Newton’s Law of Gravitation and Satellite Orbits

Expert reviewed • 22 November 2024 • 7 minute read

Introduction to Universal Gravitation

Newton’s Law of Universal Gravitation is a fundamental principle in physics that describes the gravitational interaction between masses. This law forms the basis for understanding planetary motion, satellite orbits, and the concept of weight on Earth.

What is Newton’s Law of Universal Gravitation?

Newton’s Law of Universal Gravitation states that every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. Mathematically, this is expressed as:

F = G\frac{M_1M_2}{r^2}

Where:

$F$ is the gravitational force between two masses (in Newtons, N)
$G$ is the universal gravitational constant ($6.67 × 10−11 ;\text{Nm²/kg²}$)
$M_1$ and $M_2$ are the masses of the two objects (in kilograms, kg)
$r$ is the distance between the centres of the masses (in meters, m)

What are the key Aspects of the Gravitational Force?

Universal nature: This law applies to all masses in the universe, from atoms to galaxies.
Attractive force: Gravity is always attractive; it never repels.
Infinite range: The force decreases with distance but never reaches zero.

Gravitational Field Strength

The gravitational field strength (g) at a point is defined as the gravitational force per unit mass experienced by an object at that point. It is expressed in N/kg or m/s².

g = \frac{GM}{r^2}

Where:

$g$ is the gravitational field strength
$G$ is the universal gravitational constant
$M$ is the mass of the object creating the field
$r$ is the distance from the centre of the object

Factors Affecting Gravitational Field Strength

Mass of the attracting body: The gravitational field strength is directly proportional to the mass of the object creating the field.
Distance from the centre: The field strength is inversely proportional to the square of the distance from the centre of the attracting body.
Altitude: As altitude increases, the distance from Earth’s centre increases, resulting in a decrease in gravitational field strength.
Latitude: Due to Earth’s rotation and its oblate spheroid shape, the gravitational field strength is slightly higher at the poles than at the equator.
Local geology: Variations in the density of Earth’s crust can cause small local variations in the gravitational field strength.

Orbital Motion of Satellites

Satellites in orbit around Earth are essentially in a state of continuous free fall. The satellite’s tangential velocity balances the gravitational force, resulting in a stable orbit.

Circular Orbit Velocity

For a satellite in a circular orbit, the centripetal force is provided by gravity. The velocity required for a stable circular orbit is given by:

v = \sqrt{\frac{GM}{r}}

Where:

$v$ is the orbital velocity
$G$ is the universal gravitational constant
$M$ is the mass of the body being orbited (e.g., Earth)
$r$ is the orbital radius (distance from the centre of Earth to the satellite)

Up Next

Understanding Orbital Velocity

Return to Module 5: Advanced Mechanics