* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download The motions of the Earth
Survey
Document related concepts
Observational astronomy wikipedia , lookup
Astrobiology wikipedia , lookup
Copernican heliocentrism wikipedia , lookup
International Ultraviolet Explorer wikipedia , lookup
Aquarius (constellation) wikipedia , lookup
Corvus (constellation) wikipedia , lookup
Theoretical astronomy wikipedia , lookup
Rare Earth hypothesis wikipedia , lookup
Extraterrestrial life wikipedia , lookup
Geocentric model wikipedia , lookup
Epoch (astronomy) wikipedia , lookup
Tropical year wikipedia , lookup
Astronomical unit wikipedia , lookup
Comparative planetary science wikipedia , lookup
Timeline of astronomy wikipedia , lookup
Dialogue Concerning the Two Chief World Systems wikipedia , lookup
Transcript
BASICS FOR ASTRONOMICAL OBSERVATIONS Jean-Pierre Rivet CNRS, OCA, Dept. Lagrange [email protected] © C2PU, Observatoire de la Cote d’Azur, Université de Nice Sophia-Antipolis Where is my target ? Stars, asteroids, planets, etc. are never where the catalogs pretend. Several reasons for that: Kinematic effects: Celestial objects are moving (proper motion). Fastest to slowest: artificial satellites, Moon, planets/asteroids, stars, extragalactic objects. Geometric effects: Earth’s motions are complex. So, Earth-based telescopes and reference catalogs use different frameworks (different origin points, and different axes), and they are moving one w.r.t each other. 05/05/2017 C2PU-Team, Observatoire de Nice 2 Where is my target ? Physical effects: 1) light takes some time to travel, so, moving objects are no longer where they appear to be. 2) Earth’s velocity modifies the apparent direction of incoming light rays. Atmospheric effects: Earth’s atmosphere perturbs the direction and intensity of light rays. So, lots of computations are needed to take into account all these effects, and to be able to drive your telescope to the right direction ! 05/05/2017 C2PU-Team, Observatoire de Nice 3 Earth’s motions and reference planes/directions Polar (spherical) coordinates: (r, , ) Polar axis Coordinate systems Origin PROBLEM: finding “good” reference plane and zero direction. Reference plane 05/05/2017 C2PU-Team, Observatoire de Nice 5 The motions of the Earth (I): orbital motion NOT TO SCALE ! Ecliptic plane Earth orbit Earth Sun 05/05/2017 C2PU-Team, Observatoire de Nice 6 The motions of the Earth (I): orbital motion NOT TO SCALE ! Orbit ellipsis Earth a = 149.6 106 km e = 0.0167 P = 1 “year” Sun = Focus Perihelion Center a.e (e = eccentricity) 05/05/2017 Aphelion a (a = semi-major axis) C2PU-Team, Observatoire de Nice … but what is a “year” ? depends the reference direction chosen to start/stop the chronometer ! • • • • • anomalistic year (365.25964 d) sidereal year (365.25637 d) tropical year (365.24219 d) draconic year (346.62008 d) … 7 The motions of the Earth (I): orbital motion NOT TO SCALE ! Orbit ellipsis Earth a = 149.6 106 km e = 0.0167 P = 1 “year” Sun = Focus Perihelion … but in … but what is a “year” ? real life, things are a bit more complicated depends the reference… direction chosen to start/stop a.e a the chronometer ! (e = eccentricity) (a = semi-major axis) Center Aphelion • • • • • 05/05/2017 C2PU-Team, Observatoire de Nice anomalistic year (365.25964 d) sidereal year (365.25637 d) tropical year (365.24219 d) draconic year (346.62008 d) … 8 The motions of the Earth (II): secular motions NOT TO SCALE ! Earth’s orbit now Perihelion 05/05/2017 Aphelion C2PU-Team, Observatoire de Nice 9 The motions of the Earth (II): secular motions NOT TO SCALE ! Earth’s orbit in 3000 years 05/05/2017 C2PU-Team, Observatoire de Nice 10 The motions of the Earth (II): secular motions NOT TO SCALE ! Earth’s orbit in 6000 years 05/05/2017 C2PU-Team, Observatoire de Nice 11 The motions of the Earth (II): secular motions NOT TO SCALE ! Earth’s orbit in 9000 years Perihelion slowly shifts Parameters a and e slowly change … because Earth and Sun are not alone in the Solar System ! 