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This exam covers the qualitative and quantitative understanding of telescopes, including light-collecting area, angular resolution, and the properties of refracting and reflecting telescopes. It also includes topics on the functions of telescopes in imaging, spectroscopy, and timing. Prepare with the homework and quiz solutions. Don't forget to bring your calculator and an equation sheet!
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Exam #1 First midterm on Thursday, September 27 (in class) ~ 40% multiple choice (test your qualitative understanding of topics covered + simple math problems) ~ 30% short answer (1-2 sentences typically), mostly qualitative ~ 30% quantitative problems (like the homework) Material from the book NOT covered in class will NOT be on the exam. You will have all homework/quiz solutions by Tuesday.
Exam #1 Exam will cover material through Chapter 6 (Telescopes). Closed book, but you may bring one sheet of paper with equations on it (equations only – no concepts). Don’t forget to bring your calculators! All constants/other relevant numbers will be provided to you. We will play AstroJeopardy on Tuesday. You will be divided into teams, with the winning team earning some extra credit for the exam.
This Week in Astronomy First Light From A New Planet Hunter! TESS (Transiting Exoplanet Survey Satellite) was launched April 18, 2018. Will cover 400x larger swath of sky than its predecessor, Kepler. Expected to find at least 20,000 new planets in our Galactic neighborhood, including 500—1000 Earth-sized planets.
Important Qualities of Telescopes • Light-collecting area: Telescopes with larger collecting area collect more light in less time • Angular resolution: Larger telescopes can show images with finer detail Magnification is useless without these two qualities. The two most important properties of a telescope!
Light-collecting Area: Bigger is better • A telescope’s diameter (D) gives its light-collecting area: Area= * (D/2)2 • The largest telescopes today have 10+ meter diameters.
Angular Resolution • Objects cannot be focused toinfinite precision – there is a theoretical limit based on the size of the telescope • Diffraction limit to resolution due to interference of light waves within telescope • Larger telescopes have smaller diffraction limits • Cannot resolve two objects separated by less than the diffraction limit Diffraction limit ~ 2.5 x 105 (/D) arcsec = wavelength of light D = diameter of telescope lens/mirror
Angular Resolution: Smaller Is Better Effect of Mirror Size on Angular Resolution
Example What is the diffraction limit of a 1-meter telescope for red light? Red light = 6000 Angstroms = 6 x 10-5 cm 1 meter = 100 cm Diffraction limit = 2.5 x 105 (6 x 10-5 cm / 100 cm) arcsec = 0.15 arcsec Theoretically smallest angle a telescope can resolve (set by the nature of light) – can express in radians too Diffraction limit ~ 1.2 (/D) radians
U-band image (near ultraviolet) 3900 Angstroms I-Band image (near-infrared) 8100 Angstroms Angular resolution wavelength dependence is obvious (Res. /D)
Comparison of Optic Systems Collecting Diffraction Equivalent area limit to Human Eye 2 x 10-4 m2 ~1’ a quarter viewed from ~70 m 7x35 4 x 10-3 m2 3.5” a quarter viewed Binoculars from ~1 km Hubble 2.4-meter 18 m2 0.05” reading textbook Telescope at 0.8 km 10-meter 310 m2 0.01” * reading textbook Telescope at 3.5 km Moon diameter: 30’ Jupiter diameter: 35” Pluto diameter: 0.1” *theoretical resolution
Two basic telescope designs • Refracting telescope: Focuses light with lenses • Reflecting telescope: Focuses light with mirrors
Refracting Telescope Yerkes Observatory 40-inch refractor Quality lenses are hard to make Refracting telescopes have long focal lengths Lenses cause chromatic aberration – different colors are focused at slightly different distances
Chromatic Aberration Blue light and red light focus at slightly different focal lengths.
Focusing light by Reflection • Reflection can focus parallel light rays • A mirror replaces the lens • Focus is located back along path of light 8-m Gemini-N Telescope
Reflecting Telescope • Basic design invented by Isaac Newton • Reflecting telescopes can have much larger diameters • Most astronomical telescopes are reflectors 8-meter Gemini-N
Refracting Versus Reflecting Telescopes RefractingReflecting Lens must be mounted at Can be supported from top of tube – very heavy the bottom Glass must be perfect and Only the mirrored surface error-free throughout needs to be perfect Suffers from chromatic No chromatic aberration aberration Requires a long path length Can be more compact
Magellan Observatory, Las Campanas, Chile Twin 6.5 meter telescopes
Mirrors in Reflecting Telescopes Very large mirrors are broken into many segments. Twin Keck 10m telescopes on Mauna Kea, Hawaii Segmented 10-meter mirror
Telescope (instrument) functions • Imaging: Taking pictures, deriving fluxes luminosity, colors, structure • Spectroscopy: Dispersing light into spectra • Timing:Measuring variations with time
Filters pick out a wavelength region of light. Filters can be broad (~1000-2000 Angstroms) or very narrow to only allow a small wavelength range (i.e., Hα)
Diffraction grating disperses light into spectrum Spectroscopy A spectrograph disperses light by wavelength before it hits detector Focal plane • The spectrograph reflects light off a grating: a finely ruled, smooth surface (~500 ridges per millimeter - separation of ridges comparable to wavelength of light). • Light interferes with itself and disperses into colors. • This spectrum is recorded by a charge coupled device (CCD). Slit isolates light from only one object Detector records spectrum
Spectral Resolution The minimumwavelength separationthat the spectrograph can distinguish Wider slit/fewer grooves in grating: worse spectral resolution, wider bandpass coverage Narrower slit/more grooves in grating: better spectral resolution, narrower bandpass coverage
Timing A light curve shows how intensity changes over time Light curve of the variable star Mira An example where a small telescope could perform important science.
SARA: The Southeastern Association for Research inAstronomy 0.96-meter telescope in Arizona 1.00meter telescope in La Palma, Canary Islands, Spain 0.6-meter telescope in Chile All telescopes remotely-operated.
How does Earth’s atmosphere affect ground-based observations? The best ground-based sites for astronomical observing are • Calm:not too windy • High:less atmosphere to see through • Dark:minimal background light • Dry:clear weather and low H2O
Calm, High, Dark, Dry The best optical observing sites are atop desert mountains Magellan Observatory, Chile Mauna Kea, Hawaii
Twinkling and Turbulence Turbulence in Earth’s atmosphere distorts light paths: stars appear totwinkle. Hubble Space Telescope ground-based telescope
Turbulence • Even under the best observing conditions, turbulence limits the effective angular separation of a telescope to ~0.4” or worse (called the “seeing”). • This is MUCH larger than the theoretical limit of a large ground-based telescope (0.4” vs. 0.01” for a 10-meter telescope). • Can be combated with modern-day techniques such as adaptive optics.
Atmospheric Turbulence Also Messes Up Images (on Earth) point source! 0.01 sec integration
Adaptive Optics By focusing on a laser point in the sky, turbulence can be at least partially estimated and corrected for Rapidly adjusting shapeof telescope’s segmented mirror helps compensate for turbulence
Adaptive Optics Ground-based resolution beginning to rival Hubble Space Telescope Without adaptive optics With adaptive optics
Adaptive Optics Jupiter’s moon Io observed with the Keck telescope without adaptive optics with adaptive optics
