Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum Calculator

Radial Velocity Formula:

\[ v_r = \frac{[GM.Earth] \times e_e \times \sin(\theta_e)}{h_e} \]

Eccentricity of Elliptical Orbit (e_e):

(unitless)

True Anomaly in Elliptical Orbit (θ_e):

radians

Angular Momentum of Elliptic Orbit (h_e):

m²/s

Radial Velocity of Satellite (v_r):

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1. What is Radial Velocity in Elliptic Orbit?

Radial velocity in an elliptic orbit is the component of a satellite's velocity that is directed along the line of sight from an observer on the Earth's surface. It represents how fast the satellite is moving toward or away from the observer.

2. How Does the Calculator Work?

The calculator uses the radial velocity formula:

\[ v_r = \frac{[GM.Earth] \times e_e \times \sin(\theta_e)}{h_e} \]

Where:

\( [GM.Earth] \) — Earth's Geocentric Gravitational Constant (3.986004418×10¹⁴ m³/s²)
\( e_e \) — Eccentricity of Elliptical Orbit (unitless)
\( \theta_e \) — True Anomaly in Elliptical Orbit (radians)
\( h_e \) — Angular Momentum of Elliptic Orbit (m²/s)

Explanation: This formula calculates the radial component of velocity for a satellite in an elliptical orbit based on orbital parameters and gravitational constants.

3. Importance of Radial Velocity Calculation

Details: Accurate radial velocity calculation is crucial for satellite tracking, orbit determination, collision avoidance, and understanding orbital dynamics in space missions.

4. Using the Calculator

Tips: Enter eccentricity (0-1), true anomaly in radians (0-6.2832), and angular momentum in m²/s. All values must be valid and within specified ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of eccentricity in orbital mechanics?
A: Eccentricity determines the shape of the orbit - 0 for circular, between 0-1 for elliptical, 1 for parabolic, and greater than 1 for hyperbolic orbits.

Q2: How does true anomaly differ from mean anomaly?
A: True anomaly is the actual angle between the satellite and perigee, while mean anomaly is a mathematical construct used in orbital calculations.

Q3: What factors affect angular momentum in orbits?
A: Angular momentum depends on the satellite's mass, velocity, and distance from the central body, and remains constant in an unperturbed orbit.

Q4: Why is radial velocity important for satellite communication?
A: Radial velocity affects Doppler shift in communication signals, which must be compensated for accurate data transmission.

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