What is the Escape Velocity Equation?
The Earth’s gravity pulls everything in and around it towards its core. So any object that goes to space leaving the surface of the Earth, has to travel at a certain velocity to overcome this pull. The velocity needed for an object to leave any spherical body such as the Earth overcoming its gravitational pull is called Escape Velocity. Learn how to calculate the escape velocity using the escape velocity equation.
Calculating Escape Velocity with the Escape Velocity Formula
In order to calculate the Escape velocity needed in a planet, we use this equation of escape velocity-
Ve =√(2GM/R)
Here,
Ve = Escape Velocity
G = Gravitational Constant as derived by Newton.
M = Mass of the concerned object.
R = Distance between the center of gravity, i.e., the center of the planet and the object that wants to escape.
Escape Speed Equation
As you know, velocity does not speed. Speed has no direction. Therefore we also have the formula to calculate the speed needed for an object to escape the planet and go to an infinitely far away place. The Escape Speed Equation is-
Se = √(2GM/R)
Escape Velocity of Earth Formula
Now that you know all about escape velocity formula derivation, let’s talk about the escape velocity of Earth formula-
The Escape Velocity of Earth Formula is, Ve =√(2GM/R)
The Mass of Earth is- 5.9723 × 1024 kg
The distance between the object and the Earth’s gravitational core- 6,371 km
The gravitational constant is G = 6.673×10-11 N m2 kg-2
Now substituting these values in the formula- Ve =√(2GM/R), we will get the escape velocity of Earth and that is- 11.2 KM/s
Escape Energy Formula
Using the escape velocity formula derivation, we can derive the escape energy formula. Escape energy is the kinetic energy needed for a spaceship to escape the Earth. The escape energy formula is-
KE = ½MV²
Here, K.E = Kinetic Energy
M = Weight of The Object
V = Escape Velocity
Escape Velocity Dimensional Formula
The escape velocity dimensional formula is-
M0 L1 T-1
Calculating the escape velocity and escape energy is crucial to launching any spaceship into space. It is only after a spaceship reaches the escape velocity of the earth that it can escape the gravitational force of the Earth.
FAQs on Escape Velocity Formula
1. What is the Difference Between Escape Velocity and Orbital Velocity?
Ans: The Earth’s gravitational pull does not just work inside the Earth, it also works outside the Earth up to a certain distance. So to escape the gravitational pull of the Earth we have to leave even this gravitational pull that is outside the Earth.
If an object just escapes the Earth without attaining sufficient velocity, it will get stuck in the orbit of the Earth just like a small pebble revolves around you when you attach a string to it and make it whirl. So the Orbital velocity is the velocity needed for an object to fall into the orbit of the earth but not beyond it.
2. What is the Escape Velocity of Mars?
Ans: The radius of Mars is- 3,396 km. The value of G remains the same. So the using the Escape velocity formula, we can deduce the escape velocity of Mars and that is-
5.03 KM/S.
3. If You Fire a Bullet Pointing the Gun Upward, will the Bullet Escape the Earth?
Ans: A typical gun cannot fire a bullet at 11.2KM/S for reasons like the size of the barrel, the material of which the bullet is made, etc. Secondly, the bullet does not have any propulsion system attached to it. So because of the friction with the atmosphere, the bullet will lose speed. Even if the bullet theoretically attains the escape velocity, it cannot withstand the heat generated by the velocity and the friction.
