The heliocentric solar system

Learning outcomes To appreciate how our current understanding of the Solar System is based on the work of early astronomers. To understand Kepler’s 2nd and 3rd laws of planetary motion. To perform simple calculations using Kepler’s 3rd law.

The Heliocentric Solar System Copernicus put forward a theory called the HELLIOCENTRIC theory which put the Sun at the centre of the Solar System. Observations of the movements of the planets seemed to show that this was more likely. Today the system is sometimes referred to as the 'Copernicum System'. Previously it was thought that there was a GEOCENTRIC system, which stated that everything orbited the earth.

To understand Kepler’s 2nd and 3rd laws of planetary motion Keplers Laws Kepler stated 3 laws that today form the basis for understanding orbits. Planets move in elliptical orbits around the Sun. Planets move faster the nearer they are to the Sun. There is a relationship between the distance of a planet and the time it takes to orbit the Sun

Keplers First Law Law #1. Planets move in elliptical orbits around the Sun. They do not move in circular orbits. Before Kepler astronomers did not recognise this and so their computations were flawed. An ellipse is an oval shape with two foci (a focus). The Sun is at one focus and the other is in space

Keplers Second law Law #2. The Sun-planet line sweeps out equal areas in equal times. Planets move faster when they are nearer the Sun (perihelion) and slower when they are further away (aphelion). If you imagine a line connecting the Sun to the planet, this line sweeps out equal areas in equal times. If you look at the image below you will see that the time it takes for the planet to orbit A is the same time for the planet to orbit B.

Keplers Third Law… (this ones tricky) 3. The orbital period of a planet squared is proportional to its mean distance from the Sun cubed, when different planets are compared. There is a relationship between the distance of a planet and the time it takes to orbit the Sun. Terms you need to know first... SQUARE = a number multiplied by itself e.g. 2 x 2 = 4. 4 is the square of 2 CUBE = a number multiplied by itself and then multiplied by itself again. e.g. 3 x 3 x 3 = 27. 27 is the cube of 3. T = Period/ Time it takes to orbit the Sun r = mean radius from Sun

To perform simple calculations using Kepler’s 3rd law. Third law continued Although we use the Sun as our example, this equally applies to any primary body e.g. the Earth and calculating the orbit of the Moon around it. Kepler's Third Law is this: The square of the Period is approximately equal to the cube of the Radius. T2 = r3 AU is 1 astronomical unit = a unit of measurement equal to 149.6 million kilometres, the mean distance from the centre of the earth to the centre of the sun.

Now you try….. Saturn orbits the Sun in 29.45 years. What is its orbital radius?

Worked Answer T squared = 29.45 x 29.45 = 867 Cube root of 867 = 9.53. r = 9.53 AU

And one more… Study the image below. Planet A is 3 AU from the Sun. Using Kepler's Third Law find out the time it takes to orbit the Sun. Planet B takes 10 years to orbit the Sun, Find out the distance from the Sun.

Answer From Image Question A) 3 squared = 27 27 square root = 5.2 B) Square Root of 10 = 3.16 Distance = 3.163=31.5

Apply your Knowledge Complete Keplers laws questions.

To appreciate how our current understanding of the Solar System is based on the work of early astronomers Early Astronomers Log on to the computers and research the contribution of Copernicus, Tycho and Kepler to our current understanding of the Solar System.

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