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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

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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

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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.

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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

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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.

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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.

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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.

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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

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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. Around 120 BC, he invented six different brightness classes, called magnitudes, where the brightest stars were magnitude 1 and the faintest were categorised as magnitude 6. Today, astronomers use a revised version of Hipparchus's magnitude scheme called 'apparent magnitudes', as well as 'absolute magnitudes' to compare different stars.

Apparent Magnitude The power radiated by a star is known as its luminosity. However, the apparent magnitude, m, is the power received by an observer on Earth. We can now see very faint stars using telescopes, so the scale extends beyond the magnitude 6 that Hipparchus marked down as the faintest on his scale.

Figure 3.4: Apparent magnitude scale and observational limits

As you can see, the magnitude numbers are bigger for faint stars, and magnitudes are negative for very bright stars. Since the scale is logarithmic, a magnitude 1 star is 100

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times brighter than a magnitude 6 star that is the difference between each step on the scale is equal to a decrease in brightness of 2.512 and (2.512)5 = 100.

Absolute Magnitude Comparing apparent magnitudes is a useful reference for astronomers, and these often appear next to stars on star maps. Apparent magnitude, however, does not tell us about the intrinsic properties of the star, so it is necessary to use the concept of absolute magnitude.

The absolute magnitude, M, of a star is defined as what the apparent magnitude of that star would be if it were placed exactly 10 parsecs away from the Sun. Most stars are much further away than this, so the absolute magnitude of stars is usually brighter than their apparent magnitudes.

To calculate the absolute magnitude for stars, we use the following equation:

M = m - 5 log (D/10) [3.2]

The value m-M is known as the distance modulus and can be used to determine the distance to an object, often using the following equivalent form of the equation:

D = 10 (m-M+5)/5 [3.3]

Star Star Parallax Apparent Absolute (Bayer Name) (Proper Name) (arcseconds) mag. (m) mag. (M) α Canis Majoris Sirius 0.37921 -1.44 1.45 α Carinae Canopus 0.01043 -0.62 -5.53 α Boötis Arcturus 0.08885 -0.05 -0.31

α1 Cenaturi Rigel Kent 0.74212 -0.01 4.34 α Lyrae Vega 0.12893 0.03 0.58 α Aurigae Capella 0.07729 0.08 -0.48 β Orionis Rigel 0.00422 0.18 -6.69 α Canis Minoris Procyon 0.28593 0.40 2.68 α Orionis Betelgeuse 0.00763 0.45 -5.14 α Eriadani Achernar 0.02268 0.45 -2.77

Table 3.2: Apparent and absolute magnitudes for the ten brightest stars on the night sky

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3.6 Luminosity from Stellar Spectra

Scientists use spectroscopic parallax to estimate the luminosity of a star from its spectrum (the different wavelengths shown as a band of colours when a spectrograph splits the light from a star into its electromagnetic waves).

Be careful not to confuse spectroscopic parallax with the parallax we have been discussing earlier. Scientists use spectroscopic parallax to measure the distance to stars, by assuming that spectra from distant stars of a given type are the same as those from nearby stars of the same type.

They use the Hertzsprung-Russell diagram, which gives a place to each star according to the point it has reached in its lifecycle. This method enables scientists to estimate the luminosity of a star that is far away by comparing its spectrum to those of nearer stars.

Figure 3.5: Recreated stellar spectra by class (from top to bottom): O, B, A, F, G, K, M

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Distances derived from Apparent Brightness and Luminosity Once the luminosity of a star has been estimated, its distance can be determined by using its apparent brightness. To do this, we use the inverse square law, which states that a star's apparent brightness decreases by the square of its distance. For instance, if you take two stars of the same luminosity, they will differ in brightness by four times if one star is twice as far away as the other. To determine distance, we use the following equation:

Luminosity Apparent Brightness = [3.3] 4π Distance2

L b = [3.4] 4π d2

Since the Sun is our nearest star, it is usually taken as the reference star.

By comparing another star's luminosity and apparent brightness to that of the Sun, using this formula, it is possible to determine its distance: L d2 b Star Sun Star [3.5] = 2 L Sun dStarbSun

⎛L ⎞⎛ b ⎞ 2 ⎜ Star ⎟⎜ Sun ⎟ 2 [3.6] dStar = ⎜ ⎟⎜ ⎟dSun ⎝ L Sun ⎠⎝bStar ⎠

Limits on Spectroscopic Parallax Spectroscopic parallax is only accurate enough to measure stellar distances out to about 10 Mpc. This is because a star has to be sufficiently bright to be able to measure the spectrum, which can be obscured by matter between the star and the observer. Even once the spectrum is measured and the star is classified according to its spectral type there can still be uncertainty in determining its luminosity, and this uncertainty increases as the stellar distance increases. This is because one spectral type can correspond to different types of stars and these will have different luminosities.

