13.1 Gravitational Field

2026 📋 Syllabus Objectives

By the end of these notes, you should be able to:

  1. Understand that a gravitational field is an example of a field of force, and define gravitational field strength as force per unit mass.
  2. Represent a gravitational field by means of field lines.

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1. What Is a Field of Force?

In physics, a field of force is a region of space where an object experiences a force — even without anything physically touching it. Think of it like an invisible zone of influence that surrounds a certain type of object.

There are different types of fields of force in physics. A gravitational field is one important example. Others include electric fields and magnetic fields, but for now we focus on gravity.

The key idea is this: you do not need two objects to be touching for one to exert a force on the other. A mass can exert a gravitational pull on another mass across empty space, simply because a gravitational field exists around it.

2. What Is a Gravitational Field?

A gravitational field is a region in space where any mass placed there will experience a gravitational force — that is, a pull towards the mass creating the field.

Every object that has mass creates a gravitational field around itself. This field spreads outward in all directions. Any other mass that enters this region will feel an attractive force pulling it towards the first object.

Important characteristics of gravitational fields:

  • Gravitational forces are always attractive — they only pull, never push. This is unlike some other forces (like magnetic or electric forces) which can repel.
  • The field always points towards the centre of the mass creating it.
  • The field exists everywhere around the mass — it never completely disappears, but it does get weaker as you move further away.

Real-life example: The Earth has a gravitational field surrounding it. This field is why you feel your weight when you stand on the ground — the Earth's gravitational field is exerting a downward force on you. Even an astronaut in space (but still near Earth) is inside Earth's gravitational field and feels its pull.

3. Defining Gravitational Field Strength

Now that we know what a gravitational field is, we need a way to measure how strong it is at any given point.

Gravitational field strength (given the symbol g) is defined as:

The gravitational force acting per unit mass at a point in the field.

In simpler words: if you place a small test mass at a point in a gravitational field, gravitational field strength tells you how much force acts on every kilogram of that mass at that location.

The formula is:

g=Fmg = \frac{F}{m}

Where:

  • g = gravitational field strength (unit: N kg⁻¹, which means newtons per kilogram)
  • F = the gravitational force acting on the object (unit: N, newtons)
  • m = the mass of the object placed in the field (unit: kg, kilograms)

Since g is force divided by mass, its unit is N kg⁻¹. You may also see this written as m s⁻² — both are equivalent and correct.

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