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Escape Velocity Formula:
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Escape Velocity is defined as the minimum velocity needed for a body to escape from a gravitational center of attraction without undergoing any further acceleration. It represents the speed required to break free from a celestial body's gravitational pull.
The calculator uses the Escape Velocity formula:
Where:
Explanation: The escape velocity is exactly √2 times the orbital velocity for a circular orbit at the same distance from the center of the gravitational body.
Details: Calculating escape velocity is crucial for space mission planning, satellite deployment, and understanding orbital mechanics. It determines the energy requirements for spacecraft to leave planetary orbits and venture into interplanetary space.
Tips: Enter the velocity of circular orbit in meters per second (m/s). The value must be positive and greater than zero for accurate calculation.
Q1: Why is escape velocity √2 times orbital velocity?
A: This relationship comes from energy conservation principles. The kinetic energy needed for escape is exactly twice the kinetic energy of a circular orbit, hence the √2 factor.
Q2: Does escape velocity depend on the mass of the object?
A: No, escape velocity depends only on the mass of the celestial body and the distance from its center, not on the mass of the escaping object.
Q3: What is Earth's escape velocity?
A: Earth's escape velocity at the surface is approximately 11.2 km/s, which is √2 times the orbital velocity of about 7.9 km/s.
Q4: Can escape velocity be achieved gradually?
A: Yes, through continuous propulsion rather than a single impulse. However, the total energy required remains the same regardless of how it's achieved.
Q5: How does altitude affect escape velocity?
A: Escape velocity decreases with increasing altitude from the center of the gravitational body, following an inverse square root relationship with distance.