Perigee Radius Of Parabolic Orbit Given Angular Momentum Calculator

Perigee Radius Formula:

\[ r_p = \frac{h_p^2}{2 \cdot [GM.Earth]} \]

Perigee Radius in Parabolic Orbit:

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1. What is Perigee Radius in Parabolic Orbit?

Perigee Radius in Parabolic Orbit refers to the distance between the center of the Earth and the point in a satellite's orbit that is closest to the Earth's surface. In a parabolic orbit, this represents the minimum distance the satellite reaches from Earth.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_p = \frac{h_p^2}{2 \cdot [GM.Earth]} \]

Where:

\( r_p \) — Perigee Radius in Parabolic Orbit (meters)
\( h_p \) — Angular Momentum of Parabolic Orbit (m²/s)
\( [GM.Earth] \) — Earth's Geocentric Gravitational Constant (3.986004418 × 10¹⁴ m³/s²)

Explanation: This formula calculates the closest approach distance of a satellite in a parabolic orbit around Earth based on its angular momentum and Earth's gravitational parameter.

3. Importance of Perigee Radius Calculation

Details: Calculating perigee radius is crucial for orbital mechanics, satellite mission planning, and ensuring satellites maintain safe distances from Earth while achieving desired orbital characteristics.

4. Using the Calculator

Tips: Enter the angular momentum of the parabolic orbit in m²/s. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a parabolic orbit?
A: A parabolic orbit is an open orbit where the object has exactly the escape velocity. The eccentricity equals 1, and the object will escape the gravitational field.

Q2: How is angular momentum related to orbital parameters?
A: Angular momentum is a conserved quantity in orbital mechanics that determines the shape and size of an orbit, along with the gravitational parameter.

Q3: What is Earth's Geocentric Gravitational Constant?
A: It's the product of Earth's mass and the gravitational constant (G), representing Earth's gravitational influence on orbiting bodies.

Q4: Can this formula be used for other celestial bodies?
A: Yes, but you would need to substitute the appropriate gravitational parameter for that specific celestial body.

Q5: What are typical values for angular momentum in Earth orbits?
A: Angular momentum values vary significantly depending on the orbit type and altitude, ranging from millions to trillions of m²/s for different satellite missions.