05/05/2017 C2PU-Team, Observatoire de Nice 12 The motions of the Earth (III): proper motion North ecliptic pole North equatorial pole : Obliquity 23° 27’ Ecliptic plane … but what is a “day” ? depends the reference direction chosen to start/stop the chronometer ! P = 1 “day” 05/05/2017 C2PU-Team, Observatoire de Nice • mean solar day (24 h) • sidereal day (23h 56m 04.09s) 13 The motions of the Earth (III): proper motion NOT TO SCALE ! Spring equinox Ecliptic plane Summer solstice Sun vernal direction Winter solstice Earth orbit vernal direction 05/05/2017 vernal direction C2PU-Team, Observatoire de Nice 14 Reference directions and planes Ecliptic North pole Ecliptic plane Earth North pole Orbital and proper motions of the Earth provide for 2 reference planes and 2 polar directions vernal direction 05/05/2017 C2PU-Team, Observatoire de Nice 15 Reference directions and planes Ecliptic North pole Ecliptic plane Earth North pole Orbital and proper motions of the Earth provide for 2 reference planes and 2 polar directions … but in real life, things are a bit more complicated … vernal direction 05/05/2017 C2PU-Team, Observatoire de Nice 16 The motions of the Earth (IV): precession Ecliptic North pole Ecliptic plane Earth North pole P 26 000 years Jan. 2000 05/05/2017 C2PU-Team, Observatoire de Nice 17 The motions of the Earth (IV): precession Ecliptic North pole Ecliptic plane Earth North pole P 26 000 years Jan. 2010 05/05/2017 C2PU-Team, Observatoire de Nice 18 The motions of the Earth (IV): precession Ecliptic North pole Ecliptic plane Earth North pole Jan. 2020 05/05/2017 C2PU-Team, Observatoire de Nice P 26 000 years 19 The motions of the Earth (IV): nutation Ecliptic North pole Earth North pole P 18.6 years Ecliptic plane 05/05/2017 C2PU-Team, Observatoire de Nice 20 The motions of the Earth (V): nutation Ecliptic North pole Earth North pole P 18.6 years Ecliptic plane 05/05/2017 C2PU-Team, Observatoire de Nice 21 The motions of the Earth (V): precession-nutation Precession-nutation: slow motions of the rotation (polar) axis of the Earth w.r.t. an external (astronomical) reference frame (fixed stars of quasars) True pole @ date Nutation (P 18.6 years) Precession (P 26 000 years) Mean pole @ date Ecliptic pole Mean pole @ J2000 ... because the Earth has no spherical symmetry the Moon creates a torque on Earth’s equatorial bulge 05/05/2017 C2PU-Team, Observatoire de Nice 22 Conclusion Earth’s motion is complex !!! Must be taken into account to define reliable reference systems and to find an astronomical object in the sky ! 05/05/2017 C2PU-Team, Observatoire de Nice 23 About light... Light takes its time ! NOT TO SCALE ! Moving object (asteroid, comet) Real position at time T0 Photon sent at time T0 T = T0 05/05/2017 Earth C2PU-Team, Observatoire de Nice 25 Light takes its time ! NOT TO SCALE ! Apparent position at time T0 + distance / c0 Real position at time T0 + distance / c0 Photon received at time T0 + distance / c0 T = T0 + distance / c0 05/05/2017 C2PU-Team, Observatoire de Nice 26 Earth’s velocity changes light’s direction Rain falls tilted on a running man... Photons falls tilted on a running planet... apparent position real position Bradley effect 05/05/2017 C2PU-Team, Observatoire de Nice 27 Light doesn’t go straight ! NOT TO SCALE ! Altitude-dependent atmospheric refraction index bends the light rays ! • zero at