Pendulum Motion

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Q1. Outline the historical development of the models of the universe from the time of Aristotle to the time of Newton.

Aristotle: Geocentric model of the universe involved a series of 56 concentric spheres to which celestial objects were attached. The Earth was not in motion as the stars showed no measureable parallax. Each planet, the Sun, and the Moon were in their own sphere and the stars were positioned on a larger sphere surrounding all the others.

Ptolemy: Geocentric model of the universe placed the Earth at the centre of the universe with the heavenly bodies moving around on a series of small spheres or circles called epicycles. The stars moved on a celestial sphere around the outside of the planetary spheres.

Copernicus: Heliocentric model of the universe placed the sun at the centre of the universe. In this model planets still executed uniform circular motion around the sun. Also the Moon orbited the Earth.

Kepler: Heliocentric model of the universe placed planets in an elliptical orbit around the sun. The planets sweep out an equal area in equal time as they orbit the sun. The ratio of the cube of the radius to the square of the period of the orbits is equal for all planets in our solar system. These requirements of the universe model became known as the three laws of planetary motion.

Galileo: Heliocentric model of the universe that was proved by the discovery of four moons orbiting Jupiter, which showed that there were other centers in the heavens beside the Earth. Also Galileo discovered that Venus went through phases like the moon proving it orbited the sun. The Catholic Church claiming heresy persecuted him for his findings.

Newton: Heliocentric model of the universe. Created the theory of universal gravitation and used it to explain the motion of the planets and moons. Discovered that gravity was the force that controlled the orbits of the planets around the sun and the moons around the planets.

Q2. Outline the discovery of the expansion of the universe by Hubble, following its earlier prediction by Friedman.

In 1922, Alexander Friedman discovered a solution to the equations in Einstein’s general theory of relativity. This solution required an expanding universe and therefore Friedman predicted that the universe was expanding. Edwin Hubble proved Friedman’s predictions in later years. He did this by firstly comparing the wavelengths of spectral lines of Hydrogen from nebulae to the wavelengths of the same spectral lines in the laboratory. From this the relative speeds of the nebula could be found. Using this principle he determined that there were many galaxies and by putting some data together he found a simple relationship. The further away the Galaxy is, the faster it is moving away from us. From all of this Hubble concluded that the space between the galaxies is expanding. Q3. Describe the probable origins of the universe.

The most accepted theory of the origins of our universe’s origins is that of the big bang. It was considered to be a massive explosion that created energy, matter, space and time. Scientists believe that before the big bang the entire universe was compressed into a hot, dense mass just millimeter in diameter. An unknown force caused this mass to explode and expand rapidly eventually forming the known universe. This expansion still continues today however much slower.

Q4. Identify that Einstein described the equivalence of energy and mass.

Albert Einstein first described the equivalence of energy and mass.

Q5. Describe the transformation of energy into matter following the Big Bang.

Following the Big Bang a huge amount of energy came into existence. In the fraction of a second after the Big Bang the energy was too hot for matter to exist. Once it had cooled enough, energy began to condense into matter. This process is understood due to Einstein’s mass-energy relationship. As the energy cooled it formed anti-matter and matter that then...
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