Specific Energy Of Circular Orbit Given Orbital Radius Calculator

Formula Used:

\[ \varepsilon = -\frac{GM_{\text{Earth}}}{2 \times r} \]

Specific Energy of Orbit:

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1. What is Specific Energy of Orbit?

The Specific Energy of Orbit is the total orbital energy per unit mass of an orbiting body. It represents the sum of kinetic energy and gravitational potential energy, providing insight into the stability and characteristics of an orbit.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \varepsilon = -\frac{GM_{\text{Earth}}}{2 \times r} \]

Where:

\( \varepsilon \) — Specific Energy of Orbit (J/kg)
\( GM_{\text{Earth}} \) — Earth's Geocentric Gravitational Constant (3.986004418 × 10¹⁴ m³/s²)
\( r \) — Orbit Radius (meters)

Explanation: This formula calculates the specific energy for a circular orbit, where the energy is negative indicating a bound orbit around Earth.

3. Importance of Specific Energy Calculation

Details: Calculating specific energy is crucial for orbital mechanics, satellite deployment, and mission planning. It helps determine orbital stability, transfer requirements, and energy requirements for orbital maneuvers.

4. Using the Calculator

Tips: Enter the orbit radius in meters. The value must be positive and greater than Earth's radius (approximately 6,371,000 meters) for valid orbital calculations.

5. Frequently Asked Questions (FAQ)

Q1: Why is specific energy negative for orbits?
A: Negative specific energy indicates a bound orbit where the body is gravitationally captured by the central mass (Earth). Positive energy would indicate an escape trajectory.

Q2: How does orbit radius affect specific energy?
A: Specific energy becomes less negative (closer to zero) as orbit radius increases. Higher orbits have higher (less negative) specific energy.

Q3: What are typical values for specific energy?
A: For Low Earth Orbit (LEO), specific energy is typically around -30 MJ/kg. For Geostationary orbit, it's about -4.7 MJ/kg.

Q4: Can this formula be used for elliptical orbits?
A: This specific formula is for circular orbits. Elliptical orbits require a different calculation involving semi-major axis.

Q5: What units should be used for accurate calculations?
A: Always use meters for distance and ensure consistent SI units throughout the calculation for accurate results.