1. What is the Orbital Speed Equation?

Definition: This equation calculates the velocity needed for an object to maintain a stable orbit around a celestial body.

Purpose: It's essential for satellite deployment, space mission planning, and understanding celestial mechanics.

2. How Does the Equation Work?

The equation is:

Where:

• \( v \) — Orbital speed (meters per second)
• \( G \) — Gravitational constant (6.67 × 10⁻¹¹ N m²/kg²)
• \( M \) — Mass of the central body (kilograms)
• \( r \) — Orbital radius (meters from center of mass)

Explanation: The equation balances gravitational force with centripetal force required for circular orbit.

3. Importance of Orbital Speed Calculation

Details: Accurate orbital speed calculations ensure satellites maintain proper orbits and don't fall back to Earth or escape into space.

4. Using the Calculator

Tips: Enter the gravitational constant (G), mass of the central body (M), and orbital radius (r). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the gravitational constant (G)?
A: It's a fundamental physical constant (6.67 × 10⁻¹¹ N m²/kg²) that measures the strength of gravity.

Q2: How does orbital radius affect speed?
A: Objects in lower orbits (smaller r) must move faster to maintain orbit, following an inverse square root relationship.

Q3: Does this work for elliptical orbits?
A: This formula is for circular orbits. For elliptical orbits, the speed varies throughout the orbit.

Q4: What mass should I use for Earth orbits?
A: For Earth satellites, use Earth's mass (5.97 × 10²⁴ kg).

Q5: How is this different from escape velocity?
A: Orbital speed is what's needed to maintain orbit, while escape velocity is what's needed to leave orbit completely.