A Rocket Launch, continuously accelerated by its exhaust.
Image 1: A Rocket Launch, continuously accelerated by its exhaust, need not reach ballistic escape velocity at any distance since it is supplied with additional kinetic energy by the expulsion of its reaction mass. It can achieve escape at any speed, given a suitable mode of propulsion and sufficient propellant to provide the accelerating force on the object to escape.

Definition of escape velocity

In physics, escape velocity, ( i.e., the lowest velocity ), is the minimum speed required for an independent, non-propelled object to survive the gravitational effects of a massive body. The maximum velocity required to escape the gravitational field of the Earth or any planet is also known as the migration velocity or the lowest velocity that a body must have in order to escape the gravitational attraction of a particular planet or other object.

The escape velocity is only required to send a ballistic object on a trajectory that allows the object to escape the gravity of the mass. Apart from this, any rocket or spacecraft also needs mode of propulsion and sufficient propellant i.e., fuel, to go out of gravity.

Escape velocity formula –

Any spherical star, or planet, at a distance for that body, the escape velocity is calculated by this formula –

Escapevelocityformula

OR

Escape velocity formula

Escape Velocity equals to under-root 2 multiplied by universal gravitational constant and mass of the body to be escaped from, divided by distance from the center of mass of the body to the object.

Escape velocity is denoted by –

{\displaystyle v_{e},}
Escape velocity

Here ‘G‘ is the universal gravitational constant and value of G ≈ 6.67×10−11 m3·kg−1·s−2

M‘ is the mass of the body to be escaped from, and ‘r‘ the distance from the center of mass of the body to the object.

The relationship is independent of the mass of the object escaping the massive body. Conversely, a body that falls under the force of gravitational attraction of mass M, from infinity, starting with zero velocity, will strike the massive object with a velocity equal to its escape velocity given by the same formula.

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When given initial speed ‘V’ is greater than the escape velocity then the object will asymptotically approach the hyperbolic excess speed or infinite speed, In which atmospheric friction (air drag) is not taken into account. Then the equation will be –

When given initial speed 'V' is greater than the escape velocity then the object will asymptotically approach the hyperbolic excess speed or infinite speed, In which atmospheric friction (air drag) is not taken into account.  Then the equation will be -

Video explanation

Escape Velocity: Matt Anderson

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