How to Calculate Escape Velocity?

In physics, escape velocity is the minimum speed required for a free, non-propelled object to escape the gravitational effects of a massive body. The minimum velocity required to escape the earth’s gravitational field or any planet is known as escape velocity.

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, to go out of gravity, any rocket or spacecraft also needs a mode of propulsion and sufficient propellant, i.e., fuel, to get its maximum acceleration.

How Does Escape Velocity Work?

Like orbital velocity, escape velocity is two different things, where they are estimated and knowledge based on distance. But the escape velocity varies depending on the distance the orbital velocity is, where the object is at its centre of gravity.

Simultaneously, the escape velocity is determined based on its height. The higher the height of a body from the earth, the less will be its escape velocity. This escape velocity depends on some point of the body, in which the main thing is to avoid the earth’s gravitational field completely.

Along with this, the time taken for the orbit of the earth is also important. Communication satellites use energy continuously and revolve continuously because they live at a very high altitude above the earth. Apart from this, other planes use a lot of energy because they are on the surface of the earth, and because of that energy, they remain on the surface of the earth. Rockets primarily use escape velocity, but aircraft do not use escape velocity.

Escape Velocity Of The Earth

Both the escape velocity on the surface of the earth and the escape velocity on the surface of the Moon differ from place to place. The escape velocities at the surface of earth and the Moon are 11.2 km per second (6.96 mph) and 2.4 km per second (1.49 mph), respectively. This data is not that important either.

A rocket or any body that has to be sent out from the surface of the earth, probably has to experience gravity force. For this, the rocket is propelled to its required escape velocity. For which he uses the orbital velocity.

Atmospheric resistance does not matter for escape velocity. It is sent out from the earth by increasing its velocity to escape its gravitational field.

Formula of Escape Velocity

The escape velocity for any spherical star, or planet, that body at a distance is calculated by this formula;

Escape Velocity = √2 ( Gravitational constant) ( mass of the planet or moon) / Radius of the planet or moon

V_e =  √2G.M / r

Here ‘G’ is the universal gravitational constant and whose value is 6.67 × 10-11 Newtons kg-2 m2 , & ‘M’ is the mass of the body that can be divided, and ‘r’ is the distance from the body’s centre of mass to the object. Dimensional formula of escape velocity is  [M0L1T-1]

The mass of the larger object is independent of the mass of the object escaping the body. Conversely, a body that falls on a force of gravitational attraction of mass M, starting from infinity, with zero velocity, from an object of mass equal to its escape velocity given by the same formula Will collide When the initial speed ‘V’ exceeds the escape velocity, the object will asymptotically approach hyperbolic excess speed or infinite speed. In which atmospheric friction (air drag) is not taken into account .

(v_∞)2 = (V)2 – (v_e)2

Derivation

We can also explain the escape velocity on the principle of conservation of energy, the object located in any spherical body mainly experiences gravitational force. Also, here kinetic energy (K) and gravitational potential energy (Ug) are the only two types of energies to be experienced with it. It also follows the principle of conservation of energy.

(K+Ug)_i=(K+Ug)_f

Kinetic Energy, K = 1/2 mv²

Gravitational potential energy, U = GMm / r

Ug_f is 0 since the distance is infinite, and K_f is also zero because the end velocity is zero. The minimal velocity required to escape the big body’s gravitational force is indicated by:

V_e = √ 2G.M /√ r

Conclusion

Escape velocity is the minimum speed required for a free, non-propelled object to escape the gravitational effects of a massive body. The minimum velocity required to escape the earth’s gravitational field or any planet is known as escape velocity.