Acceleration Due to Gravity

Acceleration due to gravity is an essential topic in physics. Acceleration is caused due to the change of velocity and the gravitational force or gravity. As we know, any object that falls from any height drops in a downward direction due to gravity but it has the velocity that changes due to various factors.
In this article, we will study gravity, acceleration due to gravity, its formula, and other related topics. Before starting the article, let’s understand the meaning of gravity. 

Let’s start the article by defining gravity.

Gravity

Gravitation is the other term for gravity. It is a force that pulls the objects towards the Earth. The law of gravitation was given by Sir Issac Newton, and the concept of gravity stuck him due to the fall of an apple on his head. He then thought that not only earth pulls the objects but also there is a force between the astronomical objects. This law of Newton is known as the universal law of gravitation.

Acceleration Due to Gravity

As you already know about gravity, now the question is: What is acceleration due to gravity? To understand the term acceleration due to gravity, we will do an activity. In this activity, we will throw a ball that will fall towards the earth due to gravity. But due to gravitational pull, the magnitude of the velocity of the ball will change. This change in velocity is due to acceleration, which is due to the earth’s gravitational force. Due to this reason, it is known as acceleration due to gravity or acceleration due to gravitational pull.  The S.I unit of acceleration due to gravity is m/s-2.

Acceleration Due to Gravity Formula

Let derive the acceleration due to gravity formula:

The magnitude of the gravitational force (F) is the product of acceleration due to gravity and the mass of the earth.

F = mg

According to the universal law of gravitation

F = Gm ✕ Mr2

Where, 

m = mass of the first object

M = mass of the Earth

G = Gravitational Constant and its value is 6.7 10-11Nm2/kg2

r2 = distance between the centres of the masses

Hence,

 m g =  Gm ✕ Mr2

g = G Mr2

Therefore, acceleration due to gravity formula is G Mr2.

Ex.1 The radius of the Mars is 3.38 106 m and the mass of the Mars is 6.39 1024 kg. Find out the acceleration due to gravity on the surface of Mars.

Solution: On the surface of the mars, the distance to the centre of mass will be the same as the radius.

Thus,  r = 3.38 106 m.

Mass of the object i.e. mars,

m = 6.39 1024 kg

As we know that, universal gravitational constant G = 6.7 10-11Nm2/kg2

The acceleration due to gravity on the surface of the mars can be calculated by using the formula as below:

g = G Mr2

g = 6.7 10-11× 6.39 1024(3.38 106)2

g = 6.7 10-11 × 0.55 1012

g = 3.75 m/s2

Factors affecting g or Acceleration due to Gravity

Acceleration due to gravity is majorly affected by the following factors:

• Depth below the Earth’s surface: The value of r is 0 at the centre of the earth. As we go down into the Earth the acceleration due to gravity decreases.

• Altitude above the Earth’s surface: The value of g decreases with an increase in altitude of an object. Thus, the value of g becomes 0 at an infinite distance from the earth.

• Rotational motion of the Earth: The value of g is minimum at the equator. Thus, acceleration due to gravity is minimum at the equator and maximum at the poles.
• The shape of the Earth: As we all know that earth shape is not fully spherical. Hence, acceleration due to gravity increases when one moves from the equator to the pole.

Conclusion

Gravity causes the acceleration in the change in velocity of fall of the object, while the change of velocity is due to change in magnitude. There are three ways which can cause change in acceleration, it is either by changing the speed or direction or by changing both. In the above article, we have discussed the acceleration due to gravity, formula, factors affecting the acceleration and so on for deep and clear understanding of the topic.