Universal Law of Gravitation Simplified , Definition, Formula, Examples & Problems

Universal Law of Gravitation Simplified - Interactive Problems Included

Introduction (Problem – Agitate – Solution)

Problem

Every student at some point has asked: “Why do things fall down?” or “Why doesn’t the Moon crash into the Earth?” These sound like simple questions, but when the Universal Law of Gravitation enters the picture, many students suddenly feel lost. Equations, forces, masses, distances-everything starts to look like abstract symbols with little meaning.

Agitate

This confusion isn’t small. If you misunderstand gravitation, it can ripple into struggles in physics chapters like motion, satellites, planetary motion, and even energy concepts. In exams, you may face derivations, problem-solving questions, or conceptual reasoning based on gravitation. In real life, the same principle governs the tides, satellite communication, and why astronauts appear weightless. Missing the basics means missing the bigger picture.

Solution

So, let’s break it down step by step-clear, practical, and connected to real-world examples. By the end of this guide, you won’t just memorize Newton’s Universal Law of Gravitation-you’ll understand it. And to test yourself, we’ll include some interactive-style problems so you can apply what you learn immediately.

Section 1: The Birth of the Law

Before Newton, people already knew about gravity in a basic sense. Everyone could see that apples fall downward, not upward. But nobody had connected the falling of an apple to the orbit of the Moon.
Newton asked: What if the force that pulls the apple down is the same force that keeps the Moon moving around Earth?
This simple yet revolutionary thought gave us the Universal Law of Gravitation.

Section 2: Stating the Law

The law says:
Every object in the universe attracts every other object with a force. This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Written mathematically (without symbols, for clarity):
Gravitational Force = Gravitational Constant × (Mass 1 × Mass 2) ÷ (Distance between their centers) squared
Where:

Mass 1 and Mass 2 are the two interacting objects
Distance is the separation between their centers
Gravitational Constant (G) has a fixed value: 6.67 × 10⁻¹¹ Newton meter² per kilogram

Section 3: Breaking It Down with Examples

1 . Let’s make sense of this.

Dependence on Mass
Bigger masses → Stronger gravitational pull.

Example: Earth has more mass than a football, so it pulls you much more strongly.

2 . Dependence on Distance

Greater distance → Weaker gravitational pull.

Example: The farther a spacecraft moves from Earth, the weaker Earth’s gravitational pull on it becomes.

3 .Why Square of Distance?

Newton realized that as the sphere of influence spreads out, the effect reduces quickly, not linearly but by the square of distance. That’s why if distance doubles, the force becomes one-fourth.

Section 4: Real-Life Relevance

Tides: The gravitational pull of the Moon (and the Sun) causes ocean tides on Earth.
Satellites: Artificial satellites stay in orbit because Earth’s gravity pulls them inward while their speed pushes them outward.
Weight: Your weight is just the force with which Earth’s gravity pulls you.
Space Travel: Rockets must overcome Earth’s gravity to reach orbit, which is why they consume so much fuel.

Section 5: Step-by-Step Example

Example 1: Force between Earth and Moon

Mass of Earth = 6 × 10²⁴ kilograms
Mass of Moon = 7.35 × 10²² kilograms
Distance between Earth and Moon = 3.84 × 10⁸ meters
G = 6.67 × 10⁻¹¹

Force = G × (Mass of Earth × Mass of Moon) ÷ Distance²
Plugging values:
= 6.67 × 10⁻¹¹ × (6 × 10²⁴ × 7.35 × 10²²) ÷ (3.84 × 10⁸)²
≈ 2 × 10²⁰ Newtons

This is the force that keeps the Moon revolving around Earth!

Section 6: Common Misunderstandings

Only Earth has gravity - Wrong. Every object, even you, exerts gravity. But only massive objects like Earth or stars exert it strongly enough to notice.
Gravity acts only downward - Wrong. Gravity acts along the line joining the centers of the two bodies. On Earth, it looks downward because Earth is beneath you.
No gravity in space - Wrong. Astronauts experience “weightlessness” not because there is no gravity, but because they are in free fall around Earth.

Section 7: Interactive Problems

Now, let’s test your understanding. Try to solve these before checking the solutions.

Problem 1: Everyday Objects

Two people, each of 60 kg, stand 1 meter apart. Find the gravitational force between them.
Hint: Use the formula with masses = 60 and 60, distance = 1 meter.

Problem 2: Weight on the Moon

Your mass is 50 kg. The mass of the Moon is 7.35 × 10²² kg and its radius is 1.74 × 10⁶ m. Find your weight on the Moon.
Hint: Weight = Force = G × (mass of body × mass of Moon) ÷ radius².

Problem 3: Distance Effect

If the distance between two bodies becomes three times, how does the gravitational force change?
Think: Inverse-square law applies.

Problem 4: Earth vs. Jupiter

The mass of Jupiter is 318 times Earth’s mass, and its radius is about 11 times Earth’s radius. How does the gravitational pull on the surface of Jupiter compare with Earth?

Problem 5: Satellite in Orbit

A satellite of mass 1000 kg is orbiting Earth at a height where the distance from Earth’s center is 7000 km. Earth’s mass = 6 × 10²⁴ kg. Find the gravitational force acting on the satellite.

Section 8: Solutions to Problems

Solution 1:

Force = 6.67 × 10⁻¹¹ × (60 × 60) ÷ (1²)
≈ 2.4 × 10⁻⁷ Newtons

This is extremely small, which is why you don’t feel it.

Solution 2:

Force = G × (50 × 7.35 × 10²²) ÷ (1.74 × 10⁶)²
≈ 80 Newtons

So your weight on the Moon would be about one-sixth of your Earth weight.

Solution 3:

Force reduces by factor of (3²) = 9.
So new force = 1/9th of original.

Solution 4:

Gravitational pull ∝ Mass ÷ Radius²
For Jupiter relative to Earth = (318) ÷ (11²) ≈ 2.6
So Jupiter’s surface gravity is about 2.6 times Earth’s.

Solution 5:

Force = 6.67 × 10⁻¹¹ × (1000 × 6 × 10²⁴) ÷ (7 × 10⁶)²
≈ 8.2 × 10³ Newtons

That is the force keeping the satellite in orbit.

Section 9: Why Understanding This Matters

Exams: Questions can range from numerical problems to conceptual reasoning.
Higher Studies: Gravitation links directly to astrophysics, space science, and orbital mechanics.
Daily Awareness: Knowing how tides, orbits, and weightlessness work connects classroom knowledge with the real world

Section 10: Quick Recap

Newton’s Universal Law: Every mass attracts every other mass.
Force ∝ Masses product; inversely ∝ square of distance.
G is universal and constant.
Real-world applications: satellites, tides, space missions.
Misconceptions must be cleared: gravity is everywhere, not just Earth.Practicing problems cements understanding

Next time you drop a pen, look at the Moon, or hear about a satellite launch, remember-it’s all governed by the same universal law. Newton didn’t just explain why the apple fell-he unified the heavens and the Earth under one principle.
So, ask yourself: If the same law controls both the smallest pebble and the largest planet, how powerful must it be?

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