: Flattening (f) = 1 - b/a. Eccentricity relates as e² ≈ 2f - f² for small f.

Q5: Can I calculate if b > a?
A: The calculator will automatically use the larger value as 'a' to maintain a ≥ b.