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Teachers Notes Booklet 3: Stellar Distances Page 1 of 27 The European Space Agency The European Space Agency (ESA) was formed on 31 May 1975. It currently has 17 Member States: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland & United Kingdom. The ESA Science Programme currently contains the following active missions: Venus Express – an exploration of our Cluster – a four spacecraft mission to sister planet. investigate interactions between the Rosetta – first mission to fly alongside Sun and the Earth's magnetosphere and land on a comet XMM-Newton – an X-ray telescope Double Star – joint mission with the helping to solve cosmic mysteries Chinese to study the effect of the Sun Cassini-Huygens – a joint ESA/NASA on the Earth’s environment mission to investigate Saturn and its SMART-1 – Europe’s first mission to moon Titan, with ESA's Huygens probe the Moon, which will test solar-electric SOHO - new views of the Sun's propulsion in flight, a key technology for atmosphere and interior future deep-space missions Hubble Space Telescope – world's Mars Express - Europe's first mission most important and successful orbital to Mars consisting of an orbital platform observatory searching for water and life on the Ulysses – the first spacecraft to planet investigate the polar regions around the INTEGRAL – first space observatory to Sun simultaneously observe celestial objects in gamma rays, X-rays and visible light Details on all these missions and others can be found at - http://sci.esa.int. Prepared by Anne Brumfitt Content Advisor Chris Lawton Science Editor, Content Advisor, Web Integration & Booklet Design Karen O'Flaherty Science Editor & Content Advisor Jo Turner Content Writer © 2005 European Space Agency Teachers Notes Booklet 3: Stellar Distances Page 2 of 27 Booklet 3– Stellar Distances Contents 3.1 Introduction .................................................................. 4 3.2 The Parsec .................................................................... 5 3.3 Stellar Parallax .............................................................. 6 3.4 Distance Using parallax................................................... 8 3.5 Apparent and Absolute Magnitude .................................. 10 3.6 Luminosity from Stellar Spectra ..................................... 12 3.7 Cepheid Variables ........................................................ 14 3.8 Cepheids as Standard Candles ....................................... 17 3.9 Examples.................................................................... 18 3.10 Cepheid Variables from Hipparcos and Tycho Catalogues ... 20 3.11 Other Materials............................................................ 26 Tables 3.1 Distance to Astronomical Objects ..................................... 5 3.2 Apparent and Absolute Magnitude for 10 Brightest Stars ... 11 1.3 Dates of Primary Meteor Showers..................................... 9 1.4 Brightest Open and Globular Star Clusters ....................... 13 Figures 3.1 Measurement of Parallax................................................. 6 3.2 Starburst Cluster NGC 3603 ............................................ 8 3.3 Orion Constellation......................................................... 8 3.4 Apparent Magnitude and Observational Limits .................. 10 3.5 Recreated Stellar Spectra.............................................. 12 3.6 Variation in Star Size and Luminosity with Time ............... 14 3.7 The Lightcurve for Classic Cepheid SV Vul ....................... 15 3.8 The Lightcurve for Classic Cepheid Su Cas ....................... 15 3.9 Period-Luminosity Relationship for Cepheids .................... 17 Teachers Notes Booklet 3: Stellar Distances Page 3 of 27 3.1 Introduction On a clear, dark night we may be able to see a few thousand stars in the sky, a tiny proportion of the billions of stars that are thought to exist in the Milky Way alone. Although the stars we see with the naked eye look similar in size, they vary enormously in their distance from the Earth. Furthermore, how bright a star appears is ultimately no indication as to how close it is to us. Astronomers use many different ways to determine just how far away a star is. Almost all are based on parallax. Parallax If you hold one finger at arm's length in front of your face and close each eye in turn, you will see that the finger appears to move compared to distant objects behind it. This apparent movement is known as parallax. Astronomers use this effect to measure the distance to stars by determining the angle between the lines of sight of a star from two different positions of the observer. ESA's Hipparcos Mission Launched in 1989 the ESA Hipparcos mission used the parallax method to observe positions of stars within the galaxy. As a result of the mission two catalogues of observations were produced: • The Hipparcos Catalogue - 120 000 stars to a precision 200 times better than any previous observations. • The Tycho Catalogue - detailed distribution and data map of a further 1.2 million stars. Teachers Notes Booklet 3: Stellar Distances Page 4 of 27 3.2 The Parsec Since stars are distant, the parallax angle is very small and is usually measured in arc seconds (fractions of a degree) rather than degrees. The term parsec is derived from: The distance at which an object has a parallax of one arcsecond An arcsecond is equivalent to 1/3600 of a degree, that is an angle of one second of arc (") is equal to one sixtieth of one minute of arc ('), and one minute of arc equals one sixtieth of a degree. 