08-06-2015 Atoms to Astronomy How can we say so much about small twinkling specks of light in the sky? Mayank N Vahia Tata Institute of Fundamental Research Homi Bhabha Road, Mumbai 400 005 Atoms to Astronomy 1 Atoms to Astronomy 2 [email protected] We study the light from the distant objects with increasing accuracy and correlate it to our knowledge of material on earth We measure and compare size, shape, distance and time variability. We look at how the intensity light is divided between various Part 1:Technology of observation wavelengths. We look at how light intensity changes with time. We try and do this from the smallest possible region of the sky. We correlate it to our understanding of how matter behaves in our laboratories to what we see from the heavens. Atoms to Astronomy 3 Atoms to Astronomy 4 Measuring angle in sky Distances in the sky are given in angular measure. Angular measure can be approximated using ones hand as show above. 5 1 08-06-2015 Local Sky – Finding Sky Charts North The limiting magnitude from a dark site is between 5 and 6. The changing sky As the Earth orbits the Sun, the Sun appears to move eastward along the ecliptic. At midnight, the stars on our meridian are opposite the Sun in the sky. Using telescopes to magnify the images of objects 10 Main Types of optical telescopes • Refracting telescope 1: Primary lens 2:Secondary lens 3: Eye 4: Object 5: first inverted image 6: Final inverted image 7: Telescope tube • Reflecting telescope In refracting telescope, the secondary lens is replaced by a reflecting mirror that focuses the beam. This significantly shortens the telescope size and is more tolerant of manufacturing problems. They can be of a variety of types. 11 2 08-06-2015 Stereoscopic Telescope • Binoculars are actually two refracting telescopes hinged together. • 7 X 50mm means the binocular magnifies the object 7 times and 50mm is the size of the objective lens. 16 Properties of a telescope Resolution • Focal Length: Point where the is focused? Longer the focal length, the narrower the field of view. Thinner the • Angular resolution θ: better. sin(θ) = 1.22 λ/D • Angular Magnification: Decides how big the object will θ is in radians be. The thicker the lens the better. λ the wavelength in meters • Field of View: Decides how much of the sky you can D the diameter of the lens aperture in m. observe at a time. The bigger the lens the better. Note that this is the theoretical limit. • Resolving Power: Decides how close by objects can • Spatial resolution, Δℓ: be resolved. The thicker the lens the better. Δℓ = 1.22 f λ/D • Limiting Magnitude: Decides what is the faintest object where f is the focal length of the objective you can see. 17 18 3 08-06-2015 Chromatic Aberrations 19 Atoms to Astronomy 20 Spherical Aberration Coma 21 22 Astigmatism Distortion • problem arising from a non-constant magnification of a lens is called distortion. Astigmatism is caused because the focal length along one diameter differs from that along another. When the object is on the axis, the two planes are identical, so there is no astigmatism. When the object is not focused, it is seen like an ellipse. 23 24 4 08-06-2015 Focal plane instrumentation The capabilities of a telescope are critically dependent on the type of detectors put at the focus. These can be: – Photographic films – CCD Camera – Spectroscopic devices like gratings – Any other light to electricity converting device They then have the appropriate ‘read out’ electronics which feed the signal to a computer for analysis. 25 Telescopes mounts Types of Mounts for Optical Telescopes – Alt-azimuth Mount: mounts allow telescopes to be moved in altitude, up and down, or azimuth, side to side, as separate motions. – Equatorial Mount: A mount for instruments that follows the rotation of the sky (celestial sphere) by having one rotational axis parallel to the Earth's axis of rotation. – Dobsonian Mount: Simplest and easy to use mount for quick observations with large amateur 27 Atoms to Astronomy 28 telescopes, The Seasons Part 2: Quantifying the sky 29 30 5 08-06-2015 Rising Point of Sun Over the Year 21/7 21/8 21/9 21/10 21/11 21/6 21/5 21/4 21/3 21/2 21/1 21/12 Angle depends on latitude E SS WS Rise Points A Gnomon Astronomy in stones 32 Sunrise on: Direction of Sun Summer Sunrise on: Solstice tml Winter Solstice http://www.jaloxa.eu/resources/daylighting/sunpath.sh Summer Solstice Equinox Equinox Winter Solstice Summer Solstice Winter Solstice Direction of Shadow Movement of Sun over 6 6 overMONTHS Movementof Sun Direction of shadow during the DAY 34 Two