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The Semi Major Axis of an Ellipse is half of the longest diameter of the ellipse. It is a fundamental parameter that defines the size and shape of the ellipse, along with the semi minor axis and eccentricity.
The calculator uses the formula:
Where:
Explanation: This formula calculates the semi major axis of an ellipse given its semi minor axis and eccentricity, using the mathematical relationship between these parameters.
Details: The semi major axis is crucial in various applications including astronomy (orbital mechanics), engineering (ellipse design), and physics. It helps determine the size, shape, and properties of elliptical orbits and structures.
Tips: Enter semi minor axis in meters, eccentricity as a dimensionless value between 0 and 1. Both values must be valid (b > 0, 0 ≤ e < 1).
Q1: What is the range of possible values for eccentricity?
A: Eccentricity values range from 0 (circle) to values approaching 1 (highly elongated ellipse).
Q2: How does eccentricity affect the semi major axis?
A: For a fixed semi minor axis, as eccentricity increases, the semi major axis also increases to maintain the elliptical shape.
Q3: Can this formula be used for circles?
A: Yes, when eccentricity is 0, the formula simplifies to a = b, which is correct for a circle where both axes are equal.
Q4: What are typical applications of this calculation?
A: This calculation is used in astronomy for planetary orbits, in engineering for elliptical designs, and in various mathematical and physics applications involving elliptical shapes.
Q5: Are there limitations to this formula?
A: The formula is mathematically exact for perfect ellipses. It assumes the ellipse follows the standard mathematical definition and may not apply to distorted or irregular elliptical shapes.