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Semi Minor Axis of Ellipse given Eccentricity and Semi Major Axis Calculator

Formula Used:

\[ b = a \times \sqrt{1 - e^2} \]

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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:

\[ b = a \times \sqrt{1 - e^2} \]

Where:

Explanation: The formula calculates the semi minor axis using the semi major axis and eccentricity, which defines the shape of the ellipse.

3. Importance of Semi Minor Axis Calculation

Details: The semi minor axis is crucial for determining the area and perimeter of an ellipse, as well as understanding its geometric properties in various applications including astronomy, engineering, and architecture.

4. Using the Calculator

Tips: Enter the semi major axis in meters and eccentricity (a value between 0 and 1). Both values must be valid (semi major axis > 0, eccentricity between 0-1).

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between semi major and semi minor axes?
A: The semi minor axis is always smaller than or equal to the semi major axis, with equality only in the case of a circle (eccentricity = 0).

Q2: What are valid values for eccentricity?
A: Eccentricity ranges from 0 (circle) to values approaching 1 (highly elongated ellipse).

Q3: How is this formula derived?
A: The formula is derived from the standard ellipse equation and the definition of eccentricity as \( e = \sqrt{1 - \frac{b^2}{a^2}} \).

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but you can use any consistent unit system as long as both axes are in the same units.

Q5: What if eccentricity equals 1?
A: When eccentricity equals 1, the shape becomes a parabola, not an ellipse, so this formula doesn't apply.

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