Derivation of Escape Velocity: Overview, Questions, Preparation

It is one of the most common topics of kinematics in physics. Escape velocity is used to calculate the minimum speed of an object through gravitational pull on the non-propelled object. It makes it reach an infinite distance from the object.

The formula of escape velocity is:

 Here, Escape Velocity is denoted as Ve.

The gravitational constant is denoted as G.

Mass is denoted as M.

We denote the distance from the object as r

The escape velocity of the earth is 40,270 km approximately, which is equal to 11,186 m/s.

 The acceleration due to gravity from the earth is g = 9.8 m/s2

Radius is 6.4 x 106 m

Escape velocity is Ve = √2 × 9.8 × 6.4 × 106

That is why Ve  = 11.2 x 103 m/s = 11.2 km/s

The formula of initial potential energy is:

PEi = GMm / Ri

Here, M is the mass of escaping body

m is the mass of attracting body

G is the gravitational constant

Ri is the separation between the bodies

The formula of initial kinetic energy is

KE = ½ mve 2

Here, M is the mass of the object.

Ve is the initial velocity or escape velocity.

Now, the sum of kinetic and potential energy will give us:

TEi = KEi + PEi

TEi. = mve / 2 - GMm / Ri

Now, TEi = TE ∞

KEi + PEi = 0

After substituting the values, we will get,

mve / 2 - GMm / Ri = 0

Let us now add both the sides by GMm / Ri

Now, we have ve2 = 2GM / Ri

Now, apply square root on both sides.

Ve = +- √ (2GM / ri)

The gravitational convention is far away from the other object so that the escape velocity will be negative, and we will get out a final formula which is as follows:

The chapter 'Introduction to Motion' holds a weightage of 6 marks. It includes 3 questions in total. These 3 questions consist of one objective type question of 1 mark, one very short question of 2 marks, and one short question of 3 marks bringing a total up to 6 marks.

Example 1) Illustrates the formula of escape velocity.

Answer – the formula of escape velocity is Ve = - √ (2GM / RI)

Example 2) State the formula of initial potential energy.

Answer – the formula of initial potential energy is PEi = GMm / Ri

Example 3) Illustrate the formula of initial kinetic energy.

Answer – the formula of initial kinetic energy is KE = ½ mve 2

Question 1) What do you mean by escape velocity?

Question 2) what is the escape velocity of the sun, moon, and earth in km/s?

Question 3) write the difference between escape velocity and orbital velocity.

Question 4) On what escape velocity is dependent on?

Question 5) What is the escape velocity of Jupiter?