Universal Gravitation

Mass vs Weight

Mass

• Mass is the amount of matter in an object.

• It determines how heavy or light something is.

• Mass is an inherent property of an object.

• It does not change whether the object is:

  • On Earth

  • On the Moon

  • In space

• Mass determines inertia (resistance to change in motion).

Type of quantity:

• Scalar (has magnitude only)

SI unit:

• Kilogram (kg)

Weight

• Weight is the force of gravity acting on an object’s mass.

• It depends on the gravitational pull of the place where the object is.

• Weight changes depending on location:

  • Less on the Moon

  • More on Earth

• Weight is not a property of the object itself, but of the gravitational field acting on it.

Type of quantity:

• Vector (has magnitude and direction)

SI unit:

• Newton (N)

Relationship Between Mass and Weight

Weight=Mass×Gravity\text{Weight} = \text{Mass} \times \text{Gravity}Weight=Mass×Gravity

• Same mass + different gravity = different weight

Quick Comparison Table (Exam-Ready)

One-sentence summary (perfect for tests)

Memory trick 🧠

• Mass = matter

• Weight = pull

• Mass stays, weight changes

Why astronauts jump higher on the Moon 🌙

• The Moon’s gravity is much weaker than Earth’s

• Gravity on the Moon ≈ 1/6 of Earth’s gravity

• Because gravity pulls less, astronauts weigh less, so they can jump higher and land softly

📌 Their bodies did NOT change — only gravity did.

Mass vs Weight (the core difference)

Mass

• Amount of matter in an object

• Never changes

• Same on Earth, Moon, Jupiter, space

• Measured in kilograms (kg)

Weight

• Force of gravity acting on mass

• Changes with gravity

• Measured in newtons (N) (or kg-force in everyday language)

Examples from the passage

On Earth 🌍

• Person: 60 kg

• Machine: 1000 kg

On the Moon 🌙 (1/6 gravity)

• Person: 10 kg

• Machine: 166 kg

On Jupiter 🟠 (2.5× Earth gravity)

• Person: 150 kg

• Machine: 2500 kg

👉 The numbers change, but the amount of matter does not.

Why food is labeled by mass 🍎

• Mass is constant everywhere

• Weight depends on gravity

• So food packets use mass (kg or g), not weight

The formula you’re about to learn

This answers the question at the end:

Weight formula

Weight=Mass×Gravity\textbf{Weight} = \textbf{Mass} \times \textbf{Gravity}Weight=Mass×Gravity

• On Earth: gravity ≈ 9.8 m/s²

• On Moon: gravity ≈ 1.6 m/s²

• On Jupiter: gravity ≈ 24.5 m/s²

One-sentence exam summary

2. Connecting this to weight

• Weight is a force

• The force causing weight is gravity

• Gravity causes an acceleration called g

So for a falling object:

• Acceleration = g (acceleration due to gravity)

4. Direction of weight

• Weight always acts toward the center of the Earth

• Because gravity pulls everything inward

That’s why weight is a vector (it has direction).

Values of g (important)

• Earth: 9.8 m/s²

• Moon: ~1.6 m/s²

• Jupiter: ~24.5 m/s²

Inverse Square Law (Plain Explanation)

1. What Newton noticed

By studying how planets move, Newton realized:

Not just weaker — weaker by the square of the distance.

3. What happens when distance changes?

Let’s say the distance from Earth’s center changes:

👉 Double distance → gravity becomes 4 times weaker
👉 Triple distance → gravity becomes 9 times weaker

4. Why gravity weakens so fast

Gravity spreads out in all directions (like ripples in water 🌊).
As distance increases, the same force is spread over a much larger area.

More area → less force per area → weaker pull.

Key points

• Gravity is strongest close to Earth

• Gravity weakens rapidly with distance

• Doubling distance → force becomes 1/4

• Tripling distance → force becomes 1/9

Moon fact

• Moon is 60× farther than Earth’s surface

• Gravity on Moon = 1/3600 of Earth’s surface gravity

One-sentence exam summary

Memory trick 🧠

• Distance × 2 → force ÷ 4

• Distance × 3 → force ÷ 9

• Square the distance, then divide

Explanation (Plain Language)

1. Mass matters in gravity

Newton realized gravity depends on more than distance.

• More mass → stronger gravitational pull

• A heavier object feels a greater force of gravity than a lighter one (if distance is the same)

So gravity is directly proportional to mass.

👉 Directly proportional means:

• If mass increases, gravity increases

• If mass decreases, gravity decreases

2. Newton’s Third Law (Action–Reaction)

Newton’s third law says:

So:

• Earth pulls on an object

• The object pulls back on Earth

• The forces are equal in size, opposite in direction

📌 Even a small object pulls on Earth, but Earth’s huge mass means it barely moves.

3. Gravity depends on BOTH masses

The gravitational force depends on:

• Mass of Earth

• Mass of the object

• Distance between their centers

So gravity is:

• Directly proportional to both masses

• Inversely proportional to the square of the distance

Where:

• Fg = gravitational force

• G = universal gravitational constant

• M = mass of Earth (or one object)

• m = mass of the other object

• r = distance between their centers

Clean Study Notes (Exam-Ready)

Universal Law of Gravitation

• Gravitational force:

  • Increases with mass

  • Decreases with distance

• Depends on both interacting masses

• Acts equally on both objects (action–reaction)

Key relationships

• More mass → more gravity

• More distance → less gravity

• Force is mutual between objects

One-sentence exam summary

The Value of G (Universal Gravitational Constant)

What is G?

• G is a constant number that appears in the Universal Law of Gravitation.

• It tells us how strong gravity is everywhere in the universe.

• The value of G is the same everywhere (on Earth, in space, in other galaxies).

How was G discovered?

• Lord Henry Cavendish measured G using a device called a torsion balance.

• This experiment measured the very tiny gravitational force between small masses in a lab.

• It was done almost 100 years after Newton.

📌 Newton knew the formula for gravity, but not the numerical value of G.

Gravity in the Solar System (Explained Simply)

Newton did NOT “discover” gravity

• Gravity already existed.

• Newton discovered that gravity is universal:

  • The same law applies on Earth

  • And in the solar system

  • And throughout the entire universe

Gravity and the Sun 🌞

• The Sun has a very large mass, so it has a strong gravitational pull.

• Planets closer to the Sun feel a stronger pull.

• Planets farther away feel a weaker pull.

This happens because gravitational force:

• Decreases with distance

• Follows the inverse square law

📌 If distance increases, gravity decreases rapidly.

Clean Study Notes (Exam-Ready)

Key ideas

• Gravity is universal

• All objects attract each other

• More mass → stronger gravity

• More distance → weaker gravity

• Gravity follows an inverse square law

Solar system

• Sun’s gravity keeps planets in orbit

• Inner planets feel stronger gravity than outer planets

One-sentence exam summary

Memory trick 🧠

• Big mass = big pull

• Far away = weak pull

• Same law everywhere

What this result means (VERY important)

Key conclusions

• The value of g does NOT depend on the object’s mass

• All objects fall at the same acceleration (ignoring air resistance)

• Gravity at a location depends only on:

  • Earth’s mass

  • Distance from Earth’s center

📌 That’s why a feather and a hammer fall together on the Moon.