![]() For example, imagine an object moving in a circle in a horizontal plane. SHM can be interpreted as a projection onto one axis of an object that is moving with a uniform circular motion (UCM). Plotting a graph of these motions (distance from the central point against time) produces the characteristic form of a sine wave ( figure 2). Simple harmonic motion (SHM) is the term used to describe regular periodic motions such as the swinging of a pendulum or the oscillations of an object attached to a spring. Ribeiro Simple harmonic motion and uniform circular motion Figure 2: Plotting the motion of an object attached to a spring against time produces a sine wave. I spent four months working on the project with my students, but if you do not have time to run the whole project with your students, you could select individual activities from it. The duration of the project will vary depending on how the teacher decides to approach it. At the end of the project, students produce a report (a document or presentation) to describe their findings and the whole process – and, ideally, share this with students from other countries so they can learn to communicate scientific work internationally. To do this, students collect data about the movement of the moons using a computer simulation, and then show that this movement has the characteristics of simple harmonic motion, with Jupiter as the centre. The aim of the project is for your students to prove that Galileo was right when he claimed that the ‘stars’ near Jupiter were in fact the planet’s satellites. The current project is enquiry-based, and aims to engage students with a rich variety of scientific processes – from exploring historical contexts to obtaining and analysing experimental results and communicating their conclusions to others. The project builds on a similar activity I developed earlier, about the motion of the Galilean moon Io ( Ribeiro, 2012). This discovery of Galileo’s forms the basis of a project that I devised for my 12th-grade physics students (17–18 years old) when teaching the topic of simple harmonic motion. Galileo Galilei in Sidereus Nuncius ( Starry Messenger 1610) Figure 1: Jupiter and the ‘… I should disclose and publish to the world the occasion of discovering and observing four PLANETS, never seen from the very beginning of the world up to our own times….” Galileo concluded that the ‘stars’ were in fact planets orbiting Jupiter – the Medicean planets, as he named them at the time, but which are now known as the Galilean moons in honour of their discoverer ( figure 1). He continued his observations for about two months, and over this time realised that there were actually four ‘stars’, which changed their position around Jupiter. On a January night in 1610, Galileo Galilei looked at Jupiter through his telescope and saw what he thought were three stars near the planet. Learn how you and your students can use mathematics to study Jupiter’s moons.
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