1. What is the Semi Minor Axis of Ellipse?

The Semi Minor Axis of an Ellipse is half of the length of the shortest diameter of the ellipse. It is perpendicular to the semi major axis and passes through the center of the ellipse.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( b \) — Semi Minor Axis of Ellipse (m)
• \( c \) — Linear Eccentricity of Ellipse (m)
• \( e \) — Eccentricity of Ellipse (dimensionless)

Explanation: This formula calculates the semi minor axis using the linear eccentricity and eccentricity of the ellipse, taking into account the geometric relationship between these parameters.

3. Importance of Semi Minor Axis Calculation

Details: The semi minor axis is a fundamental parameter in ellipse geometry, used in various applications including orbital mechanics, optics, and engineering design where elliptical shapes are involved.

4. Using the Calculator

Tips: Enter linear eccentricity in meters, eccentricity as a dimensionless value between 0 and 1. Both values must be valid (c > 0, 0 < e < 1).

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid values for eccentricity?
A: Eccentricity values range from 0 (circle) to 1 (parabola), but for ellipses specifically, the range is 0 ≤ e < 1.

Q2: How does semi minor axis relate to semi major axis?
A: The semi minor axis is always smaller than or equal to the semi major axis, with b = a√(1-e²) where a is the semi major axis.

Q3: Can this formula be used for circles?
A: Yes, when eccentricity is 0, the formula simplifies and the semi minor axis equals the radius (same as semi major axis).

Q4: What are practical applications of this calculation?
A: Used in astronomy for planetary orbits, in engineering for elliptical gears and mirrors, and in architecture for elliptical designs.

Q5: Are there limitations to this formula?
A: The formula assumes a perfect mathematical ellipse and may not account for real-world imperfections in elliptical shapes.