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3.7 Cepheid Variables

Cepheid variables are very luminous stars that pulsate in a regular cycle, with rapid brightening followed by gradual dimming. They are named after the star delta Cephei, a naked eye star, which was the first of this type to be identified. Cepheids are relatively rare, but their unique properties enable scientists to measure the distance to stars in galaxies more than 10 Mpc away. Since it is very difficult to tell the difference between a light source that is far away and a dimmer source that is nearer to us, measuring the distance to other galaxies is one of the greatest challenges facing astronomers. Cepheid variables are a fantastic tool to help them.

Light Curves The outer layers of a Cepheid variable star pulsate in a manner that is predictable. The outer layers of the star periodically expanding and contracting cause this pulsation.

Figure 3.6: Variation in star size and luminosity over time

Observations of Cepheids with well-known distances showed that a well-defined correlation exists between the average luminosity of a Cepheid star and its pulsation period. If a pulsating star, therefore, is detected in a distant galaxy, and it is identified as a Cepheid from its period and its spectral characteristics, its apparent brightness and its pulsation period can be used to determine its distance, which can also be defined as the distance to the cluster or galaxy in which it is found. Astronomers, therefore, have used the period-luminosity relationship to determine distances to galaxies.

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Figure 3.7: Lightcurve for a classic Cepheid (SV Vul) - period of 44.96 days

Figure 3.8: Lightcurve for a classic Cepheid (SU Cas) - 1.949 days

You can find the light curves for these and other Cepheids on the Hipparcos web pages at: http://www.rssd.esa.int/hipparcos/EpochPhot.html

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Period - Magnitude Relationship To determine the average absolute magnitude for Cepheids, the following equation is used:

M = -2.78 log (P) - 1.35 [3.7]

Where M is the absolute magnitude of the star and P is the period measured in days.

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3.8 Cepheids as Standard Candles

When we observe another galaxy, we can assume that all its stars are around the same distance from the Earth. A source of known luminosity in that galaxy enables us to make comparisons with all the other stars in the galaxy to determine their luminosity. Cepheid variable stars, which are thousands of times more luminous than the Sun, provide us with such a benchmark, known in astronomy as a "standard candle". By observing the period of any Cepheid, you can deduce its absolute brightness. Then, using an observation of its apparent brightness, the distance to it can be calculated. Henrietta Leavitt first discovered the period-luminosity relationship of Cepheids in 1912 for Cepheids in the nearby galaxy called the Small Magellanic Cloud.

Distance to Cepheids It is possible to estimate the distance to a Cepheid in a far-off galaxy as follows: firstly, locate the Cepheid variable in the galaxy, then measure the variation in its brightness over a given period of time. From this you can calculate its period of variability. You can then use the luminosity-period graph (below) to estimate the average luminosity. Finally, armed with the average luminosity, the average brightness and using the inverse square law, you can estimate the distance to the star.

Figure 9: Period-luminosity relationship for Cepheids

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3.9 Examples

Spectroscopic Parallax 1 - Spica • Apparent magnitude, m = 0.98 • Spectral type is B1 • From H-R diagram this indicates an absolute magnitude, M, in the range: -3.2 to • -5.0

Using equation 3.2 we derive:

D = 10 (m-M+5)/5 M= -3.2, D = 10 (0.98 - (-3.2) +5)/5 = 68.54 pc M= -5.0, D = 10 (0.98 - (-5.0) +5)/5 = 157.05 pc The Hipparcos measurements give d = 80.38 pc

2 - Tau Ceti

• Apparent magnitude, m = 3.49 • Spectral type is G2 • From H-R diagram this indicates an absolute magnitude, M, in the range: +5.0 to +6.5

Using equation 3.2 we derive:

D = 10 (m-M+5)/5 M= +5.0, D = 10 (3.49 -5.0 +5)/5 = 5.00 pc M= +6.5, D = 10 (3.49 -6.5 +5)/5 = 2.50 pc The Hipparcos measurements give d = 3.64 pc

