Universal Law Of Gravitation Simplified - Interactive Problems Included

Gravity Basics Law of Gravitation Free Fall Weightlessness

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

Universal Law of Gravitation Simplified - Interactive Problems Included

In this guide, we’ll explain gravitation step by step, using simple logic and real-life examples.
By the end, you’ll truly understand the law - not just memorize it - and practice it with easy interactive problems.

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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

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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

1. Tides: The gravitational pull of the Moon (and the Sun) causes ocean tides on Earth.
2. Satellites: Artificial satellites stay in orbit because Earth’s gravity pulls them inward while their speed pushes them outward.
3. Weight: Your weight is just the force with which Earth’s gravity pulls you.
4. 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!

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Section 6: Common Misunderstandings

1. 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.
2. 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.
3. 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.

Section 8: Solutions to Problems

Solution 1: Everyday Objects

 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: Weight on the Moon

 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: Distance Effect

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

Solution 4: Earth Vs. Jupiter

 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: Satellite in Orbit

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

 That is the force keeping the satellite in orbit.

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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?

Problem

Many students wonder: Why do things fall? or Why doesn’t the Moon fall onto Earth?
But when formulas and symbols appear, gravitation suddenly feels confusing.

Agitate

If this concept isn’t clear, students struggle with topics like satellites, motion, energy, and planetary movement. It also affects exam answers and real-life understanding of tides and space science.

If you want to practice this topic, you can take a quiz in Curious Corner for better practice.