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ASTR 2020 Space Astronomy Week 3:Tuesday Review: EM waves, Structure of matter Announcements: Observing at SBO tonight Review of Electro-magnetic (EM) Waves: [wavelength][frequency = [speed of light] Energy of Photons (particles of light) Momentum: ln=c E(photon) = hn = hc / l P=h/l Blackbody radiation: lpeak = 0.29 / T(K) Luminosity of a sphere, Radius R: L = 4 p R2 s T4 s = 5.67 x 10-5 (Stephan-Boltzmann constant) Flux at distance D: F = L / 4 p D2 Doppler Effect: f / f = l / l = V / c Diffraction: Resolution of a telescope with diameter D: qradian = l / D Telescopes: refraction (refractors) vs. reflectors Spectra: Interaction of light (EM waves) with matter Spectrographs Detection of EM waves: At short l, treat as particles At long l, treat as waves Observing in the Radio i.e. The NRAO GBT (D ~ 100 m) qradian = l / D at 21 cm = 1.420 GHz l 21cm q= » = 7.2' D 10000cm at 0.3 cm = 100 GHz l 0.3cm q= » = 0.10' = 6.2' ' D 10000cm Planetary Radar imaging: Doppler shift + time delay = 2D map Beating the diffraction limit Redshift Blueshift Radar Pulse Early echo Late echo UV Venus Radar Radar Venus Radar Introduction to Geometric optics: Fermat’s Principle: Variation in photon time-of-flight is minimum (Optical Path) = (time-of-flight)= 0 Snell’s law of Refraction: V = c / n n = refractive index Focal-Length: 1 / f = 1 / Dobject + 1 / Dimage f/ = f / D Aberrations: Chromatic, Spherical, Coma, Astigmatism, Field Curvature, Distortion Properties of simple optical systems: Microscopes Telescopes: refractor vs. reflector Newtonian, Cassegrain, Gregorian, Catadioptric Schmidt, Schmidt-Cassegrain, Maksutov, …. Magnification, resolution, light gathering power https://en.wikipedia.org/wiki/Optical_telescope Chabot 8” refractor European Southern Observatory VISTA 4-meter reflector Refraction: Snell’s Law: n1 sin(2) = n2 sin(1) 1 n1 = refractive index in region 1 n1 n2 n2 = refractive index in region 2 n = c / v = lvacuum / lmedium 2 l1 1 n1 sin 1 = n2 sin 2 2 l2 Refraction: Magnification: Telescope types Functions of a Telescope: - Gather light (as much as possible) - Resolve small angles 7 detail - If used visually, to magnify Spectrographs Focal Plane collimator camera detector Dispersing element Slit Telescope Spectrograph Spectra of Galaxies: (Calcium H+K lines) Spectrum of Comparison lamp (He + Ne + Ar) Spectrum of galaxy Spectral lines: Specific wavelengths & Frequencies Emitted or absorbed by atoms & molecules. Spectral lines: Specific wavelengths & Frequencies Emitted or absorbed by atoms & molecules. Spectral lines: Spectra of elements (in emission) at visual wavelengths Absorption Features (lines, bands): Star emits continuum - light at energy equal to an atomic transition is absorbed - that light is then reemitted in a random direction the observer sees all the wavelengths except those at the atomic transition energy an absorption spectrum The Solar Spectrum (from Kitt Peak’s McMath-Pierce Solar Telescope): 2960 – 8,000 Angstroms (.29 to 0.8 mm) Spectra of Stars Spectra of Stars Spectra of Stars HerzsprungRussell (HR) Diagram Luminosity vs Temperature L= 4p R2 sT4 s = 5.67x10-5 T(K) ~ 0.29 / lpeak Why do atoms only emit certain frequencies & wavelengths (spectral lines)? Wave nature of matter: momentum: p = mV = h/l E = hf = hn l = h/p Atoms: ~10-8 cm Nuclei: ~ 10-13 cm Niels Bohr (1885 - 1962, Denmark) - early quantum physics, “planetary” model of the atom E = hn = hc/l p = E/c = h/l x p ~ h => Heisenberg Uncertainty x = l ~ h / mV ASTR 2020 Space Astronomy Week 3: Thursday Review: energy levels, H Structure of matter Gravity, energy, momentum Orbits, escape speed Homework #2 posted on D2L Hydrogen spectrum: g b a b Balmer n = R [ 1/nl2 – 1 /nu2] R = 3.288 x 1015 Hz Lyman 13.6 eV a Spectrum of hydrogen 13.6 eV = 912 Angstroms 10-18 Lyman lines n-3 Balmer lines Wavelength (1 / photon energy) Ultraviolet (UV) Visual n 1 2 3 4 Astronomers Periodic Table Electron “waves” Copper-oxide lattice Outline: Gravity and Orbits - Laws of Motion (Newton’s mechanics) position, velocity, acceleration mass, inertia, force, centrifugal force - The inverse square law: Newton’s law of gravity falling apples, and the moon - Escape speed velocity needed to escape - Orbits balance between gravity and centrifugal force - Kepler’s Laws of planetary motions Motion - Velocity (or speed): V = [change in position] / [ time interval] Example: Car moving. Covers 100 meters in 60 seconds 100 m = 104 cm, V = 104 / 60 = 166 cm/sec = 1.67 m/sec = 65 ft/sec = 44.7 mi/hr - Acceleration: a = [change in velocity] / [time interval] Example: Drop a rock in Earth’s gravity …. Speed increases by 980 cm/sec every second (until air resistance sets in) a = 980 cm s-2 (= 32 ft sec-2) Mass, inertia, force, centrifugal force - Mass, M: a measure of the amount of material Example: Mo = Mass of the Sun = 2 x 1033 grams Mearth = Mass of the Earth = 6 x 1027 grams Weight = the downward force a given mass exerts in the Earth’s gravitational field: Note: The acceleration of gravity at the Earth’s surface is a = 980 cm s-2 g = 980 cm s-2 This is used so often we call it little ‘g’ acceleration at Earth’s surface - Force = [mass] x [acceleration] Weight = m g F = ma Forces - Acceleration in presence of a force, F a=F/m - The four (known) fundamental Forces: - Gravity (planets, stars, galaxies, …) FG = - GmM / r2 - Electro-magnetism (atoms, molecules) FEM = - q1q2 / r2 + q1 VxB / c Isaac Newton - Strong nuclear force (binds atomic nuclei) - Weak nuclear force (radioactive decay, binds electrons to protons) Gravity Falling objects on Earth most motions in astronomy F = G Mm / r2 inverse square law! Force pulls together objects with MASS (mass has TWO roles - inertia AND creating gravity) Force is weaker when the distance between them is greater Force is stronger when the distance between them is smaller This formulation of FORCE predicts motions of planets accurately! Mass, inertia, force, centrifugal force - Inertia, M: a measure of the resistance to a force In a vacuum (space) object in motion stay in motion those at rest, stay at rest (unless there is a force). - Centrifugal Force - actually a consequence of inertia When tethered to a string, a rock is forced by the string to move in a circle … but inertia wants to make it move in a straight line. The resulting force on the string is: Fcent = [mass] x [ Velocity2] / [ radius ] Fcent = mV2 / r Example: m = 100 g, radius r = 100 cm, velocity = 100 cm/sec F = 100 1002 / 100 = 104 (g cm sec-2) Orbits: Balance of opposing forces Gravity <=> Centrifugal force G M m / R2 = m V2orbit / R Solve for Vorbit: M m Vorbit = (GM / R)1/2 Newton’s constant: Vorbit G = 6.67 x 10-8 c.g.s. Reaching Orbit: Vorbit = {GM / (R+H)}1/2 Mearth ~ 5.97 x 1027 g G = 6.67 x 10-8 c.g.s. R = 6,371 km H = 300 km Vorbit = {[6.67 x 10-8][5.97 x 1027 g]/[6.371e8 +3e7]}1/2 = 7.73 x 105 cm/sec = 7.73 km/s Rockets: Tsiolkovsky’s equn. V = Vejecta ln (Minitial/Mfinal) M Minitial = Mfinal exp (Vorbit / Vejecta) ~ Mfinal exp (7.7/3) ~ 13 Mfinal Vorbit De Laval Nozzle: Hydrazine: N2H4 Vejecta ~ 1.7 - 2.9 km/s Liquid: O2 + H2 Vejecta ~ 2.9 - 4.5 km/s Solid: Vejecta ~ 2.1 - 3.2 km/s Echo (1960 - 1964) Telstar-1 (1962) Relay 1 Andover, Main Crawford Hill A. Penzias R. W. Wilson signal Mixers LO mixed signal 0 Hz original signal frequency Mixers signal The negative frequencies in the difference appear the same as a positive frequency. LO mixed signal 0 Hz original signal frequency To avoid this, we can use “Single Sideband Mixers” (SSBs) which eliminate the negative frequency components. Amplification Amplification is in units of deciBells (dB) logarithmic scale 3 dB = x2 5 dB = x3 10 dB = x10 20 dB = x100 30 dB = x1000 V1 dB = 10 log10 ( ) V2