zenith, max. near the horizon • affects both H and This is “atmospheric refraction”. Star’s apparent position Star’s actual position 05/05/2017 C2PU-Team, Observatoire de Nice 28 Light doesn’t go straight ! NOT TO SCALE ! Atmospheric refraction depends on: - star elevation - atmospheric pressure - temperature - relative humidity - air composition - wavelength Star’s apparent position Star’s actual position 05/05/2017 C2PU-Team, Observatoire de Nice 29 What is “airmass” NOT TO SCALE ! Star at zenith Airmass = 1.0 Airmass = e / e0 = function of elevation h (relative thickness of atmosphere trough which a star is seen) Airmass turbulence and absorption Rule of thumb: Avoid airmass > 2 Star close to the horizon Airmass > 1.0 05/05/2017 C2PU-Team, Observatoire de Nice 30 Conclusion Light propagation is complex !!! Must be taken into account to find an astronomical object in the sky ! 05/05/2017 C2PU-Team, Observatoire de Nice 31 Space coordinates Coordinate systems (r, , ) Polar axis Polar (spherical) coordinates: Origin Fundamental plane 05/05/2017 A reference system = - Origin point - Fundamental plane (or polar axis) - Zero direction A reference frame = - Reference system - Definition of time C2PU-Team, Observatoire de Nice 33 Angular units, angular formats Degrees: 1 turn = 360° • Decimal format. example: 41.234° (French style: 41,234°) • Sexagesimal format. example: 41° 14’ 02.4’’ (Sumerian/Babylonian legacy) Radians: 1 turn = 2 rad (mostly used in mathematics and computation) • Decimal format. example: 1.612 rad (French style: 1,612 rad) Gradians: 1 turn = 400 gon(*) (only used in topography) • Decimal format. example: 53.256 gon (French style: 53,256 gon) Hours: 1 turn = 24 hrs (mostly used in astronomy) • Decimal format. example: 5.0336 h (French style: 5,0336 h) • Sexagesimal format. example: 5h 02m 01s (Sumerian/Babylonian legacy) * from the Greek “”: angle 05/05/2017 C2PU-Team, Observatoire de Nice 34 A fancy angular unit : the “hour” 1 turn = 360o = 24 hours 1 24 turn = 15o = 1 hour Format for angles expressed in hours, minutes and seconds: 5h 02m 01s Format for angles expressed in degrees, minutes and seconds: 75° 30’ 15’’ ¼ turn = 90o = 6 hours ½ turn = 180o = 12 hours ¾ turn = 270o = 18 hours 05/05/2017 C2PU-Team, Observatoire de Nice Phonetic disambiguation: • Say “fifteen arc-seconds” (quinze seconds d’arc) for 15’’ or “thirty arc-minutes” (trente minutes d’arc) for 30’ • Say “one time-second” (une seconde d’heure) for 01s or “two time-minutes” (deux minutes d’heure) for 02m 35 Ecliptic North Ecliptic coordinates e Sun • Origin: Sun center (heliocentric) or Solar System barycenter (barycentric) or other . • Fundamental plane: Ecliptic plane • Polar axis: Ecliptic North • Zero direction: vernal direction • le : ecliptic longitude (in degrees) • e: ecliptic latitude (in degrees) • r : heliocentric or barycentric distance le Ecliptic plane 05/05/2017 several variants depending on which direction is chosen… J2000 coordinates EOD coordinates C2PU-Team, Observatoire de Nice 36 North pole Equatorial coordinates Sun • Origin: Earth center (geocentric) or observatory position (topocentric) or other . • Fundamental plane: Equatorial plane • Polar axis: Geographic North pole • Zero direction: vernal direction • : right ascension (in hours !) • : declination (in degrees) • r : geocentric or topocentric distance Equatorial plane 05/05/2017 several variants depending on which and polar directions are chosen… J2000 coordinates EOD coordinates C2PU-Team, Observatoire de Nice 37 North pole Mount coordinates Sun • Origin: observatory position (topocentric). • Fundamental plane: Equatorial plane • Polar axis: Geographic North pole • Zero direction: Local meridian • H : hour angle (in hours !) • : declination (in degrees) • r : topocentric distance H Equatorial plane These are the natural coordinates for a telescope equatorial mount, delivered by its angular encoders !!! Beware ! H angle defined from star meridian to local meridian ! 