Escape Velocity Calculator:
Enter the values of mass of the celestial body, M(kg) and radius of the celestial body, r(m) to determine the value of escape velocity, ev(m/s).
Escape Velocity Formula:
Escape velocity is the minimum velocity required for an object to escape the gravitational influence of a celestial body without further propulsion. This velocity is crucial for determining the energy needed for spacecraft to leave a planet or moon.
Escape velocity, ev(m/s) in metres per second is equated by the square root of product of two times of mass of the celestial body, M(kg) in kilograms, gravitational constant, G(m3/kg/s2) is 6.674 * 10-11 m3/kg/s2 and then divided by radius of the celestial body, R(m) in metres.
Escape velocity, ev(m/s) = √( 2 * M(kg) * G(m3/kg/s2) / R(m))
ev(m/s) = escape velocity in metres per seconds, m/s.
M(kg) = mass of the celestial body in kilograms, kg.
G(m3/kg/s2) = gravitational constant, 6.674 * 10-11.
R(m) = radius of celestial body in metres, m.
Escape Velocity Calculation:
1.Calculate the escape velocity from the Moon, mass of the moon is 7.342 * 1022kg and radius of the moon is 1.737 * 106.
Given: M(kg) = 7.342 * 1022kg, G(m3/kg/s2) = 6.674 * 10-11, R(m) = 1.737 * 106.
Escape velocity, ev(m/s) = √( 2 * M(kg) * G(m3/kg/s2) / R(m))
ev(m/s) = √( 2 * 7.342 * 1022 *6.674 * 10-11 / 1.737 * 106 )
ev(m/s) = √( 5.642 * 106 )
ev(m/s) = 2375m/s.
2.Suppose we want to find the radius of a planet where the escape velocity is 5000m/s, the mass of the planet 4.5×1024kg, and the gravitational constant is 6.674×10-11m3/kg/s2.
Given: M(kg) = 4.5 * 1024kg, G(m3/kg/s2) = 6.674 * 10-11, ev(m/s) = 5000m/s.
Escape velocity, ev(m/s) = √( 2 * M(kg) * G(m3/kg/s2) / R(m))
R(m) = 2 * M(kg) * G(m3/kg/s2) / ev2(m/s)
R(m) = 2 * 4.5 * 1024 * 6.674 * 10-11 / 50002
R(m) = 6.0066 * 1015 / 25,000,000
R(m) = 2.40264 * 109m.