ay16-CDeMeo

We can use a model of a parcel of air at some distance r above earth's surface to determine different characteristics of the atmosphere including how density changes at different r values, and how gravitational acceleration changes at different r values. We can assume that the earth's atmosphere is comprised of an ideal gas which allows us to use the ideal gas law: $P=n \times k_B \times T$ n is the number density of particles (in $cm^3$) $k= 1.4 \times 10^{-16} erg K^{-1}$ which is the Bolzmann constant.  a) Think of a small cylindrical parcel of gas, with the axis running vertically in the Earth's atmosphere. The parcel sits a distance r from the Earth's center, and the parcel's size is defined by a height $ \delta r $ is much less than r and a circular cross sectional area A. The parcel will feel pressure pushing up from gas below $P_{up} = P(r)$ and down from above $P_{down} = P(r+ \delta r)$ where pressure is expressed as a function of r. Draw a picture to desc...

      Introduction      To measure the distance between the earth and the sun (the AU), we used a heliostat to determine the angular size of the sun using the heliostat, measure the rotational speed of the sun using the spectrograph, and measure the rotational period of the sun using analysis of sunspots. The rotational speed ($v_{rot}$) and rotational period (P) will allow us to calculate the radius (R) of the sun using the equation $v_{rot}= \frac{2 \pi R}{P}$. Then, we can use triangle geometry to solve for the distance between the sun and the earth as shown in Figure 1. Figure 1 : Solving for distance between the earth and the sun given the radius of the sun and the angular diameter of the sun. Methods Angular Diameter : A heliostat was used to measure how long it takes for the sun to move a length of its own diameter. A heliostat is a series of mirrors that reflects the light of the sun into the lab classroom and onto a table ( Figure 2 ). Once lined u...

  #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...