05/05/2017 C2PU-Team, Observatoire de Nice 38 Equatorial vs Mount coordinates North pole Earth’s rotation Obs. Star Ts : True Local Sidereal “Time” = the angle of rotation of the Earth : Right ascension of the star H : Hour angle of the star H = Ts - Equatorial plane H Ts 39 Equatorial vs Mount coordinates Star Earth’s rotation H Obs. Ts H = Ts - vernal direction (fixed, more or less) North pole Ts : True Local Sidereal “Time” = the angle of rotation of the Earth : Right ascension of the star H : Hour angle of the star 05/05/2017 C2PU-Team, Observatoire de Nice 40 Equatorial vs Mount coordinates H(t) = Ts(t) - Thus, time-dependent (stars rise and set) Constant (more or less) Time-dependent (rotation of the Earth) Ts : True Local Sidereal “Time” = the angle of rotation of the Earth Approximately linear with time: 1 turn in 23h 56m 04.09s (sidereal day) 05/05/2017 C2PU-Team, Observatoire de Nice 41 Zenith Horizontal coordinates East h Sun • • • • • • • Origin: observatory (topocentric). Fundamental plane: Equatorial plane Polar axis: Geographic North pole Zero direction: Local meridian a : azimuth (in degrees) h : elevation (in degrees) r : topocentric distance West a Horizontal plane Convention: North: a = 0° East: a = 90° South: a = 180° West: a = 270° Beware ! a angle defined from star vertical plane to local North ! 05/05/2017 C2PU-Team, Observatoire de Nice 42 What is a “good” reference system ? • Fundamental plane must be steady w.r.t. distant celestial objects (quasars) • Zero direction must be steady w.r.t. distant celestial objects (quasars) • Origin must have constant velocity w.r.t. distant celestial objects (quasars) EXAMPLE: the “J2000” coordinates • Fundamental plane: mean (nutation corrected) equator at J2000* • Zero direction: mean (nutation corrected) vernal direction at J2000* • Origin: barycenter of Solar System An improved version thereof (ICRS system) is used in astronomical catalogs and planets ephemeris computation softwares/servers. (*) J2000 = 01/01/2000 12:00 UTC 05/05/2017 C2PU-Team, Observatoire de Nice 43 What is a “handy” reference system ? Must be directly connected to your telescope EXAMPLE: The topocentric mount coordinates • Fundamental plane: true Earth’s equator • Zero direction: meridian (south) direction • Origin: your observatory The two angles in this reference system are those given by the telescope’s angular encoders 05/05/2017 C2PU-Team, Observatoire de Nice 44 And the winner is : BOTH ! • Catalogs or ephemeris servers give target’s J2000 coordinates (actually, ICRS coordinates) at a reference date • Your telescope needs mount coordinates conversions are needed between ICRS coordinates and mount coordinates .... 05/05/2017 C2PU-Team, Observatoire de Nice 45 Conversion flowchart Get ICRS coordinates at reference date (J2000) Correct for target’s proper motion (compute ICRS coordinates at observation date) Change from ICRS to mount coordinates (correct for precession, nutation, parallax, Earth’s rotation) Subtract delay from observation date Compute target-telescope distance and the associated delay “distance/C0” Correct for Bradley effect Correct for atmospheric refraction Send to telescope 05/05/2017 C2PU-Team, Observatoire de Nice 46 Do we need to care ? NO ! our software does it for you ! 