Perigee Radius of Hyperbolic Orbit Given Angular Momentum and Eccentricity Calculator

Perigee Radius Formula:

\[ r_{perigee} = \frac{h_h^2}{[GM.Earth] \times (1 + e_h)} \]

Perigee Radius:

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1. What is Perigee Radius of Hyperbolic Orbit?

The Perigee Radius of a Hyperbolic Orbit refers to the distance between the center of the Earth and the point in a hyperbolic orbit that is closest to the Earth's surface. It is a crucial parameter in orbital mechanics for understanding spacecraft trajectories.

2. How Does the Calculator Work?

The calculator uses the Perigee Radius formula:

\[ r_{perigee} = \frac{h_h^2}{[GM.Earth] \times (1 + e_h)} \]

Where:

\( h_h \) — Angular Momentum of Hyperbolic Orbit (m²/s)
\( [GM.Earth] \) — Earth's Geocentric Gravitational Constant (3.986004418E+14 m³/s²)
\( e_h \) — Eccentricity of Hyperbolic Orbit (≥1)

Explanation: The formula calculates the closest approach distance in a hyperbolic orbit based on angular momentum and orbital eccentricity.

3. Importance of Perigee Radius Calculation

Details: Accurate perigee radius calculation is essential for mission planning, trajectory analysis, and ensuring safe spacecraft operations during Earth flybys or hyperbolic departure trajectories.

4. Using the Calculator

Tips: Enter angular momentum in m²/s and eccentricity (must be ≥1). All values must be valid positive numbers.

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.

Q2: Why is eccentricity ≥1 for hyperbolic orbits?
A: Eccentricity values ≥1 indicate open trajectories (parabolic when e=1, hyperbolic when e>1), as opposed to closed elliptical orbits (e<1).

Q3: What are typical values for angular momentum in hyperbolic orbits?
A: Angular momentum values vary significantly depending on the specific mission and trajectory, but are typically in the range of 10^8 to 10^11 m²/s for Earth-centered hyperbolic orbits.

Q4: How does perigee radius affect spacecraft operations?
A: The perigee radius determines the closest approach distance, which affects atmospheric drag considerations, thermal loading, and gravitational assist maneuvers.

Q5: Can this formula be used for other celestial bodies?
A: Yes, but the gravitational parameter ([GM]) must be replaced with the appropriate value for the specific celestial body being orbited.