13 1 parsec = 3.26 light years = 3.09 x 10 km = 206 265 AU Object km AU Light Time Parsec Moon 3.84 x105 2.57 x10-3 1.28[1] 1.25 x10-8 Sun 1.50 x108 1.00 499[1] 4.85 x10-6 Saturn 1.48 x109 9.54 79.33[2] 4.63 x10-5 Proxima Centauri 3.99 x1013 2.67 x105 4.22[3] 1.294 Pleiades Cluster 4.26 x1015 2.85 x107 450[3] 1.38 x102 LMC/SMC 1.31 x1017 8.73 x108 13 803[3] 4.23 x103 Andromeda 2.18 x1019 1.45 x1011 2 300 000[3] 7.05 x105 Table 3.1: Distances to various astronomical objects in different units. It is clear from this table why different units are used for defining distances to different objects. Table notes: • Light Time is the distance as measured if travelling at the speed of light: [1] Light Seconds [2] Light Minutes [3] Light Years • Proxima Centauri is the closest star to the Sun • The Pleiades Cluster is a nearby open cluster of stars also known as the Seven Sisters • The Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) are small satellite galaxies of own galaxy visible from the southern hemisphere • Andromeda is the nearest major galaxy to the Milky Way Teachers Notes Booklet 3: Stellar Distances Page 5 of 27 3.3 Stellar Parallax To determine the distance to a star, astronomers measure the apparent change in its position over one year. As the Earth orbits the Sun during this period, the observer (taking measurements at the opposite sides of the Earth's orbit) notices an apparent movement of the star compared to more distant stars. The closer a star is to the Earth the greater the observed parallax. Figure 3.1: Astronomers measure the apparent shift in the star's position at different times of the year. As in the diagram, the lines of sight and the line connecting the observer's position form a triangle, with the star at the apex. The parallax of the star is equal to the angular radius of the Earth's orbit as seen from the star. The distance d to the star (measured in parsecs) is equal to the reciprocal of the parallax angle p (in arc-seconds): d(parsec) = 1/ p(arcsecond) [3.1] Limits on Parallax The greater the distance to the star, the wider the baseline required for obtaining a discernible parallax. The baseline for observations from the Earth is limited to our planet's orbit around the Sun. Parallax angles smaller than about 0.01 arcsecond are very difficult to measure accurately from Earth, therefore stellar distances for stars further than around 100 parsecs cannot be measured from Earth. Teachers Notes Booklet 3: Stellar Distances Page 6 of 27 However, ESA's Hipparcos satellite, unrestricted by the Earth's orbit or its atmosphere, spent three and a half years measuring star positions with unprecedented accuracy. Hipparcos allowed astronomers to measure the parallaxes of 120 000 stars, up to 500 light years (about 150 parsecs) from the Sun. Another experiment on the Hipparcos satellite, called Tycho, measured parallaxes for more than 1 million stars in the Galaxy, although to lesser accuracy. Teachers Notes Booklet 3: Stellar Distances Page 7 of 27 3.4 Distance Using Parallax Figure 3.2: Starburst cluster NGC 3603 (ESO) To the eye all the stars look like they are at the same distance, but some are closer and others further away. Figure 3.3: The stars in the constellation of Orion all look like they are at the same distance. Turn the constellation through 90° and the stars are actually at different distances. Teachers Notes Booklet 3: Stellar Distances Page 8 of 27 Calculating Distance from Parallax Consider the star α Canis Major, also known as Sirius, the brightest star on the night sky. Sirius has a parallax on 0.37921 arcseconds. To calculate the distance, in terms of light-years, we use Equation 3.1 introduced earlier: d(parsec) = 1/p (arcsecond) Distance = 1/0.37921 = 2.637 parsecs To convert from parsecs into light years this result must be multiplied by 3.26. Distance to α Canis Major = 2.637 x 3.26 = 8.6 light years Teachers Notes Booklet 3: Stellar Distances Page 9 of 27 3.5 Apparent and Absolute Magnitude Some stars appear very bright but are actually fainter stars that lie closer to us. Similarly, we can see stars that appear to be faint, but are intrinsically very bright ones lying far away from Earth. The Greek astronomer Hipparchus was the first to categorise stars visible to the naked eye according to their brightness.