1. © KCL. WCED. PENTECH. 2002 The falling Moon 1. Galileo Galilei (1564-1642) lived in what we now call northern Italy. He was a professor of mathematics. He studied the patterns in motion. He became interested in motion in the heavens - the movement of the Moon, planets, comets and stars, as well as motion on the Earth - things falling to Earth. At the time Galileo was studying motion there was a big debate over whether motion in the Heavens was governed by the same rules as motion on the Earth. Some people thought the Earth was stationary and at the centre of the universe. They argued that this is what was written in old books such as that written by the Greek Aristotle (384-322 BCE) and in the Bible. They said if the Earth were moving then one would expect two things to happen: (1) objects dropped from tall buildings or ships’ masts would fall to the West of the point from which they were dropped (they did not); (2) there would be a constant strong wind as the Earth rotated, & moved around the Sun. Galileo was the first to report his observations of the Moon with a telescope. He also reported that the planet Jupiter had four moons. These had not been seen ever before. People also knew about comets and how they came and went. Taken together, this evidence persuaded Galileo and his followers that the Heavens were no different from the Earth in terms of motion. Using his telescope Galileo observed the spots on the Sun. He saw how over time they changed, both in nature and in terms of their orientation. He deduced the Sun itself was spinning. He decided this evidence showed that Copernicus’s (1473-1543) Sun centred model of the universe was correct. The Earth and planets moved around a spinning Sun. A big problem for the Sun centred theory was the question of what kept the Earth and planets moving around the Sun ? Galileo could not think of a reason. PREPARE two sets of notes (briefs) for the lawyers who will be at Galileo’s trial. One for the prosecution, to show the views of those who disagreed with Galileo. A second brief, for the defence, setting out the views held by Galileo.

2. © KCL. WCED. PENTECH. 2002 The falling Moon 2. Issac Newton (1642-1727) lived in England. He studied at the University of Cambridge. Like Galileo, Newton was also a skilled mathematician. At Cambridge he read both what Galileo thought and what others thought about Galileo’s ideas. Newton became interested in motion in the heavens and on the Earth. Newton decided that if motion in the heavens were governed by the same mathematical rules as on Earth, he should be able to use those rules for the motion in the heavens. Newton had the idea that the moon must be falling towards the Earth in the same way that an apple falls to the Earth. The mathematical rules must be the same. From Galileo’s work Newton knew the value for the acceleration of the apple (10ms -2 ). He also knew how far away the Moon was from the Earth (3.84x10 8 m). What is more, he knew that the Moon goes once around the Earth in 27.3 days (27.3x24x60x60 seconds = 2.36x10 6 s). So he could calculate both the speed of the Moon as it goes round the Earth (1022ms -1 ) and the acceleration of the Moon as it falls towards the Earth (0.0027ms -2 ). This was an amazing achievement. But Newton was not convinced that the gravitational Force pulling both the Moon and the apple could be treated as acting from the centre of the Earth. This worried Newton. He put away his work on the Moon until he could be sure about the gravitational force acting from the centre of the Earth. 20 years later, using mathematics he invented specially for the job, he had convinced himself the force acted from the centre of the Earth. He published his ideas in a book entitled ‘Principia’ - The Principle (of motion in the heavens and on Earth). DESIGN and DRAW a poster to be used to advertise Newton’s book, Principia. The advertisement must help people to see what it is that makes this book so special and why they should buy a copy for themselves.

3. © KCL. WCED. PENTECH. 2002 The falling Moon 3. The force of gravity of the Earth pulls objects towards the centre of the Earth. A slowly moving projectile travels in a curved path and hits the Earth. A faster moving projectile travels further, and curves around more. Only a high speed projectile will be able to keep moving around the Earth even though gravity pulls it to the centre of the Earth. RE-DRAW the diagrams. For each diagram ADD arrows to show the direction of the force of gravity. Slow projectile Faster projectile High speed projectile

4. © KCL. WCED. PENTECH. 2002 The falling Moon 4. Gravitational pull of Earth on Moon Moon’s motion Moon pulled round (accelerated) towards Earth. This illustration is commonly found in Physics textbooks. Newton realised that motion in a straight line, with a constant speed, did not have to be explained. What required an explanation - a force being an explanation for change - was a change in speed or direction. Use the diagram to EXPLAIN how the force of gravity of the Earth causes the Moon to constantly fall towards the Earth.

5. © KCL. WCED. PENTECH. 2002 The falling Moon 5. Distance from the centre of the Earth in Earth diameters Force pulling one kilogram in Newtons 2 1 3456 0.61.19.82.50.40.3 Here is a table of data that gives values for the force accelerating one kilogram towards the centre of the Earth at different distances from the centre of the Earth. PLOT the data on the axes below. Label the axes carefully.

6. © KCL. WCED. PENTECH. 2002 The falling Moon 6. Newton found that the gravitational pull of the Earth drops off as the square of the distance from the Earth. Doubling the distance gives one quarter of the force. EXPLAIN how the diagram helps us to understand Newton’s results.

7. © KCL. WCED. PENTECH. 2002 The falling Moon 7. Force pulling on 1kg. Distance from Earth’s centre in Earth diameters 246 10 5 x x x x x x DESCRIBE the pattern in the graph in your own words. 0 This graph shows how the force of gravity varies as one moves away from the Earth. 1

8. © KCL. WCED. PENTECH. 2002 The falling Moon 8. The London Gazette November 1686 Newton comes clean Professor Issac Newton, the famous Lucasian professor of Mathematics from the University of Cambridge, who recently caused a sensation with the publication of his book Principia, today admitted that he did not know what caused masses to attract with the force of gravity. Prof. Newton said that, “he made no hypothesis” on the nature of the gravitational attraction. However, he did claim to have been the first to work out the mathematical rules by which we can compute the gravitational force between any two masses separated by any distance. He said that one day, using his ideas, men will land on the Moon. The Gazette says “ pigs might fly Professor”. Here is an imaginary newspaper report. WRITE a new article for tomorrow’s Cape Argus newspaper.