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

is the mass of the planet

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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