Astronomical Techniques

Transcription

1 Astronomical Techniques Lecture 2 Yogesh Wadadekar ISYA 2016, Tehran ISYA 2016, Tehran 1 / 51

2 How sun moves? How do stars move in the sky? ISYA 2016, Tehran 2 / 51

3 Celestial sphere ISYA 2016, Tehran 3 / 51

4 Celestial sphere - definitions ISYA 2016, Tehran 4 / 51

5 Circumpolar stars ISYA 2016, Tehran 5 / 51

6 Circumpolar stars ISYA 2016, Tehran 6 / 51

7 Right ascension (α) and Declination (δ) ISYA 2016, Tehran 7 / 51

8 Hour angle (HA) ISYA 2016, Tehran 8 / 51

9 Local sidereal time (LST) is the hour angle of the vernal equinox. It can also be defined as the right ascension of the meridian. Do sidereal time clocks run slower or faster depending on whether the earth is closer or further from the sun in its elliptical orbit? ISYA 2016, Tehran 9 / 51

10 Local sidereal time (LST) is the hour angle of the vernal equinox. It can also be defined as the right ascension of the meridian. Do sidereal time clocks run slower or faster depending on whether the earth is closer or further from the sun in its elliptical orbit? Compute the local sidereal time at 6 pm local time on 22 December (winter solstice)? ISYA 2016, Tehran 9 / 51

11 Computing HA HA = LST - α What is the hour angle of an object at RA=23:00:00 at 6 pm local time on 22 December (winter solstice)? ISYA 2016, Tehran 10 / 51

12 tidal friction and longer days There is a secular increase in length of day of about 2.3 milliseconds per century which mostly results from slowing of the Earth s rotation by tidal friction. How much longer before we have 48 hour days? ISYA 2016, Tehran 11 / 51

13 tidal friction and longer days There is a secular increase in length of day of about 2.3 milliseconds per century which mostly results from slowing of the Earth s rotation by tidal friction. How much longer before we have 48 hour days? 86400/ = 3800 million years ISYA 2016, Tehran 11 / 51

14 Ecliptic latitude and longitude What is the ecliptic latitude and longitude of the summer solstice point? What is the ecliptic latitude of the north celestial pole? ISYA 2016, Tehran 12 / 51

15 Galactic Coordinates ISYA 2016, Tehran 13 / 51

16 Milky way in galactic coordinates ISYA 2016, Tehran 14 / 51

17 Summary year, equation of time, precession, coordinate systems: horizon, equatorial, ecliptic, galactic. Any questions on these topics? For more details see: Spherical Astronomy by R. M. Green and Astronomical Algorithms by Jean Meeus ISYA 2016, Tehran 15 / 51

18 Universe is a 2D surface! ISYA 2016, Tehran 16 / 51

19 Smallest measurable angular separations (arcsec) Optical 10 3 best Radio 10 6 Space Very-Long Baseline Interferometry (VLBI)) X-ray 2 limited by spacecraft γ-ray 3600 limited by properties of γ-ray detectors How far would a 2 rupee coin ( 2 cm diameter) be if it subtends an angle of 1 milliarcsec? ISYA 2016, Tehran 17 / 51

20 Smallest measurable angular separations (arcsec) Optical 10 3 best Radio 10 6 Space Very-Long Baseline Interferometry (VLBI)) X-ray 2 limited by spacecraft γ-ray 3600 limited by properties of γ-ray detectors How far would a 2 rupee coin ( 2 cm diameter) be if it subtends an angle of 1 milliarcsec? /10 5 = 4000 km. ISYA 2016, Tehran 17 / 51

21 Angular separation between 2 coordinates on the sky z 1 = sin δ 1 (1) y 1 = cos δ 1 cos α 1 (2) x 1 = cos δ 1 sin α 1 (3) where α and δ represent RA and Dec respectively. ISYA 2016, Tehran 18 / 51

22 Angular separation between 2 coordinates on the sky z 1 = sin δ 1 (1) y 1 = cos δ 1 cos α 1 (2) x 1 = cos δ 1 sin α 1 (3) where α and δ represent RA and Dec respectively. For unit vectors ˆr 1 and ˆr 2, cos θ = ˆr 1 ˆr 2 cos θ = sin δ 1 sin δ 2 + cos δ 1 cosδ 2 cos(α 1 α 2 ) Will this formula work on a computer for small angular separations θ? ISYA 2016, Tehran 18 / 51

23 For small angular separations... tan(θ/2) = ˆr 1 ˆr 2 / ˆr 1 + ˆr 2 ISYA 2016, Tehran 19 / 51

24 Hipparchos and Gaia Between 1989 and 1993, the Hipparcos satellite, launched by the European Space Agency (ESA), measured parallaxes for about 100,000 stars with an astrometric precision of about 0.97 milliarcseconds, and obtained accurate measurements for stellar distances of stars up to 1,000 pc away. ESA s Gaia satellite, launched in 2013, is intended to measure one billion stellar distances to within 20 microarcseconds, producing errors of 10% in measurements as far as the Galactic Center, about 8,000 pc away. ISYA 2016, Tehran 20 / 51