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Period-Luminosity Relationship Consider the star W Geminorum:

Period of Oscillation = 7.9153 days

Using equation 3.7 this gives: Magnitude (M) = -2.78 x log (7.9153) – 1.35 = -3.848

Apparent magnitude (max) = 6.725 Apparent magnitude (min) = 7.585

Average apparent magnitude (m) = 7.155

Using Equation 3.2 this gives:

D = 10 (m-M+5)/5

⎛ ⎞ ⎜ 7.155- (-3.848) +5 ⎟ ⎜ 5 ⎟ 3.20 D = 10⎝ ⎠ = 10 = 1587 pc

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3.10 Cepheid Variable Stars from the Hipparcos and Tycho Catalogues

Guidelines The following table contains data from the Hipparcos and Tycho Catalogues. The data gives the magnitudes and periods for all the Cepheids contained in the catalogue. The data can be used as outlined earlier and plotted on the blank graph to enable students to derive the values for the period luminosity relationship.

DataTables

This table contains some data extracted from The Hipparcos and Tycho Catalogues. These catalogues are the scientific product of the European Space Agency's Hipparcos mission. For more information about the Hipparcos mission visit the web pages at http://sci.esa.int/hipparcos. Hipparcos data is available in plain ASCII format, thus no specialist software is required to start using it.

The data for all 118218 Hipparcos stars is available to download from the web (see http://www.rssd.esa.int/Hipparcos/research.html). Lightcurves for all of these Cepheid variable stars can be created using the Hipparcos Epoch Photometry Search facility at: http://www.rssd.esa.int/hipparcos/EpochPhot.html To use this tool you need only know the HIP number given in column B above.

Notes on Table

Variable star name: this is the name commonly used by scientists. HIP number: this is the identifying number of this star in the Hipparcos catalogue. Vmax: this is the magnitude at maximum luminosity as measured by Hipparcos. Vmin: this is the magnitude at minimum luminosity as measured by Hipparcos. Period: this is the period of variability, in days, measured by Hipparcos.

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Star HIP No. Vmax Vmin Period (D) Star HIP No. Vmax Vmin Period (D) FM_Cas 1162 8.968 9.594 5.810 bet_Dor 26069 3.563 4.244 9.842 SY_Cas 1213 9.592 10.409 4.072 ST_Tau 27119 7.904 8.701 4.035 DL_Cas 2347 8.815 9.401 8.001 EU_Tau 27183 8.050 8.398 2.102 XY_Cas 3886 9.811 10.413 4.502 RZ_Gem 28625 9.624 10.560 5.529 VW_Cas 5138 10.556 11.274 5.994 AA_Gem 28945 9.511 10.141 11.305 UZ_Cas 5658 11.066 11.910 4.260 CS_Ori 29022 10.881 11.924 3.889 BP_Cas 5846 10.678 11.445 6.272 SV_Mon 30219 8.066 8.960 15.241 V636_Cas 7192 7.237 7.411 8.376 RS_Ori 30286 8.222 9.031 7.571 RW_Cas 7548 8.708 9.977 14.787 T_Mon 30541 5.803 6.737 27.029 BY_Cas 8312 10.355 10.738 3.222 RT_Aur 30827 5.066 5.939 3.728 VV_Cas 8614 10.440 11.358 6.207 DX_Gem 31306 10.698 11.127 3.138 VX_Per 9928 9.195 9.810 10.887 BB_Gem 31361 11.016 12.132 2.308 UX_Per 10332 11.060 12.180 4.566 W_Gem 31404 6.725 7.585 7.915 V440_Per 11174 6.367 6.468 7.573 CV_Mon 31624 10.005 10.639 5.376 SZ_Cas 11420 9.726 10.120 13.636 BE_Mon 31905 10.395 10.993 2.706 alf_UMi 11767 2.093 2.124 3.971 AD_Gem 32180 9.637 10.281 3.789 DF_Cas 12817 10.697 11.306 3.833 V508_Mon 32516 10.409 10.861 4.134 SU_Cas 13367 5.879 6.299 1.949 TX_Mon 32854 10.850 11.499 8.704 RW_Cam 18260 8.343 9.187 16.408 EK_Mon 33014 10.910 11.465 3.957 RX_Cam 19057 7.456 8.204 7.912 TZ_Mon 33520 10.612 11.383 7.428 SX_Per 19978 10.888 11.704 4.290 AC_Mon 33791 9.891 10.619 8.013 AS_Per 20202 9.355 10.234 4.972 V526_Mon 33874 8.576 8.898 2.675 SZ_Tau 21517 6.495 6.856 3.149 zet_Gem 34088 3.782 4.328 10.151 AW_Per 22275 7.228 8.017 6.465 V465_Mon 34421 10.321 10.716 2.714 SV_Per 22445 8.705 9.520 11.116 TV_CMa 34527 10.324 11.117 4.670 AN_Aur 23210 10.262 10.929 10.293 RW_CMa 34895 10.951 11.612 5.730 RX_Aur 23360 7.470 8.133 11.626 RY_CMa 35212 7.858 8.606 4.678 CK_Cam 23768 7.345 7.960 3.295 RZ_CMa 35665 9.518 10.120 4.255 BK_Aur 24105 9.305 9.976 8.003 TW_CMa 35708 9.418 10.095 6.995 SY_Aur 24281 8.866 9.530 10.145 SS_CMa 36088 9.535 10.496 12.356 YZ_Aur 24500 10.039 10.877 18.197 VZ_CMa 36125 9.330 9.748 3.126 Y_Aur 25642 9.293 10.162 3.860 VW_Pup 36617 11.161 11.978 4.286

