1. What is Kepler's First Law?

Kepler's First Law states that all planets move in elliptical orbits with the Sun at one focus. The eccentricity (e) quantifies how much the orbit deviates from being circular.

2. How Does the Calculator Work?

The calculator uses the eccentricity formula:

Where:

• \( e \) — Eccentricity (dimensionless)
• \( a_{semi} \) — Semi-major axis (m)
• \( b_{semi} \) — Semi-minor axis (m)

Explanation: The formula calculates the eccentricity of an ellipse, which describes the shape of planetary orbits according to Kepler's First Law.

3. Importance of Eccentricity Calculation

Details: Eccentricity is crucial for understanding orbital mechanics, predicting planetary positions, and analyzing satellite trajectories. It helps determine how elliptical an orbit is compared to a perfect circle.

4. Using the Calculator

Tips: Enter semi-major axis and semi-minor axis values in meters. Both values must be positive, and the semi-major axis must be greater than or equal to the semi-minor axis.

5. Frequently Asked Questions (FAQ)

Q1: What does eccentricity value represent?
A: Eccentricity ranges from 0 (perfect circle) to 1 (parabola). Values between 0 and 1 represent elliptical orbits.

Q2: What are typical eccentricity values for planets?
A: Most planets have low eccentricity (near 0): Earth ~0.0167, Mars ~0.0934. Comets have high eccentricity (near 1).

Q3: Can eccentricity be greater than 1?
A: For closed orbits (ellipses), eccentricity is always less than 1. Values greater than 1 represent hyperbolic trajectories.

Q4: How does eccentricity affect orbital period?
A: According to Kepler's Third Law, orbital period depends only on semi-major axis, not eccentricity.

Q5: What's the relationship between eccentricity and orbital energy?
A: For a given semi-major axis, higher eccentricity means the orbit has more kinetic energy at periapsis and less at apoapsis.