Specific Energy Of Elliptic Orbit Given Angular Momentum Calculator

Specific Energy of Elliptical Orbit Formula:

\[ \varepsilon_e = -\frac{1}{2} \times \frac{[GM.Earth]^2}{h_e^2} \times (1 - e_e^2) \]

Specific Energy of Elliptical Orbit:

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1. What is Specific Energy of Elliptical Orbit?

Specific Energy of Elliptical Orbit is the total orbital energy per unit mass of an orbiting body. It represents the sum of the kinetic energy and the gravitational potential energy of the orbiting object relative to the central body.

2. How Does the Calculator Work?

The calculator uses the specific energy formula:

\[ \varepsilon_e = -\frac{1}{2} \times \frac{[GM.Earth]^2}{h_e^2} \times (1 - e_e^2) \]

Where:

\( \varepsilon_e \) — Specific Energy of Elliptical Orbit (J/kg)
\( [GM.Earth] \) — Earth's Geocentric Gravitational Constant (3.986004418 × 10¹⁴ m³/s²)
\( h_e \) — Angular Momentum of Elliptic Orbit (m²/s)
\( e_e \) — Eccentricity of Elliptical Orbit (dimensionless, 0 ≤ e ≤ 1)

Explanation: The formula calculates the specific orbital energy based on angular momentum and orbital eccentricity, using Earth's gravitational parameter.

3. Importance of Specific Energy Calculation

Details: Specific orbital energy is a fundamental parameter in celestial mechanics that determines the size and shape of an orbit. It helps in understanding orbital stability, transfer maneuvers, and spacecraft mission planning.

4. Using the Calculator

Tips: Enter angular momentum in m²/s and eccentricity (value between 0 and 1). Both values must be valid positive numbers with eccentricity not exceeding 1.

5. Frequently Asked Questions (FAQ)

Q1: What does negative specific energy indicate?
A: Negative specific energy indicates a bound elliptical orbit. The more negative the value, the more tightly bound the orbit is to the central body.

Q2: How does eccentricity affect specific energy?
A: For a given angular momentum, higher eccentricity results in less negative (higher) specific energy, meaning a less bound orbit.

Q3: What are typical values for angular momentum?
A: Angular momentum values vary greatly depending on the orbit. For low Earth orbits, typical values range from 5×10¹⁰ to 7×10¹⁰ m²/s.

Q4: Can this formula be used for other celestial bodies?
A: Yes, but you would need to replace [GM.Earth] with the gravitational parameter of the specific celestial body being orbited.

Q5: What is the relationship between specific energy and semi-major axis?
A: Specific energy is inversely proportional to the semi-major axis: ε = -GM/(2a), where a is the semi-major axis.