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Star HIP No. Vmax Vmin Period (D) Star HIP No. Vmax Vmin Period (D) X_Pup 36685 8.032 9.405 25.975 RY_Vel 50655 8.025 8.988 28.134 MY_Pup 37174 5.696 5.878 5.694 AQ_Car 50722 8.672 9.331 9.768 VZ_Pup 37207 9.095 10.421 23.163 UW_Car 51142 9.119 9.993 5.346 EK_Pup 37506 10.611 11.006 2.626 YZ_Car 51262 8.268 9.192 18.171 WW_Pup 37511 10.220 11.188 5.517 UX_Car 51338 7.908 8.776 3.682 WX_Pup 37515 8.873 9.572 8.937 XX_Vel 51894 10.398 11.275 6.985 AD_Pup 38063 9.500 10.600 13.596 UZ_Car 51909 9.133 9.791 5.205 BM_Pup 38241 10.471 11.242 7.198 HW_Car 52157 9.120 9.458 9.196 KZ_Pup 38441 11.690 12.848 2.019 EY_Car 52380 10.199 10.675 2.876 AP_Pup 38907 7.190 7.859 5.084 VY_Car 52538 7.007 8.150 18.901 WY_Pup 38944 10.366 11.144 5.251 SV_Vel 52570 8.286 9.229 14.098 AQ_Pup 38965 8.097 9.199 30.119 SX_Car 52661 8.806 9.618 4.860 WZ_Pup 39144 10.002 10.859 5.027 WW_Car 53083 9.446 10.234 4.677 BN_Pup 39666 9.282 10.634 13.673 WZ_Car 53397 8.711 10.102 23.015 AH_Vel 40155 5.620 5.987 4.227 XX_Car 53536 8.739 10.002 15.706 AT_Pup 40178 7.655 8.626 6.665 U_Car 53589 5.897 7.109 38.830 RS_Pup 40233 6.660 7.775 41.490 CY_Car 53593 9.578 10.142 4.266 V_Car 41588 7.213 7.851 6.697 FN_Car 53867 11.338 11.992 4.586 RZ_Vel 42257 6.567 7.975 20.411 XY_Car 53945 9.008 9.868 12.439 T_Vel 42321 7.835 8.471 4.640 HK_Car 54066 10.094 10.446 6.695 SW_Vel 42831 7.654 8.898 23.435 XZ_Car 54101 8.197 9.220 16.651 SX_Vel 42926 8.055 8.832 9.550 ER_Car 54543 6.689 7.298 7.719 ST_Vel 42929 9.510 10.186 5.858 GH_Car 54621 9.148 9.457 5.725 BG_Vel 44847 7.569 8.038 6.924 V898_Cen 54659 7.933 8.214 3.527 W_Car 45949 7.344 8.092 4.371 IT_Car 54715 8.095 8.439 7.531 DP_Vel 46610 11.644 12.401 5.484 GI_Car 54862 8.246 8.608 4.431 DR_Vel 46746 9.280 10.016 11.198 FR_Car 54891 9.436 10.183 10.716 T_Ant 46924 8.969 9.914 5.898 AY_Cen 55726 8.670 9.235 5.309 AE_Vel 47177 10.013 10.826 7.134 AZ_Cen 55736 8.578 8.936 3.212 l_Car 47854 3.502 4.250 35.560 V419_Cen 56176 8.134 8.481 5.507 GX_Car 48663 9.104 9.921 7.197 KK_Cen 57130 11.043 11.981 12.181 CN_Car 50244 10.482 11.208 4.933 RT_Mus 57260 8.693 9.484 3.086 GZ_Car 50615 10.213 10.603 4.159 UU_Mus 57884 9.294 10.411 11.635

