ay16-CDeMeo

  #Planck Curve with maximum wavelengths marked. import  numpy  as  np import  matplotlib.pyplot  as  plt from  astropy.modeling.models  import  BlackBody from  astropy  import  units  as  u from  astropy.visualization  import  quantity_support bb = BlackBody(temperature= 300 *u.K) bb2= BlackBody(temperature= 1000 *u.K) bb3= BlackBody(temperature= 3000 *u.K) bb4= BlackBody(temperature= 6000 *u.K) bb5= BlackBody(temperature= 10000 *u.K) wav = np.arange( 100 ,  1100000 ) * u.nm flux = bb(wav) flux2 = bb2(wav) flux3 = bb3(wav) flux4 = bb4(wav) flux5 = bb5(wav) with  quantity_support():     plt.figure()     plt.semilogx(wav, flux)     plt.semilogx(wav, flux2)     plt.semilogx(wav,...

#CoLab: Homework_3.ipynb - Colaboratory (google.com) i mport  numpy  as  np import  matplotlib.pyplot  as  plt T = np.array([ 300 ,  1000 ,  3000 ,  6000 ,  10000 ]) # Physical constants in SI units: Planck's constant (J.s), # the speed of light (m.s-1), Boltzmann's constant (J.K-1) h, c, kB =  6.62606957e-34 ,  299792458 ,  1.3806488e-23 # Sun temperature, K T1 =  300 T2= 1000 T3=  3000 T4=  6000 T5= 10000 lambda_min =   1     # nm lambda_max =  10000     # nm n =  3000 wv = np.linspace(lambda_min, lambda_max, n) # Python code to demonstrate the working of # log(a,Base)   # Planck curve as a function of wavelengt...

 Worksheet 3.1 Mike Cushing discovered a new type of astrophysical object called a Y dwarf. Y dwarfs are a subclass of brown dwarf. Consider a Y dwarf, with a temperature of about 350 K and a radius of roughly the size of Jupiter's radius, residing near a sun like star. Brown dwarfs have a large mass but not large enough to be a star. They are mainly composed of hydrogen gas and have no internal energy source that stars have. They emit very little visible light so they are hard to detect, even in the Infared. (Info from  NASA - Brown Dwarf Detectives ) a) At what wavelength $\lambda_{max}$ should you observe to have the best chance of detecting the Y  dwarf? $\lambda_{max}$= $\frac {hc}{4kT}$ $\lambda_{max}$ = $\frac {0.29 cm K}{350K}$ You should observe a wavelength at $ 8.3 \times 10^{-4} cm$ for the best chance of detecting the Y Dwarf b) As measured at $\lambda_{max}$ how many photons per second, per $cm^2$ emitted from a Y dwarf at a distance of 30 lightyears would r...

 Worksheet 3 Question 2 A blackbody is a hypothetical object that absorbs radiation and does not reflect anything. The absorbed radiation becomes standing waves which bounce back and forth inside the blackbody. The absorbed radiation causes the blackbody to reach an equilibrium temperature. A true blackbody does not exist, but a spherical cow can be approximated as a blackbody and a better approximation of a blackbody is the entire universe (Figure 1). Stars and other objects can also be approximated as blackbodies and their intensity and wavelength of light emitted can be plotted on the blackbody curve to learn information such as temperature and wavelength using Wein's displacement Law and temperature and energy using Stefens Law. The blackbody curve is represented by Raleigh Jean's Law, but this law does not line up with experimental data for short wavelengths of light which is known as the ultraviolet catastrophe (Figure 2). Max Planck had the idea that inside the blackbody...

Suppose the galaxy has two types of stars, Q-type stars with twice the Sun's luminosity, and R-type stars with a third the Sun's luminosity. R-type stars are four times as numerous in the galaxy as Q-type stars, and both types are uniformly distributed in space. Note A magnitude limited survey is a survey where any star is accepted as long it is not too faint (magnitude has to be below a certain number) A volume limited survey is a survey where any star is accepted as long as it is within a certain distance and is bright enough to be picked up with the instruments you are using (max distance is used) A. If you are conducting a magnitude-limited survey of stars, compare the number of Q-type stars you'll observe to the number of R-type stars. Defining Some Variables $L_o$ = the suns luminosity $L_Q$= $2L_o$ = luminosity of Q type stars $L_R$= $\frac{L_o}{3}$ = luminosity of Q type stars $n_Q$= number of Q type stars $n_R$= number of R type stars $m_{max}$= faintest observable...

 Worksheet 2 Question 4 a) Ignoring the tilt of the Earth and clouds, how does the flux received from the Sun on the surface of the Earth vary with latitude? (Flux cares about direction of light with respect to the surface at which it is measured). Flux = $ \frac {Energy}{Area \times time}$ The sun is far enough away from the earth that we can assume that the light from the sun is traveling and hitting the Earth in the same direction (parallel lines in picture) Thus, the rays of sunlight will have the same amount of energy and time, but will be hitting different Areas of earth. The smallest area will be at the equator and the largest area will be right before the north and south poles. Since Flux = $ \frac {Energy}{Area \times time}$ , as area increases, flux decreases.  Therefore, the greatest amount of flux will be received at the equator and as latitude increases, flux will decrease. The area that the sunlight hits can be described as A= $\frac{A_{eq}}{\sin \theta}$ b) Fact...

 Worksheet 2, Question 1 When the back of your hand is about 8cm away from a 100-Watt incandescent light bulb, the bulb feels like the Sun on a sunny spring day.  The Earth-Sun distance is 1 AU or $a = 1.5 \times 10^{13}$ cm. Estimate the luminosity of the Sun ($L_o$) in units of ergs/second (1 Watt is $10^7$ ergs/sec) Since the bulb feels like the sun on a sunny spring day, we can assume that the Flux of the sun ($F_o$) is equal to the flux of the bulb ($F_b$). $F_o=F_b$ Flux = $\frac {Energy} {area \times time}$ Flux of the bulb is equal to power of the bulb ($P_b$) over area of the bulb ($A_b$) and Flux of the sun is equal to luminosity (power) of the sun ($L_o$) over area of the sun ($A_o$). $\frac{P_b}{A_b}$ = $\frac{L_o}{A_o}$ $ A_b = 4 \pi x^2$ $A_o= 4 \pi a^2$ $\frac{P_b}{4 \pi x^2}$ = $\frac{L_o}{4 \pi a^2}$ We can now solve for the luminosity of the sun! (x and a are defined in the photo) $L_o$ = $\frac {P_ba^2}{x^2}$ Plug in our values $L_o$ = $\frac  {10^...