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Mapping the Heavens How Long is a Day? 22-May-17 WILF: Be able to draw diagrams to show the phases of the moon and be able to explain what a sidereal day is. Keywords: Starter: True or false Phases of the moon 1. The sun rises in the East 2. The sun comes up at the same time each day Sidereal day Solar day 3. The moon only comes out at night 7. The moon orbits the earth once a day 4. The Earth goes around the sun 8. The Earth is closer to the sun in June than in December 5. The moon goes around the sun 6. We always see the same side of the moon 9. The moon rotates 10. There are no stars in the daytime sky. Complete the diagram Sidereal Days and Solar Days Star is seen at 23 hrs and 56 min Midday – sun is visible Midday – sun is visible The average time it takes the sun to cross the sky is 24 hrs. This is called a solar day. The Earth rotates through 3600 once every 23hrs and 56 minutes. A star would appear in the same position in the night sky therefore 23 hrs and 56 minutes later. This is called a sidereal day. Star is seen at midnight 23 hrs 56 18 12 hrs later 6 hrs later 24 hrs later minutes later Eclipses Keywords: Lunar eclipse WILF: Be able to explain how seasons occur and why eclipses are such rare events. Solar eclipse Shadow Totality Corona Umbra Penumbra Starter: the sun appears to travel across the sky once every 24 hrs yet the moon reappears every 24hrs and 49 minutes. Can you explain why this is so? Eclipses A solar eclipse happens when the Moon passes between the Sun and the Earth. This casts a shadow over the Earth. The last solar eclipse over the UK was on 11th August 1999. Solar eclipses do not occur very often. A lunar eclipse happens when the Earth passes between the Sun and the Moon. This casts a shadow over the Moon. Lunar eclipses happen in most years. What happens during a solar eclipse? During athe solar eclipse Moon moves directly Where must be forthe athe solar eclipse to take During a Moon solar eclipse Moon blocks the place? the Sun andpart theofEarth. Sun’sbetween rays from reaching the Earth. What happens during a lunar eclipse? Where must the Moon be for a lunar eclipse to take place? During aa lunar eclipse the Moon on thethe opposite During lunar eclipse the Earthisblocks Sun’s side light of thereaching Earth to the from the Sun. Moon. Why are solar eclipses so rare? - Because the moons orbit is tilted relative to the plane of the Earth’s orbit around the sun the chance of the Sun, Moon and Earth all being perfectly in a line is very rare. 22-May-17 Retrograde Motion WILF: be able to explain how the earth’s rotation causes the apparent motion of the stars and planets. Starter: Which constellations do you recognise? Keywords: Retrograde motion Constellation Polaris 21st September 21st December 21st June 21st March Retrograde Motion: To see retrograde motion for yourself: Load Stellarium Set the date to 23/11/2009 Set the time for 7pm Search for Mars Click on one of the nearby stars so the computer keeps that in the centre of the screen. Move time forward by 1 sidereal week at a time by pressing alt ] Watch the retrograde motion of Mars Can you make this happen with any other planets? Why is the effect more pronounced with Mars? Retrograde Motion: The planets generally move in one direction across the “fixed” background of stars. Sometimes they appear to slow down and even go in the reverse direction. This is known as retrograde motion. 5 4 2 3 1 Where does Mars appear? Background of fixed stars Measuring the Distance to Stars 22-May-17 WILF: Be able to describe what parallax is and be able to use it to calculate the distance to stars. Keywords: Parallax Parallax angle What is the parallax angle? The parallax angle (θ) is half of the stars apparent angular motion. Original telescope direction θ 2θ 1.5x1011m Position of Earth 6 months later 3x1011m Using trigonometry distances to stars can therefore be calculated. Examples using parallax Worked example: If the object in the diagram had a parallax angle 50. How far away is θ it? d Sin θ = Opposite/hypotenuse Sin5 = 2000/d Therefore d = 2000/sin5 Therefore d = 22947m. 2000m 4000m θ d Worked example: If a star had a parallax angle 0.020. How far away is it? Sin θ = Opposite/hypotenuse Sin0.02 = 1.5x1011/d θ Therefore d = 1.5x1011/sin0.02 d Therefore d = 4.297 x 1014m. How many light years is this? Light travels at 3x108 m/s. Therefore light travels 1.5x1011m 3x108x60x60x24x365 = 9.4608x1015 m/year 3x1011m Therefore 4.297x1014/ 9.4608x1015 = 0.045 light years. Using Really Small Angles to Measure Distances to Stars 22-May-17 WILF: Be able to use the unit of parsec to calculate distances to stars. Starter: What is the parallax angle for the object in the diagram shown? θ Keywords: Parsec Minute Second Arc d = 12000m 3000m Smaller angles In a circle there are 3600 We can split each degree of arc up into smaller measurements: 60’ (minutes) of arc = 10 So 100 = 600’ of arc. Or 0.10 = 6’ of arc. Because stars are so far away – parallax angles are even smaller than this. Therefore we need a small unit than the minute of arc. 60’’ (seconds) of arc = 1’ So 0.5’ = 30’’ of arc. So 1 second of arc (1’’) = 1 3600 of a degree Parsec An object whose parallax