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Star HIP No. Vmax Vmin Period (D) Star HIP No. Vmax Vmin Period (D) BB_Cen 57978 10.005 10.436 3.998 V482_Sco 85701 7.752 8.418 4.528 S_Mus 59551 6.029 6.581 9.660 V950_Sco 86269 7.275 7.618 3.380 AD_Cru 59575 10.782 11.528 6.398 X_Sgr 87072 4.364 5.028 7.013 SU_Cru 59996 9.508 10.013 12.847 V500_Sco 87173 8.686 9.194 9.314 T_Cru 60259 6.483 6.995 6.733 Y_Oph 87495 6.009 6.476 17.137 R_Cru 60455 6.483 7.318 5.826 W_Sgr 88567 4.393 5.243 7.594 BG_Cru 61136 5.490 5.704 3.343 CR_Ser 89013 10.554 11.302 5.301 R_Mus 61981 6.023 6.902 7.511 AP_Sgr 89276 6.727 7.510 5.059 S_Cru 62986 6.316 7.097 4.690 WZ_Sgr 89596 7.581 8.600 21.856 V496_Cen 63693 9.760 10.372 4.424 Y_Sgr 89968 5.494 6.251 5.774 V378_Cen 64969 8.419 8.800 6.460 AY_Sgr 90110 10.291 11.120 6.572 VW_Cen 66189 9.752 10.820 15.037 X_Sct 90791 9.684 10.468 4.199 KN_Cen 66383 9.389 10.415 34.050 U_Sgr 90836 6.499 7.225 6.745 XX_Cen 66696 7.452 8.416 10.953 EV_Sct 91239 10.156 10.408 3.091 V339_Cen 70203 8.645 9.184 9.465 Y_Sct 91366 9.459 10.072 10.341 V_Cen 71116 6.532 7.366 5.494 CK_Sct 91613 10.461 10.950 7.416 V737_Cen 71492 6.684 7.091 7.066 RU_Sct 91697 8.983 9.993 19.699 AV_Cir 72583 7.401 7.704 3.065 TY_Sct 91706 10.525 11.344 11.049 AX_Cir 72773 5.782 6.228 5.273 CM_Sct 91738 10.930 11.457 3.918 IQ_Nor 74448 9.404 10.061 8.218 Z_Sct 91785 9.195 10.151 12.902 R_TrA 75018 6.469 7.046 3.389 SS_Sct 91867 8.058 8.590 3.671 U_Nor 76918 8.853 9.762 12.655 V350_Sgr 92013 7.221 7.968 5.154 SY_Nor 77913 9.146 10.028 12.644 BB_Her 92067 9.985 10.567 7.507 S_TrA 78476 6.133 6.927 6.324 YZ_Sgr 92370 7.187 7.857 9.549 TW_Nor 78771 11.214 12.135 10.767 BB_Sgr 92491 6.811 7.424 6.637 RS_Nor 78797 9.765 10.524 6.198 V493_Aql 93063 10.810 11.488 2.987 GU_Nor 79625 10.179 10.723 3.453 FF_Aql 93124 5.314 5.660 4.471 S_Nor 79932 6.283 6.946 9.753 V336_Aql 93399 9.630 10.357 7.304 V340_Ara 82023 9.775 10.833 20.820 SZ_Aql 93681 8.209 9.299 17.141 KQ_Sco 82498 9.447 10.284 28.756 TT_Aql 93990 6.814 7.774 13.753 RV_Sco 83059 6.810 7.616 6.062 V496_Aql 94004 7.737 8.106 6.808 BF_Oph 83674 7.114 7.806 4.068 FM_Aql 94094 8.025 8.761 6.114 V636_Sco 85035 6.523 7.050 6.797 FN_Aql 94402 8.259 8.813 9.481

