Bending Moment Of Beam Due To Stress In Concrete Calculator

Formula Used:

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

Eccentricity of Elliptical Orbit:

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1. What is the Eccentricity of Elliptical Orbit?

The eccentricity of an elliptical orbit is a measure of how stretched or elongated the orbit's shape is. It is a dimensionless parameter that ranges from 0 (perfect circle) to values approaching 1 (highly elongated ellipse).

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( e \) — Eccentricity of Elliptical Orbit (dimensionless)
\( d_{foci} \) — 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 length.

3. Importance of Eccentricity Calculation

Details: Eccentricity is a fundamental parameter in orbital mechanics that determines the shape of an orbit. It affects orbital period, velocity variations, and stability characteristics of celestial bodies and artificial satellites.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What does an eccentricity of 0 mean?
A: An eccentricity of 0 indicates a perfectly circular orbit where both foci coincide at the center.

Q2: What is the maximum possible eccentricity value?
A: For elliptical orbits, eccentricity ranges from 0 to just below 1. A value of 1 represents a parabolic orbit, while values greater than 1 represent hyperbolic orbits.

Q3: How does eccentricity affect orbital velocity?
A: Higher eccentricity means greater variation in orbital velocity, with maximum velocity at periapsis (closest approach) and minimum velocity at apoapsis (farthest point).

Q4: What are typical eccentricity values for planetary orbits?
A: Most planets in our solar system have low eccentricities (0.01-0.2), while comets and some asteroids can have much higher eccentricities (0.5-0.99).

Q5: Can eccentricity change over time?
A: Yes, eccentricity can change due to gravitational perturbations from other bodies, tidal forces, or orbital maneuvers in the case of artificial satellites.