angle is 1 second of arc is at a distance of 1 parsec. So an object whose parallax angle is 4 seconds of arc is a distance of 0.25 parsec. As the angle decreases the distance increases. θ = 1’’ d = 1 parsec Distance in parsec = 1 Angle in seconds 1 parsec is about 3x1013km The Brightest Star 22-May-17 WILF: be able to explain the difference between luminosity and observed brightness and how the colour of a star is related to its temperature. Starter: If you look up at the night sky. Is there a way in which you can tell which stars are closest to the Earth? Keywords: Luminosity Observed brightness Spectrum Peak frequency Definitions: Luminosity – The amount of energy radiated into space every second by a star. Luminosity depends on: • The stars temperature (a hot star radiates more energy/second from a given area of its surface) • The stars size (a bigger star has more surface that radiates energy) • So a big hot star will be have a higher luminosity than a small cool star. Observed Brightness – a measure of the light reaching telescope from a star. This will depend on: • The distance the star is from the Earth • The luminosity of a star. • So just because a star appears bright does not mean it has to be close to the Earth. Black Body Radiation Applets – Explore how changing the temperature of a star affects the electromagnetic radiation emitted by it. http://webphysics.davidson.edu/alumni/MiLee/java/bb_mjl.htm http://www.astro.ubc.ca/~scharein/a311/Sim/bbody/BlackBody.html Star Colours: All hot objects emit a continuous range of electromagnetic radiation. The surface temperature of a star will determine the wavelength of the electromagnetic radiation we see emitted and hence the colour of the star. Hotter star Intensity of radiation at each frequency Colder star wavelength frequency The graph shows that: • a hotter star has a greater area under the graph so the luminosity is greater. • a hotter star produces a greater proportion of radiation at higher frequencies (it peak frequency is greater). 22-May-17 Cepheid Variable Stars WILF: Explain what a Cepheid variable star is and how they can be used to measure distances to galaxies. Keywords: Cepheid Variable Star Period Leavitt Globular Clusters Shapley Curtis Hubble Megaparsec Use the text book pg 218/219 to help you answer the following: What is a Cepheid Variable Star? • A Cepheid variable star is a star whose observed brightness varies in a regular pattern. • What causes the variation in their luminosity? • It is caused by the star expanding and contracting causing its temperature and hence its luminosity to change. • What is meant by the period of a Cepheid variable star? • The time it takes for the star to go from its brightest back to its brightest again. • What is the relationship between their luminosity and their period? • The more luminous the star the longer the period is. • How can this be used to measure the distance to a Cepheid variable star? • Measure the period of the star and calculate the luminosity based on this. • Measure the observed brightness of the star • From the luminosity and the observed brightness the distance to the star can be calculated. Read the text book pg 220/221. Complete the following table. In each column outline what theory each astronomer came up with. Shapley Curtis Thought the Milky Felt that the spiral Way was at the nebulae he had been centre of the studying were very Universe. Said distant from the there were Globular Milky Way and were Clusters (clusters in fact galaxies just of stars) orbiting like our own Milky around our Milky Way. Way galaxy. Hubble Used observations of a Cepheid variable star in a spiral nebulae to calculate its distance. Found out it was about 1 million light years away – far further away than the size of the Milky Way Hubble’s Constant WILF: be able to calculate the Hubble constant and the distance to distant galaxies given appropriate data. Keywords: Speed of recession Hubble and the Big Bang Hubble Constant Megaparsec Distance Mpc km/s S. Mag. Cloud 0.032 170 L. Mag. Cloud 0.034 290 NGC 5457 0.45 200 NGC 4736 0.5 290 NGC 5194 0.5 270 NGC 4449 0.63 200 NGC 4214 0.8 300 NGC 3627 0.9 650 NGC 4826 0.9 150 NGC 5236 0.9 500 NGC 1068 1 920 NGC 5055 1.1 450 NGC 7331 1.1 500 NGC 4258 1.4 500 NGC 4151 1.7 960 NGC 4382 2 500 NGC 4472 2 850 NGC 4486 2 800 NGC 4649 2 1090 The Hubble Constant • Hubble managed to measure the distance to different galaxies using Cepheid variable stars. • He also worked out the speed of their recession from “red shift” measurements (how fast they were going away from us). • Use his data in the table to plot a graph on the axis below – what is the general trend shown by your graph. Speed of recession (km/s) Galaxy/object Speed of recession Distance (Mpc) Distance Mpc km/s S. Mag. Cloud 0.032 170 L. Mag. Cloud 0.034 290 NGC 5457 0.45 200 NGC 4736 0.5 290 NGC 5194 0.5 270 NGC 4449 0.63 200 NGC 4214 0.8 300 NGC 3627 0.9 650 NGC 4826 0.9 150 NGC 5236 0.9 500 NGC 1068 1 920 NGC 5055 1.1 450 NGC 7331 1.1 500 NGC 4258 1.4 500 NGC 4151 1.7 960 NGC 4382 2 500 NGC 4472 2 850 NGC 4486 2 800 NGC 4649 2 1090 The Hubble constant Use his data in the table to plot a graph on the axis below – what is the general trend shown by your graph. Speed of recession (km/s) Galaxy/object Speed of recession Distance (Mpc) Plot a straight line of best fit on your graph. Work out the gradient of your line – this is the Hubble constant. The Hubble constant Use his data in the table to plot a graph on the axis below – what is the general trend shown by your graph. Speed of recession (km/s) Plot a straight line of best fit on your graph. Work out the gradient of your line – this is the Hubble constant. Distance (Mpc) From maths you should know that straight line graphs through the origin are of the form y = mx. Therefore: Speed of recession = Hubble constant x distance From this equation if we know the speed of recession of a galaxy we can work out its distance. Inside Stars and the Lives of Stars 22-May-17 What is the Sun Made Of? WILF: Explain how emission and absorption spectra allow us to know what a star is made of. Keywords: Emission spectrum Absorption spectrum Energy levels Photon Electrons in atoms only have certain values of energy. We represent this by drawing them in energy shells. All these other possible energy levels exist even though there are no electrons in them 1st2nd energy level – energy level lowest energy Sometimes it is easier to draw these energy shells as a “ladder” of energy levels. Emission Spectra When atoms get very hot – electrons are excited from their energy levels to higher energy levels. The electrons then fall back down to their original energy level and emit a photon of light that is equal in energy to the gap in the energy levels. This will correspond to a certain colour of light. Emission Spectra If excited to different energy levels they will emit different colours of light corresponding to the energy difference. Absorption Spectra Stars are blazing balls of gas where many kinds of atoms emit light of all colours. If you look at the spectrum you should therefore see all colours of the spectrum present. However as this light travels through the star’s outer atmosphere photons of certain energies will be absorbed by different atoms. These frequencies of light will therefore not appear in the spectrum seen. This is known as an absorption spectrum. Absorption Spectra Dark absorption lines appear in the spectrum when an atom absorbs a certain frequency of light causing electrons to jump out to higher energy levels. The frequencies of light not absorbed will be seen. Which of the mystery elements a, b, c or d are responsible for the absorption spectrum shown. a b c d Probing the Atom 22-May-17 WILF: Be able to explain the evidence that revealed the existence of the nucleus in the atom. Research the following: What did John Dalton think an atom was? What was the plum-pudding model of the atom? What experiment did Geiger and Marsden carry out to show the plumpudding model was wrong? How did their experiment show the existence of the nucleus in the centre of the atom? Good site with information and animation of alpha particle scattering: http://www-outreach.phy.cam.ac.uk/camphy/nucleus/nucleus1_1.htm The Strong Nuclear Force The nucleus of an atom contains neutrons and protons. + + + + But the protons are all positively charged so they should repel each other. There is another force present called the strong nuclear force. It only acts over a very small range and is able to balance out the repulsive electrostatic force. proton neutron 22-May-17 Pressure and Volume WILF: Be able to show and explain how the pressure and volume of a gas are related. Keywords: Pressure Kinetic theory Volume Now plot a graph of pressure against 1/volume. What do you notice? Volume Pressure Plot your data on a graph to show how pressure and volume are related. pressure 1/volume Conclusion: When the pressure is increased the volume ___________. The pressure is __________ proportional to the volume. Pressure is caused when the molecules of a gas collide with the container walls. Each collision causes a tiny force. Together all the forces add up to produce a gas pressure. When the volume is decreased the pressure __________. This is because…………………….. 22-May-17 Pressure and Temperature WILF: Be able to show and explain how the pressure and temperature of a gas are related. Keywords: Kelvin Temp/0C Pressure/ kPa 10 9.8 20 10.1 30 10.5 40 10.8 50 11.2 60 11.5 70 11.9 80 12.2 90 12.6 100 12.9 Absolute zero The relationship between temperature and pressure: Plot the following data on a graph with the axis shown. Extrapolate your graph back to the x axis. What is the temperature where it crosses? Temp/0C Pressure/ kPa 10 9.8 20 10.1 30 10.5 40 10.8 50 11.2 60 11.5 70 11.9 80 12.2 90 12.6 100 12.9 Pressure (kPa) 13 -300 0 Temperature (0C) 100 Absolute Zero The point where the line crosses the x axis is known as absolute zero. At this temperature the molecules are no longer moving and so there is no gas pressure -300 Pressure (kPa) 13 0 Temperature (0C) The temperature of absolute zero is -2730C 100 The Kelvin Temperature Scale The Celsius temperature scale was based on the freezing and boiling points of water. The Kelvin (K) scale starts at absolute zero. O Kelvin (0 K) is absolute zero (-2730C). Each graduation on the Kelvin scale is the same as on the Celsius scale Temperature in 0C = temperature in K – 273. 373 K 273 K 0K 100 0C 0 0C -2730C