Escape Velocity Calculator

Escape Velocity Calculator:

Enter the values of celestial body’s mass, M_(kg), gravitational constant, G_(Nm2/kg2) and radius, R_(m) to determine the value of Escape Velocity, Ev_(m/s).

Enter Mass :		kg
Enter Gravitational Constant:		Nm2/kg2
Enter Radius:		m
Result – Escape Velocity:		m/s

Escape Velocity Formula:

Escape velocity is the minimum speed an object must achieve to break free from the gravitational pull of a planet, moon, or celestial body without further propulsion. It represents the balance point where an object’s kinetic energy equals the gravitational potential energy trying to pull it back.

This velocity depends on the mass of the celestial body (M), its gravitational constant (G), and the radius of the body (R). The larger the mass or the smaller the radius, the higher the escape velocity. For planets like Earth, the escape velocity is approximately 11.2 km/s, indicating the significant energy required to overcome its gravitational pull.

Escape velocity is independent of the direction of travel and air resistance and assumes the body is spherical and the object starts from its surface. This principle is critical in space exploration, ensuring spacecraft achieve the necessary speed to enter orbit or travel to other celestial bodies.

Escape Velocity, Ev_(m/s) in metres per second equals the square root of two times the product of the celestial body’s mass, M_(kg) in kilograms and the gravitational constant, G_(Nm2/kg2) in Newton metre square per kilogram square, divided by the radius, R_(m) in metres of the celestial body.

Escape Velocity, Ev_(m/s) = √(2 * M_(kg) * G_(Nm2/kg2) / R_(m))

Ev_(m/s) = escape velocity in metres per second, m/s.

M_(kg) = mass in kilograms, kg.

G_(Nm2/kg2) = gravitational constant in Newton metre square per kilogram square, Nm²/kg²(6.674 * 10⁻¹¹ Nm²/kg²)..

R_(m) = radius in metres, m.

Escape Velocity Calculation:

1.A celestial body has a mass of 5.972 * 10²⁴ kg and a radius of 6.371 * 10⁶ m (similar to Earth). Calculate its escape velocity.

Given: M_(kg) = 5.972 * 10²⁴ kg, G_(Nm2/kg2)= 6.674 * 10⁻¹¹ Nm²/kg², R_(m) = 6.371 * 10⁶.

Escape Velocity, Ev_(m/s) = √(2 * M_(kg) * G_(Nm2/kg2) / R_(m))

Ev_(m/s) = √(2 * 5.972 * 10²⁴ * 6.674 * 10⁻¹¹ / 6.371 * 10⁶)

Ev_(m/s) = √(7.986 * 10¹⁴ / 6.371 * 10⁶)

Ev_(m/s) = 11200m/s.

2.A celestial body has a mass of 7.35 * 10²² kg (similar to the Moon), and its escape velocity is 2,380 m/s. Calculate its radius.

Given: M_(kg) = 7.35 * 10²² kg, G_(Nm2/kg2) = 6.674 * 10⁻¹¹ Nm²/kg², Ev_(m/s) = 2380m/s.

Escape Velocity, Ev_(m/s) = √(2 * M_(kg) * G_(Nm2/kg2) / R_(m))

R_(m) = 2 * 7.35 * 10²² * 6.674 * 10⁻¹¹ / (2380)²

R_(m) = 9.804 * 10¹² / 5.664 * 10⁶

R_(m) = 1.731 * 10⁶m.