On this page:
Introduction What Is Gravitational Force? Newton's Law of Universal Gravitation Gravitational Field Gravitational Field Strength Variation of g with Distance Weight and Mass Gravitational Potential Energy Gravitational Potential Equipotential Surfaces Orbital Motion Orbital Speed Orbital Period Satellites Geostationary Orbits Escape Velocity Free Fall Inverse Square Law Importance of Gravity in PhysicsWhy do objects fall to the ground when dropped? Why does the Moon move around the Earth? Why do planets orbit the Sun instead of flying away into space?
All these motions are caused by gravity, one of the four fundamental forces in nature. Gravity is the force that attracts objects with mass toward each other.
Gravity acts everywhere in the universe. It holds planets in orbit, keeps the atmosphere around Earth, and gives objects weight.
Without gravity, stars, planets, and galaxies would not exist.
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:
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.
F = Gm₁m₂ / r²
F = gravitational force (N)
G = gravitational constant
m₁, m₂ = masses (kg)
r = distance between centres (m)
G = 6.67 × 10⁻¹¹ Nm²kg⁻²
This equation shows:
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:
Near Earth's surface, the field is nearly uniform.
g = F / m
Unit: Nkg⁻¹
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.
g = GM / r²
M = mass of Earth, r = distance from Earth's centre
Gravitational field strength decreases as the distance from Earth increases.
Astronauts in orbit feel weightless because they are in continuous free fall around Earth.
Amount of matter in an object
Measured in kilograms (kg)
Constant everywhere
Gravitational force on an object
Measured in newtons (N)
Depends on gravitational field strength
W = mg
W = weight (N), m = mass (kg), g = gravitational field strength (Nkg⁻¹)
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.
Eₚ = mgh
m = mass (kg), g = gravitational field strength, h = height (m)
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:
When the object falls, gravitational potential energy converts into kinetic energy.
V = −GM / r
Unit: Jkg⁻¹
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:
Objects can move in circular paths around massive bodies due to gravity. Gravity provides the centripetal force required for circular motion.
Examples include:
Orbital motion was first described by Johannes Kepler, who discovered mathematical laws describing planetary motion.
v = √(GM / r)
v = orbital speed, M = mass of central body, r = orbital radius
T² ∝ r³
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.
Example: The Moon
Used for:
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:
These satellites are used for communication and television signals.
vₑ = √(2GM / r)
For Earth: vₑ ≈ 11.2 kms⁻¹
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:
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:
Examples:
Objects in orbit experience continuous free fall toward Earth.
Gravitational force follows the inverse square law: F ∝ 1 / r²
If the distance increases by a factor of 2 → Force becomes 1/4
If distance increases by a factor of 3 → Force becomes 1/9
Many physical forces follow this same law, including light intensity and electric force.
Gravity explains many natural phenomena, including:
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.