# Lecture 13. Doppler Effect

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1 Lecture 13 Telescopes and Optics Doppler Effect Reprise Luminosity and Brightness Summary: Light Telescopes: sensitivity Feb 15, 2006 Astro 100 Lecture 13 1 Doppler Effect Yet another thing you can get from spectra! Doppler Effect: The wavelength of light received from an object is different from that which was emitted if there is motion between emitter and observer. Quantitatively: Wavelength received = Wavelength emitted ( 1 + (radial speed)/c ) ("radial speed" is the motion along a line connecting emitter and observer; it is positive if they are receding, and negative if approaching). If you know the emitted wavelength and measure the observed, you can deduce the relative radial speed of the emitter. Feb 15, 2006 Astro 100 Lecture 13 2

2 Doppler Effect Example Suppose Voyager II spacecraft is broadcasting at emitted wavelength = cm, On Earth we now measure received wavelength = cm, then 1 + v r /c = , v r /c = +10-5, v r = +3 km/sec (+ => away from us). (v r is radial speed; we can't deduce its sideways speed, so don't get full velocity) Feb 15, 2006 Astro 100 Lecture 13 3 Doppler Effect in Astronomy Doppler Effect for an absorption or emission line spectrum notice: all wavelengths shifted by same factor: the ratios of the wavelengths are not affected. Wavelengths increased: "red shift"; decreased: "blue shift" identify the presence of a particular element (eg Hydrogen) from the pattern of its lines (eg Balmer lines) Then we look up where each line should be to get the emitted wavelength, measure the received wavelength and deduce the radial speed. Since we can measure wavelengths very accurately, this is a very useful technique for deducing motion without seeing it. Easy to confuse Doppler Effect and Wien's Law: Feb 15, 2006 Astro 100 Lecture 13 4

3 Luminosity and Apparent Brightness The amount of light is described by the total amount of energy it carries - depends on the intrinsic brightness of the source and how far we are from it Luminosity: The amount of light energy/sec emitted by an object (units: Watts). A typical light bulb has a luminosity of 75 Watts. The luminosity of the Sun is 4x10 26 Watts! Apparent Brightness: The amount of light energy/sec crossing a certain area (units: Watts/area). The apparent brightness of the sun at the Earth is 1400 W/m 2. Feb 15, 2006 Astro 100 Lecture 13 5 The Inverse Square Law For an object that radiates light equally in all direction, the apparent brightness at a certain distance is just the luminosity divided by the area of a sphere at that distance: Brightness = Luminosity / (4 πdistance 2 ) Jupiter is 5x farther from the Sun than we are. The apparent brightness of the Sun at Jupiter is 25x less Stellar magnitude is a measure of the apparent brightness (not the luminosity) at the Earth in visible wavelengths. If we know the luminosity and measure the apparent brightness, we can deduce the distance: "Standard Candle" Method - will use this a lot Feb 15, 2006 Astro 100 Lecture 13 6

4 Summary: Tricks with Light Blackbody Spectra: Wien's Law => Surface temperature Line Spectra: Pattern of line wavelengths => composition, temperature Line Spectra: Doppler Effect: => line-of sight motion All spectra: Inverse Square Law of Birghtness => Standard Candle method for Distance Feb 15, 2006 Astro 100 Lecture 13 7 Astronomical Hardware To collect astronomical data need: Collect light (Telescope/observatory) Analyze it (Instrument) Record it (Detector) Telescopes. the most important criteria: Sensitivity = (Area of Primary element) (="Light gathering power"; make as large as possible) (Exposure Time) (Good Site) (Efficiency) (Wavelength Dependent) Cost. Minimize length, weight, complexity of pointing. Feb 15, 2006 Astro 100 Lecture 13 8

5 Focusing The usual method of collecting large amounts of light: bring to focus (focal length: distance from primary element to focus). In visible, can be done in two ways: Refractor: lens (visible, near IR only; eg binoculars) Reflector: curved mirror (modern large telescopes) Advantages Disadvantages Refractor simple if small chromatic aberration, length, absorption Reflector large, short, all colors obscuration Since sensitivity is proportional to the area of the primary element, supporting and pointing this element while maintaining its optical curve is the most expensive problem Some Reflectors Feb 15, 2006 Astro 100 Lecture 13 9 Doppler Effect Figure 3.18, p109, Arny Feb 15, 2006 Astro 100 Lecture 13 10

6 Yerkes 1m Refractor Figure 4.3, p124, Arny Feb 15, 2006 Astro 100 Lecture Reflectors Figure 4.6, p126, Arny Feb 15, 2006 Astro 100 Lecture 13 12

7 WIYN 3.5m Feb 15, 2006 Astro 100 Lecture Keck 10m Feb 15, 2006 Astro 100 Lecture 13 14

8 SALT 11m Now Spectro grapheye view Computer Model Primary Mirror Feb 15, 2006 Astro 100 Lecture 13 15

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