FAQ – Newton’s Law of Universal Gravitation

What is Newton's law of universal gravitation?

Newton's law of universal gravitation states that every object with mass attracts every other object with a force called gravity. This force is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Example: Earth (mass ≈ 6×10²⁴ kg) attracts the Moon (mass ≈ 7.3×10²² kg) with a gravitational force that keeps it in orbit. This explains why the Moon doesn't fly off into space due to its tangential velocity.

What is the mathematical formula for Newton's law of gravitation?

The gravitational force F is calculated as:
F = G × (m₁ × m₂) / r²

Example: Calculate the force between two 1 kg masses 1 meter apart:
F = (6.67×10⁻¹¹) × (1 × 1) / (1)² = 6.67×10⁻¹¹ N – extremely small.

What is G in the gravitational formula?

G is the gravitational constant, approximately 6.67 × 10⁻¹¹ N⋅m²/kg².

It’s a universal scaling factor that quantifies how strong the gravitational force is. Without it, gravity would remain a proportionality without magnitude.

How does gravitational force depend on mass and distance?

Gravitational force increases with mass and decreases with the square of the distance.

Example:

• Doubling the mass of one object → doubles the force.
• Doubling the distance → reduces the force to one-fourth.

What is the direction of the gravitational force?

The gravitational force is always attractive and acts along the line joining the centers of two objects.

Example: Earth pulls the Moon toward its center, and the Moon pulls Earth toward its own center.

How does Newton’s law apply to extended bodies?

For spherically symmetric objects like planets, we can treat them as if all their mass is concentrated at their center.

Example: Earth's gravitational force on a satellite is calculated as though all Earth’s mass were at its core.

What is the Shell Theorem?

A spherical shell of mass:

• Exerts no net gravitational force on a particle inside it.
• Acts as if all its mass were concentrated at its center for particles outside it.

Example: Inside a hollow planet, you'd experience zero net gravitational pull from the shell.

Why don't we feel gravitational attraction between everyday objects?

Because the gravitational constant G is extremely small, only very massive bodies like Earth produce noticeable gravity.

Example: Two 70 kg people standing 1 meter apart feel a force of just ~3.3×10⁻⁷ N — imperceptibly tiny.

What is the difference between weight and gravitational force?

Weight is the gravitational force exerted by Earth on an object near its surface.

Example: A 60 kg person experiences a weight of:
60 kg × 9.8 m/s² = 588 N

Are the gravitational forces between two objects equal?

Yes. According to Newton’s third law, the gravitational force two objects exert on each other is equal in magnitude and opposite in direction.

Example: Earth pulls an apple down with a force F, and the apple pulls Earth up with the same force — though Earth’s huge mass means its acceleration is negligible.

How does Newton’s law explain falling objects and orbits?

Falling is due to gravity pulling objects toward Earth.
Orbiting is a continuous free-fall with sideways velocity.

Example: A satellite stays in orbit because gravity pulls it inward while its tangential speed keeps it from falling directly down.

What is gravitational acceleration (g)?

g = GM / r², where:

• G is the gravitational constant
• M is Earth's mass
• r is the distance from Earth's center

Example:
g = (6.67×10⁻¹¹ × 6×10²⁴) / (6.4×10⁶)² ≈ 9.8 m/s²

How does gravity change with altitude?

Gravity decreases with height since you're farther from Earth's center.

Example: On Mount Everest, g ≈ 9.76 m/s², slightly less than at sea level.

How do you calculate net gravitational force from multiple objects?

Use the superposition principle:
Add the gravitational forces from all sources vectorially.

Example: If two planets pull on a spacecraft, compute each force individually and then add them as vectors.

What is the connection between Newtonian gravity and black holes?

Newtonian gravity lays the groundwork for the idea of escape velocity.
When the escape speed exceeds the speed of light, a black hole forms.

Example: Escape velocity = √(2GM/r).
If this exceeds the speed of light, not even light can escape — a black hole results.

