Gravitational Force and Escape Velocity

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Gravitational Force Escape Velocity Explanation

Have you ever wondered why everything falls on the ground and does not fly up? It is the gravitational force of the earth in action. Though the earth is not the only thing in the world that has a gravitational pull, it is exercised by every massive particle in the universe.


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What is Gravitational Force?

Issac Newton gave the universal law of gravitation in the year 1687. Using this law, he explained the motion of different planets and their moons. As per Newton’s law of gravitation, every huge particle in the universe attracts another huge particle. The force of gravitation is shortly proportional to the particles’ masses' product and inversely proportional to the square of the distance that separates them.


We could answer “what is gravity?” in modern terms as:

  • Each point mass attracts each other point mass.

  • The force exerted by these point masses is along the line that intersects both the points.

  • Force is proportional to the product of both the masses.

  • The force is inversely proportional to the square of the distance that separates the two masses.

  • Gravitational force decides how much we weigh.

  • The force of gravity determines how far a ball would travel when thrown up before it returns to the earth.

  • The gravitational force on the earth is the force that the earth exerts on you, and at rest, it is equal to your weight.

  • The acceleration of gravity is different on other planets like the Moon, Venus from the earth. Hence your weight on different astronomical bodies would be different.

Newton's Law of Gravitation Formula

The law stated by Newton can be expressed in a mathematical formula which was given by Johannes Kepler in the 17th century. The formula of gravitation can be stated as:

F = G * (m1*m2)/R2

In this gravitational force equation: F → Magnitude of the gravitational force.

G → It is the gravitational constant and its size depends on the system of units used.

m1, m2 → Masses of the two objects.

R - Distance between the masses.


Key Characteristics of Gravitational Force

The important features of gravitational force are:

  • It is conservative in nature, i.e., the work done by the force is only dependent on the first and final position of the object, regardless of the path taken.

  • The force does not depend on the intervening mediums.

  • The force does not depend on the presence or absence of other bodies.

  • It is a central force.

Gravity Acceleration Formula

The acceleration that an object feels because of the force of gravity is known as gravitational acceleration.

Galileo discovered that acceleration due to gravity depended only on the mass of the object that was gravitating and not on the mass of the item pulled. So, if there is no air drag, then the rate at which a huge boulder falls on the ground is the same as the rate at which a small marble would fall, provided both are dropped from the same height. Similarly, If there is a tiny satellite at a distance from the Sun, which is the same as the orbit of the huge planet Jupiter, then both Jupiter and the tiny satellite would experience the same gravitational acceleration by the Sun. Both of them will also have the same orbital period around the Sun.


The unit of gravitational acceleration is m/s2, and it is a vector quantity, which means it has magnitude and direction. You can calculate the gravitational acceleration acting on any object by the below-given gravity acceleration formula:

g = GM / (r + h)2

Where,

g - Gravitational acceleration.

G - Universal gravitational constant = 6.674 30 x 10-11 m3 kg-1 s-2.

M - The mass of the body that is exercising gravitational force on the given object.

r - Planet radius.

H - The height of the object from the body surface.


Escape Velocity

Whenever you throw something in the air, it comes down due to the force of gravitation. Did you ever think that it is possible to throw something with such a force that it escapes the gravitational pull and never comes back? This is where the escape velocity comes into the picture. It is the concept of escape velocity, which is used to launch rockets into space.


So, escape velocity is the minimum velocity required to project a body from the earth’s surface so that it escapes the earth’s gravitational field. It is denoted by Ve and

\[V_{e} = \sqrt{2GM/r}\]


Here M is said to be the mass of the planet. Planets that have more mass are harder to escape from, compared to planets with lesser mass. That is why jumping on the moon is effortless since the moon has much less mass than Earth.


The r in the escape velocity equation denotes the radius, which is measured as the distance from the center of the planet to the object that is trying to escape. Basically, r is the distance between the center of the planet and its surface. So from the equation, we can see that as an object moves away from the center of a planet, the object's gravitational pull also decreases. Hence, the velocity required to escape also lessens.

The G in the equation for Ve is Newton's universal constant of gravity.


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FAQ (Frequently Asked Questions)

Q1. How is the Universal Gravitational Constant Formula Measured?

Ans 1: The universal gravitational constant has been measured in three ways:

  1. By comparing the pull of a large natural mass with that of the Earth.

  2. By directly measuring the force existing between two objects in a laboratory.

  3. By measuring the laboratory balance of earth’s attraction upon a test mass.

The first approach of measuring the universal gravitational constant was suggested by Newton in 1774. The laboratory balance method was developed mostly by John Henry Poynting, a British physicist in the early 1880s. The most recent works in the laboratory method involved the use of torsion balance, which was devised by Michel. Michell died before he could use that method. In 1798, Cavendish gave the first reliable measure of G by employing Michell’s method. The table below displays some of the values of G found out by different scientists using separate methods:


Scientist

Year

Method

G (in Units of 10–11 m3s–2kg–1)

H.Cavendish

1798

Torsion balance (deflection)

6.754

J.H.Poynting

1891

Common balance

6.698

C.Barun

1897

Torsion balance (period)

6.658

T.J. Quinn et. al.

2001

Torsion balance (servo)

6.67553

T.J. Quinn et. al.

2001

Torsion balance (deflection)

6.67565

Q2. What is the Principle of Superposition of Gravitation?

Ans 2: The principle of superposition of gravitation states that when several point masses are exerting a gravitational force on a particle, the resultant gravitational force acting on the particle is directly equal to the vector sum of individual forces acting on that particle. Its formula is given as:


Fr = F1 + F2 + F3 +...+ Fn = Σi=1n Fi


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