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Escape Velocity is considered one the most difficult concept.
25 Questions around this concept.
A planet in a distant solar system is 10 times more massive than the Earth and its radius is 10 times smaller Given that the escape velocity from the earth is 11 km s-1, the escape velocity ( in km s-1) from the surface of the planet would be :
The kinetic energy needed to project a body of mass m from the earth's surface (radius R) to infinity is :
The escape velocity of a body depends upon mass as :
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The escape velocity for a body projected vertically upwards from the surface of the earth is 11 Km/s. If the body is projected at an angle of 45o with the vertical, the escape velocity will be :
Escape velocity is defined as the minimum velocity an object must have in order to escape from the planets gravitational pull.
Escape velocity ( in terms of the radius of the earth)
To escape a body from earth surface means to displace it from the surface of the earth to infinity.
The work done to displace a body from the surface of the earth (r = R) to infinity ( r = ) is
So if we provide kinetic energy equal to W to body at the surface of the earth then it will be able to escape from the earth's gravitational pull.
So
And Kinetic energy can be written as
Where is the required escape velocity.
By comparing we get
Using
We get
Escape velocity
Radius of earth
And using
For the earth
Escape velocity is independent of the mass of the body.
Escape velocity is independent of the direction of projection of the body.
Escape velocity depends on the mass and radius of the earth/planet.
I.e Greater the value of or
of the planet greater will be the escape velocity
If the body projected with velocity less than escape velocity ()
In this case, the first body will reach a certain maximum height ()
And after that, it may either move in an orbit around the earth/planet or may fall back down towards the earth/planet.
Let's find Maximum height attained by the body
At maximum height, the velocity of the particle is zero
So at h= it's Kinetic energy=0
By the law of conservation of energy
Total energy at surface = Total energy at the height
And using
We get
escape velocity
Projection velocity of the body
Radius of planet
If a body is projected with a velocity greater than escape velocity ()
Then By the law of conservation of energy
Total energy at surface = Total energy at infinity
And using
We get
new velocity of the body at infinity=
projection velocity
Escape velocity
Energy to be given to an object on the surface of the earth so that it's total energy is 0
Mass of planet
mass of the body
Gravitational constant
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