1. What is the Orbital Velocity Equation?

The orbital velocity equation calculates the speed needed for an object to maintain a stable orbit around a celestial body. It's derived from balancing gravitational force with centripetal force required for circular motion.

2. How Does the Calculator Work?

The calculator uses the orbital velocity equation:

Where:

• \( v \) — Orbital velocity (m/s)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)
• \( M \) — Mass of the central body (kg)
• \( r \) — Orbital radius (distance from center of mass) (m)

Explanation: This equation shows that orbital velocity decreases as distance from the central body increases, and increases with larger central mass.

3. Importance of Orbital Velocity Calculation

Details: Calculating orbital velocity is essential for satellite deployment, space mission planning, and understanding celestial mechanics. It determines the speed required for objects to maintain stable orbits without falling back to Earth or escaping into space.

4. Using the Calculator

Tips: Enter the gravitational constant (default is Earth's), mass of the central body in kilograms, and orbital radius in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the gravitational constant?
A: The gravitational constant (G) is a fundamental physical constant that measures the strength of gravity. Its value is approximately 6.67430 × 10⁻¹¹ m³/kg·s².

Q2: Does this equation work for elliptical orbits?
A: This specific equation calculates circular orbital velocity. For elliptical orbits, velocity varies throughout the orbit and different calculations are needed.

Q3: What is Earth's orbital velocity?
A: For low Earth orbit (about 200-2000 km altitude), orbital velocity is approximately 7.8 km/s. For geostationary orbit (35,786 km altitude), it's about 3.1 km/s.

Q4: How does altitude affect orbital velocity?
A: Orbital velocity decreases with increasing altitude. Objects in higher orbits move slower than those in lower orbits.

Q5: Can this calculate escape velocity?
A: No, escape velocity is different. Escape velocity is √2 times orbital velocity and represents the speed needed to break free from a gravitational field entirely.