Elliptical Orbit Time Period Given Angular Momentum And Eccentricity Calculator

Formula Used:

\[ T_e = \frac{2\pi}{[GM.Earth]^2} \times \left( \frac{h_e}{\sqrt{1-e_e^2}} \right)^3 \]

Time Period of Elliptic Orbit:

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1. What is the Elliptical Orbit Time Period Calculation?

The Elliptical Orbit Time Period calculation determines the time required for an object to complete one full orbit around a celestial body in an elliptical path, based on angular momentum and orbital eccentricity.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T_e = \frac{2\pi}{[GM.Earth]^2} \times \left( \frac{h_e}{\sqrt{1-e_e^2}} \right)^3 \]

Where:

\( T_e \) — Time Period of Elliptic Orbit (seconds)
\( h_e \) — Angular Momentum of Elliptic Orbit (m²/s)
\( e_e \) — Eccentricity of Elliptical Orbit (dimensionless)
\( [GM.Earth] \) — Earth's Geocentric Gravitational Constant (3.986004418E+14)
\( \pi \) — Archimedes' constant (3.141592653589793)

Explanation: The formula calculates orbital period by considering the conservation of angular momentum and the elliptical shape of the orbit characterized by its eccentricity.

3. Importance of Time Period Calculation

Details: Accurate orbital period calculation is crucial for satellite mission planning, orbital mechanics analysis, and predicting the position of celestial objects in elliptical orbits.

4. Using the Calculator

Tips: Enter angular momentum in m²/s and eccentricity (0 ≤ e < 1). Ensure values are physically meaningful for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is angular momentum in orbital mechanics?
A: Angular momentum is a conserved quantity that describes the rotational motion of an orbiting body around a central point.

Q2: How does eccentricity affect orbital period?
A: For the same angular momentum, higher eccentricity results in longer orbital periods due to the increased orbital energy.

Q3: What are typical eccentricity values for Earth orbits?
A: Low Earth orbits typically have eccentricities close to 0 (circular), while Molniya orbits can have eccentricities around 0.7.

Q4: Can this formula be used for other celestial bodies?
A: Yes, but the gravitational parameter ([GM]) must be replaced with that of the specific celestial body.

Q5: What are the limitations of this calculation?
A: This assumes a two-body problem and doesn't account for perturbations from other bodies, atmospheric drag, or non-spherical gravity fields.