Stress In Steel By Working-Stress Design Calculator

Formula Used:

\[ Eccentricity \text{ } of \text{ } Elliptical \text{ } Orbit = \frac{Distance \text{ } Between \text{ } Two \text{ } Foci}{2 \times Semi \text{ } Major \text{ } Axis \text{ } of \text{ } Elliptic \text{ } Orbit} \] \[ e_e = \frac{d_{foci}}{2 \times a_e} \]

Eccentricity of Elliptical Orbit:

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1. What is Eccentricity of Elliptical Orbit?

Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is. It quantifies the deviation of the orbit from a perfect circle, where an eccentricity of 0 represents a circular orbit and values closer to 1 indicate more elongated elliptical orbits.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ e_e = \frac{d_{foci}}{2 \times a_e} \]

Where:

\( e_e \) — Eccentricity of Elliptical Orbit
\( d_{foci} \) — Distance Between Two Foci (meters)
\( a_e \) — Semi Major Axis of Elliptic Orbit (meters)

Explanation: The formula calculates the eccentricity by dividing the distance between the two foci by twice the semi-major axis of the elliptical orbit.

3. Importance of Eccentricity Calculation

Details: Calculating orbital eccentricity is crucial in astronomy and orbital mechanics for understanding the shape and characteristics of planetary orbits, satellite trajectories, and other celestial motions.

4. Using the Calculator

Tips: Enter the distance between two foci and the semi-major axis in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What does eccentricity value indicate?
A: Eccentricity values range from 0 to 1, where 0 indicates a perfect circle and values approaching 1 indicate highly elongated ellipses.

Q2: What are typical eccentricity values for planetary orbits?
A: Most planets in our solar system have low eccentricity values (close to 0), while comets and some asteroids have higher eccentricities.

Q3: Can eccentricity be greater than 1?
A: For elliptical orbits, eccentricity is always between 0 and 1. Values greater than 1 indicate hyperbolic orbits.

Q4: How does eccentricity affect orbital velocity?
A: Objects in elliptical orbits travel faster when closer to the focus (periapsis) and slower when farther away (apoapsis).

Q5: What's the relationship between eccentricity and orbital energy?
A: For a given semi-major axis, higher eccentricity means the orbit has the same total energy but different distribution between kinetic and potential energy throughout the orbit.