Semi-Major Axis of Hyperbolic Orbit given Angular Momentum and Eccentricity Calculator

Formula Used:

\[ a_h = \frac{h_h^2}{[GM.Earth] \times (e_h^2 - 1)} \]

Semi Major Axis of Hyperbolic Orbit:

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1. What is Semi-Major Axis of Hyperbolic Orbit?

The Semi-Major Axis of Hyperbolic Orbit is a fundamental parameter that characterizes the size and shape of the hyperbolic trajectory. It represents half the length of the major axis of the orbit and is crucial for understanding the orbital mechanics of hyperbolic paths.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ a_h = \frac{h_h^2}{[GM.Earth] \times (e_h^2 - 1)} \]

Where:

\( a_h \) — Semi-Major Axis of Hyperbolic Orbit (m)
\( h_h \) — Angular Momentum of Hyperbolic Orbit (m²/s)
\( e_h \) — Eccentricity of Hyperbolic Orbit (must be >1)
\( [GM.Earth] \) — Earth's Geocentric Gravitational Constant (3.986004418E+14 m³/s²)

Explanation: This formula calculates the semi-major axis of a hyperbolic orbit based on the angular momentum and eccentricity, using Earth's gravitational parameter.

3. Importance of Semi-Major Axis Calculation

Details: Accurate calculation of the semi-major axis is essential for determining the characteristics of hyperbolic orbits, which are important for interplanetary missions, escape trajectories, and understanding celestial mechanics.

4. Using the Calculator

Tips: Enter angular momentum in m²/s and eccentricity (must be greater than 1). All values must be valid positive numbers with eccentricity > 1 for hyperbolic orbits.

5. Frequently Asked Questions (FAQ)

Q1: What is a hyperbolic orbit?
A: A hyperbolic orbit is an open orbit where the object has sufficient energy to escape the gravitational pull of the central body, with eccentricity greater than 1.

Q2: Why is eccentricity required to be greater than 1?
A: For hyperbolic orbits, the eccentricity must be greater than 1 by definition. Values ≤1 correspond to elliptical or parabolic orbits.

Q3: What units should be used for angular momentum?
A: Angular momentum should be entered in square meters per second (m²/s) for consistent results with the formula.

Q4: Can this calculator be used for other celestial bodies?
A: This specific calculator uses Earth's gravitational parameter. For other bodies, the appropriate gravitational constant would need to be substituted.

Q5: What are typical values for hyperbolic orbit parameters?
A: Hyperbolic orbits typically have eccentricities slightly above 1 (e.g., 1.1-2.0) and semi-major axes that can range from thousands to millions of meters depending on the mission requirements.