1. What is Escape Velocity?

Escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a massive body without further propulsion. It depends on the mass of the body and the distance from its center.

2. How Does the Calculator Work?

The calculator uses the escape velocity formula:

Where:

• \( v_{esc} \) — Escape velocity (m/s)
• \( G \) — Gravitational constant (6.67430 × 10^-11 m³/kg·s²)
• \( M \) — Mass of the celestial body (kg)
• \( r \) — Distance from the center of mass (m)

Explanation: The equation shows that escape velocity increases with the mass of the body and decreases with distance from its center.

3. Importance of Escape Velocity

Details: Escape velocity is crucial in space missions, satellite launches, and understanding celestial mechanics. It determines whether rockets can leave Earth's gravity or if atmospheres can retain gases.

4. Using the Calculator

Tips: Enter the gravitational constant (default is 6.67430 × 10^-11 m³/kg·s²), mass of the celestial body in kg, and distance from center in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's Earth's escape velocity?
A: Approximately 11.186 km/s at Earth's surface (M = 5.972 × 10²⁴ kg, r = 6.371 × 10⁶ m).

Q2: Does escape velocity depend on the object's mass?
A: No, escape velocity is independent of the escaping object's mass.

Q3: How does altitude affect escape velocity?
A: Escape velocity decreases with increasing altitude since r increases in the denominator.

Q4: What's the escape velocity at a black hole's event horizon?
A: At the event horizon, escape velocity equals the speed of light, which is why light cannot escape.

Q5: Can escape velocity be achieved without rockets?
A: In theory yes (e.g., electromagnetic launch systems), but currently rockets are the only practical method.