25 Gaia ISYA 2016, Tehran 21 / 51

26 Solid angle is the area on the unit sphere that an object covers. Since a unit sphere has an area of 4π, there are 4π steradian on the sky. How many square degrees are there in the sky? ISYA 2016, Tehran 22 / 51

27 Solid angle is the area on the unit sphere that an object covers. Since a unit sphere has an area of 4π, there are 4π steradian on the sky. How many square degrees are there in the sky? (180/π) 2 4 π = ISYA 2016, Tehran 22 / 51

28 Chromatic Aberration ISYA 2016, Tehran 23 / 51

29 Chromatic Aberration - the solution ISYA 2016, Tehran 24 / 51

30 Spherical Aberration Solution - use a parabolic mirror ISYA 2016, Tehran 25 / 51

31 Spherical Aberration - the ultimate example ISYA 2016, Tehran 26 / 51

32 Cause of the problem with Hubble optics the main null corrector had one of its lenses sitting in a groove 1.3 mm away from where it needed to be. precision but poor accuracy. there were two other null correctors of lower precision that showed that spherical aberration was present. These readings were ignored. there had been a lot of bad blood between NASA and Perkins-Elmer due to cost and schedule overruns by the company. ISYA 2016, Tehran 27 / 51

33 M100 before and after COSTAR ISYA 2016, Tehran 28 / 51

34 Coma or comatic aberration - inherent to parabolic telescopes show video ISYA 2016, Tehran 29 / 51

35 Astigmatism ISYA 2016, Tehran 30 / 51

36 Astigmatism focal surfaces Two distinct focal surfaces exist in the presence of astigmatism, a tangential focal surface and sagittal focal surface ISYA 2016, Tehran 31 / 51

37 Geometrical optics is the branch of optics where λ 0. In this approximation optical laws may be formulated using the formalism of geometry. One can then speak of a pencil of light rays that have a sharp edge (except for diffraction which affects a region of about a wavelength at the edge of the pencil). ISYA 2016, Tehran 32 / 51

38 Basic rules of ray tracing rays go through center of lens undeflected parallel rays get converged and come together at the focal length ISYA 2016, Tehran 33 / 51

39 ZEMAX ray trace for a 3D spectrograph ISYA 2016, Tehran 34 / 51

40 Simplified Prime focus astronomical telescope image scale is the ratio of angular distance in the sky to physical distance at the focus, and it depends only on the focal length. δθ/δl = 1/L ISYA 2016, Tehran 35 / 51

41 Unsimplified astronomical telescope ISYA 2016, Tehran 36 / 51

42 Refractors Magnification M = δφ/δθ = L/l ISYA 2016, Tehran 37 / 51

43 Real life eyepiece designs ISYA 2016, Tehran 38 / 51

44 the fight against chromatic aberration... ISYA 2016, Tehran 39 / 51

45 Yerkes - the largest achromatic refractor ISYA 2016, Tehran 40 / 51

46 Refractor problem What is the biggest problem with building extremely large refractors? ISYA 2016, Tehran 41 / 51

47 Reflector variants ISYA 2016, Tehran 42 / 51

48 Schmidt camera ISYA 2016, Tehran 43 / 51

49 Schmidt camera easy-to-make spherical primary mirror aspherical corrector plate located at center of curvature of primary mirror fast focal ratios - wide field of view, ideal for surveys low coma and astigmatism very strongly curved focal planes used in the Hipparcos satelite ISYA 2016, Tehran 44 / 51

50 48 inch Palomar Schmidt camera still being used for the Palomar Transient Factory! ISYA 2016, Tehran 45 / 51

51 Coma or comatic aberration - inherent to parabolic telescopes show video ISYA 2016, Tehran 46 / 51

52 Schmidt camera ISYA 2016, Tehran 47 / 51

53 Schmidt Cassegrain ISYA 2016, Tehran 48 / 51

54 Schmidt Cassegrain ISYA 2016, Tehran 49 / 51

55 Ritchey Chrétien hyperboloid primary and secondary, no coma or spherical aberration! ISYA 2016, Tehran 50 / 51

56 Almost all large telescopes are RC 3.4m INO Telescope, Iran two 10 m telescopes of the Keck Observatory four 8.2 m telescopes comprising the Very Large Telescope in Chile two 8 m telescopes comprising the Gemini Observatory 10.4 m Gran Telescopio Canarias 8.2 m Subaru telescope at Mauna Kea Observatory 3.5 m Herschel Space Observatory orbiting telescope 2.5 m Sloan Digital Sky Survey telescope (modified design) 2.4 m Hubble Space Telescope 85 cm Spitzer Space Telescope 30 m TMT ISYA 2016, Tehran 51 / 51