Teachers Notes Booklet 3: Stellar Distances Page 23 of 27

Star HIP No. Vmax Vmin Period (D) Star HIP No. Vmax Vmin Period (D) V473_Lyr 94685 6.184 6.361 1.491 IR_Cep 108426 7.753 8.125 2.114 V600_Aql 95118 9.836 10.483 7.236 CP_Cep 108427 10.255 11.041 17.864 U_Aql 95820 6.218 6.996 7.023 BG_Lac 108630 8.703 9.330 5.332 U_Vul 96458 6.927 7.623 7.991 Y_Lac 109340 8.883 9.613 4.324 V924_Cyg 96596 10.720 10.999 5.571 AK_Cep 110964 11.011 11.732 7.232 SU_Cyg 97150 6.525 7.321 3.846 V411_Lac 110968 7.834 8.073 2.908 BR_Vul 97309 10.429 11.227 5.197 del_Cep 110991 3.560 4.515 5.366 SV_Vul 97717 6.808 7.892 44.960 Z_Lac 111972 8.095 9.001 10.885 V1162_Aql 97794 7.676 8.203 5.375 RR_Lac 112026 8.571 9.379 6.416 eta_Aql 97804 3.646 4.465 7.178 CR_Cep 112430 9.596 9.959 6.233 S_Sge 98085 5.412 6.186 8.383 V_Lac 112626 8.529 9.547 4.983 X_Vul 98212 8.576 9.344 6.320 X_Lac 112675 8.349 8.758 5.444 V733_Aql 98217 9.908 10.361 6.179 SW_Cas 114160 9.496 10.148 5.440 GH_Cyg 98376 9.685 10.447 7.818 CH_Cas 115390 10.478 11.560 15.089 KL_Aql 98553 9.954 10.736 6.108 CY_Cas 115925 11.065 12.289 14.366 CD_Cyg 98852 8.379 9.655 17.071 RS_Cas 116556 9.648 10.446 6.296 V402_Cyg 99276 9.698 10.297 4.365 DW_Cas 116684 10.970 11.575 4.998 MW_Cyg 99567 9.250 9.968 5.955 CD_Cas 117154 10.507 11.304 7.801 V495_Cyg 99887 10.515 10.962 6.721 RY_Cas 117690 9.524 10.496 12.141 SZ_Cyg 101393 9.064 9.982 15.109 DD_Cas 118122 9.757 10.354 9.808 X_Cyg 102276 6.030 7.060 16.387 CF_Cas 118174 10.944 11.517 4.876 T_Vul 102949 5.504 6.201 4.435 V520_Cyg 103241 10.675 11.284 4.049 VX_Cyg 103433 9.415 10.624 20.141 TX_Cyg 103656 8.868 9.966 14.708 VY_Cyg 104002 9.334 10.145 7.856 DT_Cyg 104185 5.744 6.036 2.499 V459_Cyg 104564 10.389 11.101 7.252 V386_Cyg 104877 9.377 10.017 5.258 V1334_Cyg 105269 5.903 6.065 3.333 V532_Cyg 105369 9.041 9.418 3.284 V538_Cyg 106754 10.339 10.887 6.119 VZ_Cyg 107899 8.737 9.432 4.864 Teachers Notes Booklet 3: Stellar Distances Page 24 of 27

Period-Luminosity Relationship -2

-1.9

-1.8

-1.7

-1.6

-1.5

-1.4

-1.3 Absolute Magnitude (M) Absolute Magnitude -1.2

-1.1

-1 1 10 100 Period (P) in Days

Teachers Notes Booklet 3: Stellar Distances Page 25 of 27

3.11 Other Materials

This is booklet three in a series of six booklets currently available. The full range of titles is:

Booklet 1 Introduction to the Universe Booklet 2 Stellar Radiation and Stellar Types Booklet 3 Stellar Distances Booklet 4 Cosmology Booklet 5 Stellar Processes and Evolution Booklet 6 Galaxies and the Expanding Universe

Each booklet can be used to cover a topic on its own, or as part of a series. Booklets 5 and 6 expand on the material covered in the other booklets and there is, therefore, some overlap in content.

All the booklets can be accessed via the ESA Science and Technology at: http://sci.esa.int/teachernotes

For other educational resources visit the ESA Science and Technology Educational Support website at: http://sci.esa.int/education

Teachers Notes Booklet 3: Stellar Distances Page 26 of 27

Teachers Notes Booklet 3: Stellar Distances Page 27 of 27