Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Stars !Common Name Scientific Name Distance (light years) Apparent Magnitude Absolute Magnitude Spectral TypeSun - -26.72 4.8 G2VProxima Centauri V645 Cen 4.2 11.05 (var.) 15.5 M5.5VcRigil Kentaurus Alpha Cen A 4.3 -0.01 4.4 G2VAlpha Cen B 4.3 1.33 5.7 K1VBarnard's Star 6.0 9.54 13.2 M3.8VWolf 359 CN Leo 7.7 13.53 (var.) 16.7 M5.8VcBD +36 2147 8.2 7.50 10.5 M2.1VcLuyten 726-8A UV Cet A 8.4 12.52 (var.) 15.5 M5.6VcLuyten 726-8B UV Cet B 8.4 13.02 (var.) 16.0 M5.6VcSirius A Alpha CMa A 8.6 -1.46 1.4 A1VmSirius B Alpha CMa B 8.6 8.3 11.2 DARoss 154 9.4 10.45 13.1 M3.6VcRoss 248 10.4 12.29 14.8 M4.9VcEpsilon Eri 10.8 3.73 6.1 K2VcRoss 128 10.9 11.10 13.5 M4.1V61 Cyg A (V1803 Cyg) 11.1 5.2 (var.) 7.6 K3.5Vc61 Cyg B 11.1 6.03 8.4 K4.7VcEpsilon Ind 11.2 4.68 7.0 K3VcBD +43 44 A 11.2 8.08 10.4 M1.3VcBD +43 44 B 11.2 11.06 13.4 M3.8VcLuyten 789-6 11.2 12.18 14.5Procyon A Alpha CMi A 11.4 0.38 2.6 F5IV-VProcyon B Alpha CMi B 11.4 10.7 13.0 DFBD +59 1915 A 11.6 8.90 11.2 M3.0VBD +59 1915 B 11.6 9.69 11.9 M3.5VCoD -36 15693 11.7 7.35 9.6 M1.3VcMeasurement of Distances to Nearby StarsParallax RevisitedRParallax AngledTan Θ =RdΘMeasurement of Distances to Nearby StarsParallax RevisitedRParallax AngledFor small angles (valid for stellar measurements):Tan Θ ≈ Θ where Θ is measured in radiansΘTan Θ =RdMeasurement of Distances to Nearby StarsParallax RevisitedRParallax AngledΘ (radians) = RdΘFor astronomical measurements R and d are measured in A.U.Measurement of Distances to Nearby StarsParallax RevisitedΘ (radians) R (in A.U.)d (in A.U.) =A convenient variation: 1 radian = 206265 arc secondsΘ (radians) R (in A.U.)d (in A.U.) =Θ (arc seconds) R (in A.U.)=206265Θ (arc seconds) R (in A.U.)206265=Measurement of Distances to Nearby StarsParallax RevisitedOne parsec is defined to be 206265 A.U. AND, if you use the radius of the earth orbit for R (earth based measurements, R = 1 a.u., thenΘ (arc seconds) 1d (in parsecs) =Θ (arc seconds) 1d (a.u.) 206265 au/pc=Measurement of Speeds of Nearby StarsRadial Speed – Doppler Shift RevisitedBlue Shift toward EarthRed Shift away from EarthDoppler shifts are caused by line of sight velocities (called radial velocity) of the source.Sources moving away from the earth are red shifter.Sources moving toward the earth are blue shifted.Measurement of Speeds of Nearby StarsRadial Speed – Doppler Shift RevisitedAstrophysics and CosmologyLonger , lower fShorter , higher fIn generalApparent WavelengthTrue Wavelength Apparent FrequencyTrue Frequency Velocity of SourceWave Speed= =1 +Note: If the source and detector are moving apart, the Velocity of the Source is POSITIVE. If the source and detector are toward one another, the Velocity of the Source is NEGATIVE. Measurement of Speeds of Nearby StarsRadial Speed – Doppler Shift RevisitedMeasurement of Speeds of Nearby StarsTransverse (sideways) SpeedsMotion of Barnards Star captured: left 1997 (Jack Schmidling), right 1950 (POSS) Proper motion is defined to be the transverse motion of the star across the skyMeasurement of Speeds of Nearby StarsTransverse (sideways) SpeedsΘΘ (radians) = wdMeasurement made same time during the yearwdd x Θ (radians) w =If the time interval between measurements is measured, then v = w/ tMeasurement of Speeds of Nearby Starsvt vR Pythagorian Theorem: v2 = vR2 + vt2 vLuminosity (brightness) of a StarLuminosity is the amount of energy per second (Watts) emitted by the starRecall:The luminosity of the sun is about 4 x 1026 WAbsolute Brightness: The luminosity per square meter emitted by the star at it’s surface. This is an intrinsic property of the star.Apparent Brightness: The power per square meter as measured at the location of the earth.Luminosity (brightness) of a StarNote:Absolute Brightness =Power (or Luminosity)Surface Area of starAlso Note: Because of conservation of energy, the energy per second radiated through the area of a sphere of any radius must be a constant. ThereforeApparent Brightness =Power (or Luminosity)Surface Area of sphere of radius equal to the distance between the star and the earthLuminosity (brightness) of a StarApparent Brightness is proportional to Power (or Luminosity)d2 Apparent brightness can be measured at the earth with instruments. d is measured using parallax. These pieces of information can be used to measure the luminosity of the star.Photometer – An instrument which measure the brightness of an objectWill measure the TOTAL brightness of an object, which might be difficult to interpret. However, when combined with filters, can be used to measure the amount of light produced over a narrow range of frequencies. This can be compared with standard Blackbody radiation curves to determine the temperature of the objectPhotometry RevisitedPhotometer – An instrument which measure the brightness of an objectWill measure the TOTAL brightness of an object, which might be difficult to interpret. However, when combined with filters, can be used to measure the amount of light produced over a narrow range of frequencies. This can be compared with standard Blackbody radiation curves to determine the temperature of the objectPhotometryXIntensityWavelengthXXPhotometer – An instrument which measure the brightness of an objectWill measure the TOTAL brightness of an object, which might be difficult to interpret. However, when combined with filters, can be used to measure the amount of light produced over a narrow range of frequencies. This can be compared with standard Blackbody radiation curves to determine the temperature of the objectPhotometryXIntensityWavelengthXXPhotometer – An instrument which measure the brightness of an objectWill measure the TOTAL brightness of an object, which might be difficult to interpret. However, when combined with filters, can be used to measure the amount of light produced over a narrow range of frequencies. This can be compared with standard Blackbody radiation curves to determine the temperature of the objectPhotometryXIntensityWavelengthTemperature of object is 7000 KXXTemperature of a StarPhotometry RevisitedDifferent typical filters used:B (blue) Filter: 380 – 480 nmV
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