* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download here - Lund Observatory
Star of Bethlehem wikipedia , lookup
Dialogue Concerning the Two Chief World Systems wikipedia , lookup
Dyson sphere wikipedia , lookup
Tropical year wikipedia , lookup
Formation and evolution of the Solar System wikipedia , lookup
History of Solar System formation and evolution hypotheses wikipedia , lookup
Planetary habitability wikipedia , lookup
Corona Borealis wikipedia , lookup
Canis Minor wikipedia , lookup
International Ultraviolet Explorer wikipedia , lookup
Corona Australis wikipedia , lookup
Aries (constellation) wikipedia , lookup
Cassiopeia (constellation) wikipedia , lookup
Observational astronomy wikipedia , lookup
Stellar evolution wikipedia , lookup
Star formation wikipedia , lookup
Astronomical unit wikipedia , lookup
Stellar kinematics wikipedia , lookup
Auriga (constellation) wikipedia , lookup
Canis Major wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
Perseus (constellation) wikipedia , lookup
Cygnus (constellation) wikipedia , lookup
Cosmic distance ladder wikipedia , lookup
Timeline of astronomy wikipedia , lookup
Lund Observatory LUND August 2011 ASTB01 INTRODUCTION TO ASTROPHYSICS (7.5 ECTS CREDITS) Exercises 1 Suppose that two closely spaced objects are observed with the 10.4 m telescope (GTC) at La Palma at visual wavelengths. How large must a radio telescope, observing at a wavelength of 10 cm, be, in order to have the same resolving power? The effect of the Earth’s atmosphere can be neglected. 2 A star has been observed to have the apparent visual magnitude V. Later observations show that the star in fact is a binary with two identical components. What is apparent visual magnitude of one of these components? 3 Calculate the flux density ratio between a star of magnitude V = 27 and the Sun, which has the apparent visual magnitude V = -26.8. 4. Calculate the total velocity (space motion) of Sirius (α Canis Majoris) relative to the Sun using data from Table C.17. 5. For a star the following data has been observed In the UBV system: V = 12.25, B-V = + 1.05, U-B = 0.00. The spectral class is B2 III. Stars belonging to this class can be assumed to have intrinsic colours, (B-V)0 = -0.25, and absolute magnitudes, MV = -3.0. Calculate the distance to the star. 6. Use the data in Table C.13 for the moon Phobos for calculating the mass of the planet Mars. 7. The absolute bolometric magnitude of Capella (α Aurigae) is estimated to be -0.6 and its effective temperature is 4400 K. Corresponding values for the Sun is +4.7 and 5800 K. Determine the luminosity and radius of Capella with the luminosity and radius of the Sun, respectively, as units. 8. How large will the linear diameter of the planet Venus be on a CCD camera attached to the 5 m telescope at Mount Palomar? At the time of the observation the angular diameter of the planet is 0.70’. The aperture ratio of the telescope is f/3.3 9. An eclipsing binary with components A and B normally has the magnitude 12.2. When the brightest of the two components, A, is eclipsed by B, the eclipse is total, and the magnitude of the binary drops to 14.2. Determine the magnitude of component A. 10. The intrinsic colour of the sun is (B-V)0 = 0.62. However, the sunlight we receive is affected by the passage of the Earth’s atmosphere. Determine the maximum and minimum value during the year of the observed colour index, B-V, of the Sun when it passes the meridian in Lund. The extinction coefficient in the visual is 0.15 and 0.27 in blue. 1 11. Barnard’s star (see Table C.17) has the largest proper motion, µ = 10.3’’/year. Assuming that its space velocity is constant, what will its maximum proper motion be? 12. For five stars one has observed the following data for spectral class, luminosity class, V magnitude and B-V colour index. Sirius V B-V A1V - 1.47 + 0.01 Two components of a binary A B A1V B0V + 9.51 + 4.23 +0.11 - 0.19 Two stars in a cluster C D B0V B0V + 9.40 + 10.00 + 0.35 + 0.55 The trigonometric parallax for Sirius has been determined to 0.375’’. Stars of the same spectral and luminosity class are supposed to have the