05/05/2017 C2PU-Team, Observatoire de Nice 47 Time coordinates What time is it ? • Several ways to DEFINE the current date/time (time scales) • • • • • • • • • • • • • 05/05/2017 True local solar time Mean local solar time Greenwich Mean (solar) Time (GMT UT0, UT1) Legal Time (LT) Atomic International Time (AIT) Universal Time Coordinate (UTC) LT = UTC Ephemeris Time (ET) Terrestrial Time (TT) Terrestrial Dynamic Time (TDT) Barycentric Dynamic Time (BDT) GPS time LORAN time … C2PU-Team, Observatoire de Nice + 1 hour ( + 1 hour) Time zone DST summer time 49 What time is it ? • Several ways to WRITE the current date/time (time formats) • • • • Common date-time formats Julian date (JD) Modified Julian Date (MJD) … • Common date-time formats: • French formats : example: 14/01/2014 12h 21m 12,2s (TL or UTC) variants: 14-01-2014 12:21:12,2 (TL or UTC) 2014-01-14 12:21:12,2 (TL or UTC) 14 janv. 2014 12:21:12,2 (TL or UTC) • British formats : example: 01/14/2014 12h 21m 12,2s (LT or UTC) variants: 2014-01-14 12:21:12,2 (LT or UTC) Jan. 14th, 2014 12:21:12,2 (LT or UTC) 05/05/2017 C2PU-Team, Observatoire de Nice 50 What time is it ? • Julian date (JD): • • • • • • • Avoid ambiguities in date formats (DD/MM/AAAA vs MM/DD/AAAA) Ease calculations of time intervals Bypass the “October 1582” problem (Julian vs Gregorian calendars). Uses a single positive number to state both date and time with arbitrary accuracy Julian date = “number of days elapsed since January 1st, 4713 BC, 12h00” Example: January 1st, 2000 @ 12h00 UTC corresponds to JD = 2451545.0000 d Example: August 2nd, 2013 @ 16h 41m 49.0s UTC corresponds to JD = 2456507.19571 d • Modified Julian Date (MJD): • • • 05/05/2017 Avoids too large numbers By definition: MJD = JD – 2450000.5 d Example: August 2nd, 2013 @ 16h 41m 49.0s UTC corresponds to MJD = 6506.69571 d C2PU-Team, Observatoire de Nice 51 Do we need to care ? NO ! our software does it for you ! 05/05/2017 C2PU-Team, Observatoire de Nice 52 Magnitudes Star brightness • Ancient Greek astronomers (Hipparchus, Ptolemy) used to divide all naked-eyes visible stars in 6 brightness categories called “Magnitudes”. • This scale was reversed: Magnitude 1 corresponded to the brightest stars; Magnitude 6 corresponded to the faintest stars visible with naked eyes. • This scale was logarithmic: stars of magnitude “n” were “seen” twice as bright as stars of magnitude “n+1”. • In 1856, Norman Robert Pogson proposed a quantitative relationship: M = -2.5 Log10( I / I0 ) where I is the brightness of the star under consideration, and I0 is the brightness of a reference star (Vega), considered as a 0 magnitude star. • Magnitudes may be negative. 05/05/2017 C2PU-Team, Observatoire de Nice 54 Color-dependence • Stars have different surface temperatures, thus different “colors”. Hence, the brightness of a star depends on the observation wavelength • Several “Photometric systems” exist, each one defining a set of wavelength bands (filters) through which observations are done. • Some standard bands: U, B, V, R, I (Ultraviolet, Blue, Visible, Red, Infrared). • Magnitude measured through V band filter is called “V magnitude” and denoted “MV”. The same holds for U, B, R, and I. • If the whole spectrum is taken into account, the magnitude is said “bolometric”. 05/05/2017 C2PU-Team, Observatoire de Nice 55 Magnitudes of brightest stars Name V Magnitude Name V Magnitude Sirius -1.46 Achernar 0.50 Canopus -0.72 Adar 0.60 Rigil Kentaurus -0.27 Altair 0.77 Arcturus -0.04 Aldebaran 0.85 Vega 0.00 Spica 1.04 Capella 0.08 Antares 1.09 Rigel 0.12 Pollux 1.15 Procyon 0.34 Fomalhaut 1.16 Betelgeuse 0.42 Deneb 1.25 05/05/2017 C2PU-Team, Observatoire de Nice 56 For more informations Lecture notes on general astronomy: https://www-n.oca.eu/rivet/00Francais/IntroAstro.html 05/05/2017 C2PU-Team, Observatoire de Nice 57