Gravity and gravitational forces

Gravitational force is the attractive force between any two objects that have mass.

Even two small objects attract each other gravitationally, but the force is usually too small to notice. The force becomes noticeable when at least one object has a large mass, such as Earth.

When you drop a book, Earth pulls the book downward due to gravity. The book also pulls Earth upward, but Earth's mass is so large that the motion is not noticeable.

Gravity is always:

• Attractive
• Long-range
• Present among all masses

The gravitational force between two masses was first described mathematically by Isaac Newton. Newton discovered that every mass attracts every other mass in the universe.

G = 6.67 × 10⁻¹¹ Nm²kg⁻²

This equation shows:

• Larger masses produce stronger forces
• A greater distance reduces the force
• If the distance doubles, the gravitational force becomes four times smaller

A gravitational field is the region around a mass where another mass experiences a gravitational force.

Earth produces a gravitational field that extends into space. Any object placed in this field experiences a force toward Earth.

Gravitational field lines:

• Point toward the centre of mass
• Never cross each other
• Are closer together where the field is stronger

Near Earth's surface, the field is nearly uniform.

Gravitational field strength tells us how strong gravity is at a particular location. It is defined as the force per unit mass.

Near Earth's surface: g = 9.81 Nkg⁻¹

This means a mass of 1 kg experiences a force of 9.81 N downward.

Gravitational field strength is also equal to acceleration due to gravity: g = 9.81 ms⁻². So gravitational field strength and free-fall acceleration represent the same physical quantity.

Gravitational field strength decreases as the distance from Earth increases.

• g decreases with altitude
• g becomes very small far from Earth
• g is zero only at infinite distance

Astronauts in orbit feel weightless because they are in continuous free fall around Earth.

Example: A 2 kg object on Earth has:

W = 2 × 9.81 = 19.6 N

On the Moon, weight would be smaller because gravity is weaker.

When an object is raised in a gravitational field, it gains gravitational potential energy. This energy is stored because of the position in the gravitational field.

Example situations:

• Lifting a book onto a shelf
• Water stored in a dam
• A roller coaster at the top of a hill

When the object falls, gravitational potential energy converts into kinetic energy.

Gravitational potential is the work done per unit mass in bringing an object from infinity to a point in a gravitational field.

Gravitational potential is always negative because gravity is an attractive force. A more negative value means the object is more strongly bound to the planet.

An equipotential surface is a surface where the gravitational potential is the same everywhere.

No work is needed to move along an equipotential surface.

Around Earth:

• Equipotential surfaces are spherical
• Field lines are perpendicular to them

• Larger orbital radius → lower speed
• Lower orbit → higher speed
• Satellites close to Earth move faster than satellites far away

Orbital period is the time taken for one complete orbit.

This relationship is known as Kepler's Third Law. It shows that planets further from the Sun take longer to orbit.

Satellites remain in orbit because their sideways velocity balances gravitational attraction.

A geostationary satellite stays above the same point on Earth.

Conditions for geostationary orbit:

• Orbit above the equator
• Circular orbit
• Same rotation period as Earth (24 hours)

These satellites are used for communication and television signals.

Escape velocity is the minimum speed needed for an object to escape from a planet without further propulsion.

If an object reaches escape velocity, it never returns.

Escape velocity depends on:

• Mass of the planet
• Radius of the planet

It does not depend on the mass of the object escaping.

Free fall occurs when gravity is the only force acting on an object.

In free fall:

• Acceleration = g
• Motion is uniformly accelerated

Examples:

• Dropped objects
• Falling raindrops (ignoring air resistance)
• Orbiting astronauts

Objects in orbit experience continuous free fall toward Earth.

Many physical forces follow this same law, including light intensity and electric force.

Gravity explains many natural phenomena, including:

• Motion of planets
• Ocean tides
• Falling objects
• Satellite motion
• Structure of the universe

Gravity connects mechanics, energy, and astronomy into one unified theory.

Understanding gravity helps scientists design satellites, predict planetary motion, and explore space.

Gravity remains one of the most important topics in IB DP Physics because it combines forces, energy, and motion into a single physical model.