same absolute magnitudes and intrinsic colour indices. The interstellar reddening of the two binary components is assumed to be the same. The two cluster stars are imbedded in clouds of interstellar matter. The distance to the stars C and D is assumed to be the same. The extinction coefficient for interstellar matter is supposed to be constant everywhere. Calculate: a) The absolute magnitude MV for a B0V star b) The distance to the binary c) The distance to the cluster containing stars C and D. 13. For a star with apparent visual rnagnitude V=3.08 one has observed a radial velocity of -30 km/s and a proper motion of 0.444’’/year. Its absolute magnitude is known to be: MV= +1.2. The extinction in the visual is assumed to be AV= 0.82. Calculate the space velocity of the star. 14. The star HD 22091 is a binary, consisting of two identical components of spectral class A3V. The period of the binary is 568.22 years. The maximum angular distance between the components is 0.85’’ and the minimum distance is 0.45’’. The orbital plane is perpendicular to the line-of-sight. The parallax of the binary has been measured to be 0.006’’. Calculate from this a value for the mass of an A3V star (expressed in solar masses). 15. a) Calculate the temperature of the Sun from Wien’s displacement law if the intensity maximum for the solar radiation is 470 nm. b) At the wavelength of 430 nm the intensity of the Sun is 1.14 times higher than at 550 nm. Calculate the colour temperature of the Sun using Wien’s approximation of Planck’s law. c) Calculate the effective temperature of the Sun from the solar constant 1.368⋅103 W/m2. The distance from the Earth to the Sun is 1.496⋅108 km and the radius of the Sun is 6.96⋅105 km. 16. a) Calculate the distance to the star Deneb (α Cygni), which has an absolute magnitude of MV = -7.2 and an apparent magnitude V = 1.25 assuming space to be extinction free. 2 b) Calculate the distance to Deneb assuming an interstellar extinction of 0.8 mag. per kpc. 17. A G5 star has the apparent visual magnitude V = 9.85 and the colour index B-V = 1.15. Determine if the star is a supergiant, a giant or a main-sequence star (dwarf). The visual extinction is three times the colour excess B-V. In thr direction of the star the visual extinction, AV, can be assumed to be given by AV = a ⋅ r, where r is the distance to the star and a = 0.003 magnitudes per parsec. For G5 stars it can be assumed MV (B-V)0 Supergiant -3.8 0.85 Giant 1.0 0.79 Dwarf 5.0 0.68 18. The supernova remanant, the Crab nebula (Messier 1) has nowadays a radius of approximately 3 arc minutes. It expands with a speedreod 0.21 arc seceonds per year. One has measured a radial velocity of 1300 km/s for the nebular gas in relation to the central pulsar. We assume a symmetrical expansion. a. How far away is the crab nebula? b. How long ago did the supernova occur according to these measurements? c. How bright was it then, if a supernova of this kind has a maximum absolute magnitude of -18? 19. The luminosity of the Sun is 3.86. .1026 W. Assume that the luminosity is constant over the main sequence evolution of the Sun. We can assume that the (initial) hydrogen abundance is X = 0.73 and that each helium nucleus formed weighs 0.7 % less than the four protons, from which it was formed. a) How much mass does the Sun loose per second due to hydrogen burning? b) How much of the hydrogen in the Sun has been transformed into helium up til now if the age of the Sun is 4.5 ⋅ 109 years? 20. Observation of the spectrum of a galaxy revealed that a group of lines with rest wavelengths around 420 nm were redshifted with 2.347 nm. Calculate the radial velocity and distance to the galaxy. One can assume that the Hubble constant is H0 = 70 km s-1 Mpc-1. 3 Answers to exercises ASTB01: 1. 1.9 ⋅106 m 2. V +0.75 3. 3.3 ⋅1021 4. 18 km/s 5. 1.9 ⋅103 pc 11. 25.4’’ 12. a) -3.9, b) 1.9 kpc, c) 360 pc 13. 46 km/s 14. 2.0 M 15. a) 6100kK, b) 6300K, c) 5780K 6. 6.43 ⋅ 1023 kg 7. 130 L, 20 R 8. 3.4 mm 9. 12.4 10. 1.25 and 0.75 16. a) 490 pc, b) 420 pc 17. Giant 18. a) 1.3 kpc, b) 860 years, c) -7.4 19. a) 4.3 ⋅109 kg, b) 6 % 43. 1675 km s-1; 24 Mpc 4