Introduction

For most of ancient and medieval history, people believed the Earth stood still at the centre of the universe while the Sun, Moon and planets circled around it. This was the geocentric model, developed in its most complete form by the Greco-Roman astronomer Claudius Ptolemy in the 2nd century AD. It matched naked-eye observations of the Sun and Moon reasonably well, but it badly struggled to explain the motion of Mars and Jupiter.

In the 15th century the Polish astronomer Nicholas Copernicus (1473-1543) proposed the opposite idea: the heliocentric model, in which the Sun sits at the centre and every planet, including the Earth, orbits it. Around the same time, Galileo showed experimentally that all objects near the Earth fall with the same acceleration, and Tycho Brahe (1546-1601) spent his whole life recording extraordinarily precise naked-eye positions of the planets. It was Tycho's assistant, Johannes Kepler (1571-1630), who analysed this mountain of data and distilled it into three simple mathematical laws describing planetary motion -- Kepler's laws, covered in the next section.

Kepler's laws described how planets move but not why. That explanation had to wait for Isaac Newton, who in the late 17th century showed that a single force law -- the law of universal gravitation -- could account for both the fall of an apple and the orbit of the Moon. Gravitation remains an active area of physics research even today: in 2017 the Nobel Prize in Physics was awarded for the direct detection of gravitational waves, ripples in space-time that Einstein had predicted purely theoretically back in 1915.

By the end of this unit you should be able to: state and use Kepler's three laws; state Newton's law of gravitation and connect it to Kepler's laws; calculate gravitational field and potential; calculate how acceleration due to gravity varies with altitude, depth and latitude; calculate escape speed and the energy of satellites; explain weightlessness; explain why the heliocentric model is preferred over the geocentric one; and describe how Eratosthenes measured the radius of the Earth using nothing more than high-school geometry.