### Escape Velocity Calculator:

Enter the Mass (M) in weight of the Earth (Earths), Radius (R) in R⊕, First cosmic velocity in 7.91 km/s, and you get the calculation of Escape velocity (vₑ) in 11.186 km/s.

Escape Velocity Formula:

Escape velocity formula is V_{e(m/s)} in meter per second is equal to the root of the two gravitational constant 2G_{(kgf)} kilogram force and multiply the mass of the planet M_{(kg)} in kilogram and divided by the Radius of the planet R_{(m)} inmeter.Hence the escape velocity formula can be written as

V_{e(m/s)} = √ (2G_{(kgf)}*M_{(kg)} /R_{(m)})

Where

V_{e} = Escape Velocity in meter per se

G = earth’s gravitational constant in KgF

M= Mass of the planet in kg

R = Radius of the planet in meter

From the above equation you can find the cosmic velocity and which is the velocity that an object need to orbit the celestial body

Hence, First cosmic velocity = √ (GM /R)

### Example:1

Calculate escape velocity from planet earth? R = 6.38 *10^{6} m and the M = 3.18 *10^{24 }kg .

### Answer:

Given that

Mass of the planet earth M=3.18 *10^{24 }kg

Radius of earth R =5.18 *10^{6} m

Escape velocity is V_{e} =√ (2GM /R)

V_{e} =√ (2 *6.673*10^{-11} *3.18 *10^{24} ) / 5.18 *10^{6} )

V_{e} =√ 8.48106 *10^{13} / 5.18 *10^{6}

=1.777850 *10^{12}

=Therefore, the escape velocity is 1.777850 m/s

### Example:2

Calculation the radius of the earth is 8 m and the weight or mass is 4.05 kg . What is the escape velocity?

### Answer:

Given that

Mass of the planet earth M=4.05 ^{ }kg

Radius of earth R =8 m

Escape velocity is V_{e} =√ (2G*M /R)

V_{e} =√ (2 *6.673*10^{-11} *4.05 ) /(8 )

V_{e} =√ 5.40513 ) /8

=0.290611 m/s

=Therefore, the escape velocity is 0.290611 m/s