Preview
IB DP Physics — Unit D: Fields | SL & HL | D.1 Gravitational Fields
📋 What You Will Learn
- Observe and describe the motion of planets and satellites using Kepler's three empirical laws
- Define gravitational field strength, gravitational force, and all key quantities used in this topic
- Derive Newton's Law of Universal Gravitation and connect it to Kepler's Third Law through circular orbit analysis
- Apply Newton's gravitational law and orbital mechanics equations to solve figure-based and data-based problems
- Analyse gravitational field strength graphs and orbital period–radius relationships graphically
- Evaluate common misconceptions about gravity and connect this topic to energy, circular motion, and field theory
🌍 Real-World Context Every satellite orbiting Earth, every planet circling the Sun, and every moon tracing its path around a gas giant is governed by the same invisible force — gravity. The GPS system that guides your phone relies on satellites whose orbital periods are calculated to extraordinary precision using the very laws you are about to study. When engineers at NASA plan a mission to Mars, they use Kepler's laws to calculate the exact trajectory and timing of the spacecraft's journey. These are not abstract mathematical curiosities — they are the rules that govern the architecture of the entire solar system, and they were discovered centuries before anyone had ever launched a rocket.
🔍 Guiding Question How does the gravitational interaction between masses determine the structure and motion of planetary systems, and how can we use mathematical models to predict orbital behaviour?
Physical Setup: Planetary Orbits and the Solar System
Long before Newton formulated his law of gravitation, the astronomer Johannes Kepler spent years analysing the meticulous observational data collected by Tycho Brahe. What Kepler found was remarkable: the planets do not move randomly — they follow precise, repeatable paths around the Sun, and the relationship between their orbital sizes and their orbital periods follows a beautifully simple mathematical pattern.
To understand gravitational fields, we begin by looking at the solar system as a whole. The Sun sits at the centre, and the planets orbit it at different distances, each completing one full revolution in a different amount of time. Mercury, the closest planet, completes its orbit in just 88 days; Neptune, the most distant, takes 165 years. The question Kepler asked — and answered — was: is there a mathematical relationship connecting the size of an orbit to the time it takes to complete it?
Notice in the diagram that the orbits are ellipses, not perfect circles, and that the Sun is not at the geometric centre of each ellipse but at one of its two focal points. This is Kepler's First Law in action. Also notice that the planet moves faster when it is closer to the Sun and slower when it is farther away — this is the key insight behind Kepler's Second Law.
Kepler's Three Laws of Planetary Motion
Kepler published his three laws between 1609 and 1619, based entirely on observational data. They are empirical laws — meaning they describe what happens without explaining why. It was Newton, nearly 70 years later, who provided the physical explanation. We will study Kepler's laws first, then derive Newton's gravitational law, and finally show how Newton's law mathematically produces Kepler's Third Law.
📖 Kepler's First Law — The Law of Ellipses Each planet orbits the Sun in an ellipse, with the Sun located at one of the two foci of the ellipse.
An ellipse is a closed