Newton’s Law of Universal Gravitation

✅ Lesson Overview

This lesson explains how every object in the universe attracts every other object using Newton's law of universal gravitation, and how to calculate and interpret this force.

What You’ll Learn

• How to calculate gravitational force between two masses
• The meaning of the gravitational constant (G) and its small value
• Why gravitational force follows an inverse square relationship
• How to express gravitational force as a vector with direction
• The application of Newton's third law to gravity
• Examples that show gravity is universal and always attractive

Key Concepts Covered

• Newton's law of universal gravitation
• Gravitational force
• Gravitational constant (G)
• Inverse square law
• Vector form of gravitational force
• Unit vector r-hat (r̂)
• Newton's third law
• Gravitational acceleration

Why This Lesson Matters

This topic is crucial for understanding everything from why objects fall on Earth to how planets orbit the Sun. It's a foundational concept for AP Physics, IB Physics, JEE, and NEET physics exams, and essential for mastering orbital motion, mass interactions, and force calculations.

🔗 Prerequisite or Follow-Up Lessons

• Newton’s Second Law: F = ma
• Gravitational Potential Energy and Fields

Full Lesson: Newton’s Law of Universal Gravitation

The Gravity That Grounds Us

Earth’s gravity is perfectly tuned. It keeps us anchored but doesn’t crush us. If it were weaker, we might float away. If it were stronger, we'd struggle to even walk.

People always knew that Earth pulls things downward, but in 1665, Isaac Newton realized that this same force pulls the Moon toward Earth too. Because the Moon also moves sideways, it orbits instead of falling. Newton concluded that every object in the universe attracts every other object. This mutual attraction is called gravitational force.

Newton's Law of Gravitation

The formula for gravitational force between two masses is:

F = G × (m1 × m2) / r²

Where:

• F is the gravitational force
• m1 and m2 are the two masses
• r is the distance between the centers of the masses
• G is the gravitational constant: 6.674 × 10⁻¹¹ N·m²/kg²

This tiny value of G explains why gravity is so weak unless at least one mass is enormous, like a planet.

Everyday Examples

• A 100-gram apple experiences about 0.98 newtons of gravitational force from Earth.
• Earth feels the same force from the apple, but its acceleration is tiny:

a = F / m = 0.98 / (5.972 × 10²⁴) ≈ 1.64 × 10⁻²⁵ m/s²

This is why Earth doesn’t move when the apple falls. The force is there, but the effect is negligible due to Earth's huge mass.

Gravity Between Two People

Two people each weighing 70 kg and standing 1 meter apart attract each other with a force:

F ≈ 3.4 × 10⁻⁷ newtons

That’s about the weight of an eyelash—real, but imperceptible.

Gravity Has Direction

Gravitational force is not just a number—it points from one object to the other. To express this direction, we use a unit vector called r-hat (r̂):

F (vector) = G × (m1 × m2) / r² × r̂

This tells us the direction of the force: along the line joining the two masses. Be careful not to confuse r̂ (the direction) with r (the distance). r̂ has no units—it only gives direction.

Equal and Opposite Forces

Newton’s third law tells us that forces come in equal and opposite pairs. So the force mass 1 exerts on mass 2 is:

F12 = -F21

The forces are equal in size but opposite in direction. That’s why gravitational force is always mutual.

Gravity Can’t Be Blocked

Unlike electric or magnetic forces, gravity can’t be shielded. It always acts, no matter what’s in the way. That’s why we say gravity is universal and always attractive.

Final Apple-Earth Calculation

Let’s calculate the force between a 100-gram apple and Earth:

F = (6.674 × 10⁻¹¹) × (0.1 × 5.97 × 10²⁴) / (6.371 × 10⁶)² ≈ 0.982 N

Now, calculate the acceleration of Earth due to this force:

a = 0.982 / (5.972 × 10²⁴) ≈ 1.64 × 10⁻²⁵ m/s²

This is unimaginably small—so small it would take longer than the age of the universe to change Earth’s speed by even 1 mm/s due to this apple.