Newton’s Universal Law of Gravitation

State Newton’s Universal Law of Gravitation.
Understand the significance of gravitational force in everyday life and space.
Solve numerical problems related to the law using the appropriate formula.

📖 Introduction

Have you ever wondered why objects fall to the ground when dropped, or how the moon orbits the Earth? The answer lies in one of the most important scientific discoveries of all time — Newton’s Universal Law of Gravitation. This fundamental law helps us understand the invisible but powerful force that acts between all objects in the universe.

📌 What is Gravitation?

Gravitation is a natural force of attraction between two objects due to their mass. It is responsible for:

Keeping planets in orbit around the Sun.
Holding the moon around the Earth.
Causing objects to fall to the ground when dropped.

🌍 Newton’s Universal Law of Gravitation – Statement

“Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.”

🔢 Mathematical Expression

Where:

= Gravitational force (in newtons, N)
= Universal Gravitational Constant =
$m_{1}$ and $m_{2}$ = Masses of the two objects (in kilograms, kg)
= Distance between the centres of the two masses (in meters, m)

📌 Key Features of Gravitational Force:

It is mutual: both objects experience the same magnitude of force.
It is always attractive, never repulsive.
It acts along the line joining the two objects.
It is a universal force, meaning it works everywhere in the universe.

🧠 Conceptual Understanding

Let’s consider two objects, like the Earth and an apple. Even though Earth is much larger than the apple, both attract each other. The apple falls toward the Earth because of this gravitational pull — and yes, the Earth also moves slightly toward the apple, but the movement is negligible because of the Earth’s massive size.

🧮 Numerical Problem 1

Question:
Find the gravitational force between two bodies of mass 5 kg and 10 kg placed 2 meters apart.
Given:

Solution:

$F=Gm1m2/r2=6.674×10−11×5×10/2^2$

$F \approx 8.3425 \times 1 0^{-10} N$

Answer: The gravitational force is approximately newtons.

🧮 Numerical Problem 2

Question:
What is the force of attraction between the Earth (mass $10^{24}$ kg) and an object of mass 1 kg located on its surface? (Radius of Earth = $10^6$ m)

Solution:

$F=6.674×10−11×6×10^24×1/(6.4×10^6)^2$

$\approx 9.8 N$

Answer: The gravitational force (or weight) is approximately 9.8 newtons, which is the weight of 1 kg on Earth.

🌟 Real-Life Applications of Gravitational Law

Launching satellites and planning their orbits.
Understanding planetary motion.
Designing space missions and rockets.
Explaining ocean tides due to the moon’s gravity.
Calculating weight on different planets.

📚 Summary

Newton’s Universal Law of Gravitation explains how every object in the universe attracts every other object.
The force depends on the product of masses and the inverse square of distance.
The gravitational constant (G) is a very small number, explaining why the force is weak unless one of the objects is massive.
This law is crucial for understanding motion in space and natural phenomena on Earth.

✅ Self-Practice Questions

Two objects of mass 12 kg and 8 kg are placed 5 meters apart. Calculate the gravitational force.
If the distance between two objects is doubled, what happens to the gravitational force?
Why don’t we feel the gravitational force between two school bags placed near each other?

You Can Also Read:

🌍 Gravitation

🌍 Gravitation: MCQ Practice Set

CDC

Echoes Within

📘 Lesson Title: Newton’s Universal Law of Gravitation

🎯 Learning Objective