Circles Motion of the stars The Celestial Equator Stars near the north celestial pole are circumpolar and never set. – Projection of the Earth‚equator on We cannot see stars near the south celestial pole. the sky The Ecliptic – Relative path of the Sun in the sky for a terrestrial observer This star never sets Their Crossing Point Vernal (Spring) Equinox (ascending node) ♈ Autumnal Equinox (descending node) This star Inclination of Ecliptic w.r.t. Celestial equator: 23.5° never rises 35 6 08-06-2015 Geometry of the Sphere Geometry of the Sphere Great Circle: Any circle on the surface of sphere. Its centre coincides with centre of the sphere. Cosine Rule Small circle: All other circles on the surface cos(c) = cos(a) cos(c) of the sphere. + sin(a) sin(b) cos(C) Spherical angle: Angle between the planes Sine Rule of any two great circles. Sin(A) / sin(a) = sin(B) / sin(b) = sin(C) / sin(c) Properties of Spherical triangle: Analogue of Cosine Rule All three sides are arcs of great circles. sin(a) cos(B) = cos(b) sin(c) – sin(b) cos(c) cos(A) Any two sides are together greater than the third side. o The sum of the three angles is greater than 180 . Four Parts Formula o, Each spherical angle is less than 180 cos(a) cos(C) = sin(a) cot(b) – sin(C) cot(B) 37 38 Lines of Declination Lines of right ascension Spring Equinox 39 Equatorial Coordinates (absolute) The extraterrestrial solar illuminance (Eext): Declination: 푑푛−3 퐸푒푥푡 = 퐸푠푐 1 + 0.033412. cos 2휋 365 Right Ascension (RA): Angle from VE in hours: • dn=1 on January 1 and so on. = t - H (Eastwards) • dn-3 is used, because in modern times Earth's perihelion, the Both coordinates are closest approach to the Sun and the maximum E occurs ext time and place independent around January 3 each year. Vernel Equinox (VE) changes • The value of 0.033412 is determined knowing that the ratio between the perihelion (0.98328989AU) squared and the its position slowly aphelion (1.01671033 AU) squared is approximately 0.935338. Another parameter is needed Stardate Earth's axis is not fixed in space (Precession, Nutation) Reference to star date of VE, e.g. 1950.0 or 2000.0 Atoms to Astronomy 41 42 7 08-06-2015 Ecliptic Coordinates Transformations Axial tilt of the Earth, e = 23.439281° Ecliptic Latitude b: North or south of the Ecliptic to Equatorial Ecliptic -90o to +90o sin = sin e sin l cos b + cos e sin b cos cos = cos l cos b Ecliptic Longitude l: sin cos = cos e sin l cos b - sin e sin b 0o to 360o from VE eastwards Equatorial to Ecliptic Best system for sin b = cos ε sin - sin cos sin e solar system objects. cos l cos b = cos cos sin l cos b = sin e sin + sin cos cos e 43 44 Galactic Coordinates Time & Calendar True Sun: Hour angle of the Sun + 12h Time shown by a sundial Mean Sun: Hour angle of the Sun assuming it moves with the constant agular velocity Difference between true and mean Sun can be up to 16 min: • Orbit of the Earth is elliptical • Obliquity of the ecliptic . Equation of time (= true – mean) solar time Effect: sunrise in early January to a nearly fixed time, although day length is increasing. Analemma Shape created by plotting Analamma arises position of the Sun in the from the projection of sky as observed from the celestial plane on the Equatorial plane. same place at same time In this projection, the on different days. sun moves fastest midway of the curve. The shape depends on Latitude of the place (lp), inclination of orbit (e) and accentricity of orbit (e) 47 Atoms to Astronomy 48 8 08-06-2015 Equation of Time 푀 − θ + λ − α Δ푡 = λ = θ + λ ω 푝 Spring Eq Summer S Autumn Eq Winter SS 49 Atoms to Astronomy 50 Solar and Sidereal Times (Solar) Day: Time between two successive culminations of the Sun Sidereal Day: Time between two successive culminations of given distant star The Earth moves 1° per day around the Sun Solar day is longer by 4 min than the sidereal day 1Sidereal day ≈ 23h56m4s.091. 52 The Year Duration of a month Tropical Year: Time between two successive passages of the Sun d h m s through the Vernal Equinox = 365 05 48 46 = 365.242199 d. Month type Length in days Sidereal Year: One revolution around the Sun w.r.t. the distant Anomalistic 27.554549878 - 0.000000010390 × Y stars 365d06h09m10s = 365.2564 d (Longer due to the Earth's precession). Sidereal 27.321661547 + 0.000000001857 × Y Anomalistic Year: Time between two successive passages of earth Tropical 27.321582241 + 0.000000001506 × Y through its perihelion (or aphelion) point 365d06h13m53s = 365.2596 d (Differs from sidereal year due to precession of Draconic 27.212220817 + 0.000000003833 × Y perihelion).