Historical Context & Motivation
Humans have always wondered why objects fall to the ground, why the Moon circles the Earth, and why planets trace predictable paths across the night sky. For centuries, thinkers proposed different explanations—some mystical, some mechanical—but none could unify terrestrial and celestial motion into a single framework. The concept of a gravitational field eventually emerged as the key idea that ties all of these phenomena together, describing how mass warps the space around it and influences other masses at a distance.
The central question that motivates this topic is: How can we describe the gravitational influence of a mass at every point in space, even before another object arrives to 'feel' it? Answering this question leads us to the field concept—a powerful tool that lets us map gravitational effects around any mass, predict orbital motion, and calculate escape speeds.
Core Principles & Definitions
A gravitational field is a region of space in which a mass experiences a gravitational force. Instead of thinking about forces acting mysteriously across empty space, we say that any object with mass creates a field around itself, and any other mass placed in that field feels a force. This shifts our perspective from 'action at a distance' to something more tangible: the field exists whether or not a second mass is present to detect it.
Gravitational Field Strength (g)
Field Lines
Uniform vs. Radial Fields
Newton's Law of Universal Gravitation
Visualising Gravitational Fields
Diagrams are essential for understanding gravitational fields. The following diagram shows two scenarios side by side: a radial field around an isolated point mass (or spherical body like Earth) and a uniform field near the surface of a planet over a small region. Notice how field lines in the radial diagram converge toward the centre and grow farther apart as you move away, while the uniform field lines are parallel and equally spaced.
In the radial field diagram, notice that the arrows all point inward—toward the mass. This is a distinguishing feature of gravitational fields: unlike electric fields, which can be attractive or repulsive, gravitational fields are always attractive. The spacing between lines tells you about the field strength at different distances. Close to the mass, lines are bunched together, meaning g is large. Far away, lines spread apart and g is weaker. In the uniform field approximation on the right, we treat the surface as flat and the field lines as perfectly parallel, which works well for problems involving projectile motion and free fall near Earth's surface.
Mathematical Framework
The mathematics of gravitational fields follows directly from Newton's law. We begin with the force law itself, then derive the gravitational field strength formula. These two equations are the workhorses of IB gravitational field problems.
The gravitational field strength at a point is defined as force per unit mass. If we place a small test mass m in the field of a larger mass M, we can divide both sides of Newton's law by m to isolate the field strength.
Field Patterns & the Inverse-Square Law
The inverse-square law is central to understanding how gravitational field strength changes with distance. Because g ∝ 1/r², doubling the distance from the centre of a mass reduces the field strength to one quarter of its original value. Tripling the distance reduces it to one ninth. This rapid decrease explains why gravity from the Sun is strong enough to hold Earth in orbit but far too weak for us to feel on our skin.
The graph above is one of the most commonly examined visuals in IB Physics. Notice that the curve has a steep initial drop and then flattens out gradually. Gravitational field strength theoretically extends to infinity but becomes negligibly small at large distances. Inside the planet (the shaded blue region), the relationship changes: g increases approximately linearly from zero at the centre to its surface value, because only the mass enclosed within your radius contributes to the field. For IB D.1, you primarily deal with the region outside the mass (r ≥ R).
| Distance from centre | Field strength g | Fraction of surface value |
|---|---|---|
| r = R (surface) | g₀ | 1 (100%) |
| r = 2R | g₀ / 4 | 1/4 (25%) |
| r = 3R | g₀ / 9 | 1/9 (≈ 11%) |
| r = 4R | g₀ / 16 | 1/16 (≈ 6.3%) |
| r = 10R | g₀ / 100 | 1/100 (1%) |
Worked Example
Let's work through a typical IB-style problem that combines Newton's law of gravitation with the concept of gravitational field strength.
Gravitational vs. Electric Fields
IB Physics treats gravitational and electric fields together under the Fields topic. Understanding their similarities and differences will deepen your grasp of the field concept and help you transfer knowledge from one topic to the other. The table below highlights the key comparisons.
| Property | Gravitational Field | Electric Field |
|---|---|---|
| Source | Mass | Electric charge |
| Nature | Always attractive | Attractive or repulsive |
| Field strength formula | g = GM/r² | E = kQ/r² |
| Potential formula | V = −GM/r (always negative) | V = kQ/r (sign depends on charge) |
| Distance dependence | Inverse-square (1/r²) | Inverse-square (1/r²) |
| Shielding possible? | No — cannot be blocked | Yes — conductors can shield |
| Relative strength | Extremely weak | Much stronger (≈ 10³⁶ times) |
Connection to General Relativity
Newton's gravitational field model works brilliantly for almost every scenario you will encounter in IB Physics—and indeed for most engineering applications. However, it breaks down in extreme situations: near black holes, at speeds close to the speed of light, or when measuring tiny effects like the precession of Mercury's orbit. Einstein's general theory of relativity (1915) reinterprets gravity not as a force transmitted through a field, but as the curvature of spacetime itself. Masses cause spacetime to warp, and other objects follow curved paths (geodesics) through that warped spacetime.
| Feature | Newtonian Gravity | General Relativity |
|---|---|---|
| Nature of gravity | Force between masses | Curvature of spacetime |
| Speed of propagation | Instantaneous (assumed) | Speed of light, c |
| Works well for… | Everyday masses, moderate speeds, weak fields | All scenarios including extreme mass & speed |
| Mathematical difficulty | Algebra and basic calculus | Tensor calculus (university-level) |
| IB Exam relevance | Core tool — used in calculations | Conceptual awareness only |
For the IB exam, you should know that general relativity exists and that it predicts phenomena Newton's model cannot explain—such as gravitational lensing (the bending of light around massive objects), gravitational time dilation (clocks running slower in stronger gravitational fields), and gravitational waves (ripples in spacetime detected for the first time in 2015 by LIGO). However, all numerical calculations in IB D.1 use Newton's equations.
Practice Problems
Lesson Summary
A gravitational field is a region of space where a mass experiences a gravitational force. The gravitational field strength g = GM/r² tells us the force per unit mass at any point and has units of N kg⁻¹. Newton's law of universal gravitation (F = GMm/r²) describes the attractive force between any two masses. The inverse-square law means that doubling the distance from a mass quarters the field strength. Near a planet's surface, the field is approximately uniform (parallel, equally spaced field lines), while farther away it is radial (lines converging toward the centre).
Gravitational potential V = −GM/r is always negative (gravity is always attractive) and represents the energy per unit mass needed to move a test mass to infinity. The gravitational potential energy E_p = −GMm/r follows the same pattern. Remember that r is always measured from the centre of the mass. Gravitational fields share the same mathematical structure as electric fields but are exclusively attractive and cannot be shielded. For extreme scenarios, Einstein's general relativity replaces Newton's model, but Newtonian gravity remains the primary calculation tool for IB D.1.