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 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 exploration, determining the energy required to launch spacecraft. It also affects atmospheric retention by planets.

4. Using the Calculator

Tips: Enter mass in kilograms and radius in meters. Both values must be positive numbers. For Earth, use M = 5.972 × 10²⁴ kg and r = 6.371 × 10⁶ m.

5. Frequently Asked Questions (FAQ)

Q1: What's Earth's escape velocity?
A: Approximately 11.186 km/s at Earth's surface.

Q2: Does escape velocity depend on the object's mass?
A: No, it's independent of the escaping object's mass - only depends on the source body's mass and radius.

Q3: How does altitude affect escape velocity?
A: Escape velocity decreases with 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.

Q5: Can you achieve orbit without reaching escape velocity?
A: Yes, orbital velocity is lower than escape velocity (about 7.8 km/s for low Earth orbit).