Stress In Steel Using Working-Stress Design Calculator

Formula Used:

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

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.

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: Eccentricity is a fundamental parameter in orbital mechanics that helps determine the shape and characteristics of orbits, which is crucial for satellite deployment, astronomical observations, and space mission planning.

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.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of possible values for eccentricity?
A: For elliptical orbits, eccentricity ranges from 0 (perfect circle) to values less than 1 (increasingly elongated ellipse).

Q2: How does eccentricity affect orbital characteristics?
A: Higher eccentricity means more elongated orbits with varying orbital speeds and greater distance variations between the orbiting body and the focus.

Q3: Can eccentricity be exactly 1 or greater than 1?
A: Eccentricity of 1 indicates a parabolic orbit, while values greater than 1 indicate hyperbolic orbits, both of which are open trajectories rather than closed elliptical orbits.

Q4: What are some real-world applications of eccentricity calculations?
A: Used in satellite orbit design, planetary motion studies, comet trajectory analysis, and spacecraft mission planning.

Q5: How accurate is this calculation method?
A: The formula provides exact mathematical results for ideal elliptical orbits based on the given parameters.