Escape Speed Formula

Escape Speed

Velocity or Escape speed is the speed of a body at which the total of the kinetic energy and gravitational potential energy is zero. The escape velocity from earth’s surface is about 11,186 m/s. In a different sense, it can be described as the speed required to break the gravitational attraction. The formula for escape speed is articulated as,

\(\begin{array}{l}v_{e}=\sqrt{\frac{2GM}{r}}\end{array} \)

Where,

G is the gravitational constant

M is the mass of the planet

r is the distance from the centre of gravity.

Solved Example

Let us discuss some numerical on escape speed to learn more about this concept.

Example 1: The mass of the Jupiter is given as 1.898×1027Kg and the radius is given as 71492km. Compute the escape speed?

Answer:

Known parameters are,

Mass of the Jupiter, M = 1.898×1027kg

radius, r = 71492km

G = 6.673×10-11m3/kgs2
Formula for escape speed is,

\(\begin{array}{l}v_{e}=\sqrt{\frac{2GM}{r}}\end{array} \)

 

\(\begin{array}{l}v_{e}=\sqrt{\frac{2\times 6.673\times 10^{-11}\times 1.898\times 10^{27}}{71492}}=188.23km/s\end{array} \)

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