Apogee Velocity In Elliptic Orbit Given Angular Momentum And Apogee Radius Calculator

Formula Used:

\[ v_{apogee} = \frac{h_e}{r_{e,apogee}} \]

Velocity of Satellite at Apogee:

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1. What is Apogee Velocity in Elliptic Orbit?

Apogee Velocity in Elliptic Orbit refers to the speed at which a satellite travels when it is at its farthest point from the celestial body it is orbiting. This velocity is determined by the angular momentum of the orbit and the apogee radius.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ v_{apogee} = \frac{h_e}{r_{e,apogee}} \]

Where:

\( v_{apogee} \) — Velocity of Satellite at Apogee (m/s)
\( h_e \) — Angular Momentum of Elliptic Orbit (m²/s)
\( r_{e,apogee} \) — Apogee Radius in Elliptic Orbit (m)

Explanation: The formula calculates the orbital velocity at apogee by dividing the angular momentum by the apogee radius. This relationship is derived from the conservation of angular momentum in orbital mechanics.

3. Importance of Apogee Velocity Calculation

Details: Calculating apogee velocity is crucial for satellite mission planning, orbital maneuver calculations, and understanding the energy requirements for maintaining stable orbits. It helps in determining the satellite's behavior at its farthest point from the central body.

4. Using the Calculator

Tips: Enter the angular momentum in m²/s and apogee radius in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is angular momentum in orbital mechanics?
A: Angular momentum is a conserved quantity that represents the rotational motion of an orbiting body around a central point. It remains constant throughout the orbit unless external torques act on the system.

Q2: How does apogee velocity compare to perigee velocity?
A: In an elliptical orbit, the satellite travels slowest at apogee (farthest point) and fastest at perigee (closest point) due to the conservation of angular momentum.

Q3: What factors affect apogee velocity?
A: Apogee velocity is primarily determined by the angular momentum of the orbit and the distance from the central body at apogee. It is inversely proportional to the apogee radius.

Q4: Can this formula be used for circular orbits?
A: Yes, for circular orbits where apogee and perigee distances are equal, the formula still applies and gives the constant orbital velocity.

Q5: What units should be used for accurate calculations?
A: Use consistent SI units: meters for distance, meters squared per second for angular momentum, and meters per second for velocity.