Point of Zero Intensity - Explanation and Solved Example

Gravitational Force

We are aware of the fact that all objects are attracted towards the centre of the earth. Any object that is thrown up is pulled downwards by a force called gravitational force. The gravitational force decides how much we weigh and how far a cricket ball must travel before it returns to the surface of the earth. The value of gravitational force differs for different astronomical bodies.

The gravitational force is explained by Newton’s Law of Universal Gravitation. The law states that every object attracts every other object with a force that is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

Let us consider two masses, m₁ and m_2, separated by a distance of r. Newton’s gravitational law can be written as

F = G (m₁m₂/r²)

Here, G is called the gravitational constant.

Point of Zero Intensity

Point of zero intensity

When there are two objects that are gravitationally locked, and if a mass is placed at the centre of these two objects, the mass is attracted more by the heavier object. For example, if an object is placed between the earth and the moon, the object will get attracted more towards the earth since the earth is heavier than the moon.

The point of zero intensity of the gravitational force or the null point will not be in the centre of the two objects. If we consider the example of earth and the moon, the null point will be closer to the moon. The reason is that when the object is closer to the moon, the moon can attract the mass with a gravitational force equal to that of the earth despite its smaller mass.

Let us determine the point at which the gravitational intensity will be zero. Let m_m be the mass of the moon, and m_e be the mass of the earth at a distance r from each other. Consider a point m placed at a distance x from the moon. The mass m is at a distance (r-x) from the earth. The force with which the mass (m) is attracted by the moon is given as F_m, and the earth attracts the mass (m) with force F_e. At the point of zero intensity, F_m will be equal to F_e.

F_m = F_e

\(\begin{array}{l}\Rightarrow \frac{GM_{m}m}{x^{2}}=\frac{GM_{m}m}{(r-x)^{2}}\end{array} \)

The above equation can be solved to find the value of x.

\(\begin{array}{l}x = \frac{r}{1+\sqrt{\frac{m_{e}}{m_{n}}}}\end{array} \)

Solved Example

1. Imagine an object of mass m is placed between the earth and the moon system. Find the distance at which the gravitational intensity acting on the object is zero. (Earth is approximately 81 times heavier than the moon, and the distance of the moon from the earth is 3,85,000 km).

Answer: 38500 km from the moon

Solution:

The distance of the point of zero intensity is given by the equation

\(\begin{array}{l}x = \frac{r}{1+\sqrt{\frac{m_{e}}{m_{n}}}}\end{array} \)

Given:

r = 3,85,000 km

m_e = 81m_n

\(\begin{array}{l}x = \frac{385000}{1+\sqrt{81}}\end{array} \)

x = 38500 km

Therefore, the point of zero intensity will be at a distance of 38500 km from the moon.

Related Video

Point of Zero Intensity – Video Lesson

Point of Zero Intensity

Frequently Asked Questions on Point of Zero Intensity

Q1

What exactly is the gravitational null point?

The null point is the point between the earth and the moon where the earth’s gravitational field is cancelled out by the moon’s gravitational field.

Q2

What is the distance of the null point from the moon?

The null point is at a distance of 38500 km from the moon.

Q3

What is gravity?

Gravity is the force of attraction between all masses in the universe, particularly between the earth’s mass and bodies near its surface.

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