ay16-CDeMeo

Introduction Accurate descriptions of low mass stars are difficult to obtain and the most accurate data comes from eclipsing binary stars. Measuring these systems can allow us to calculate the radii, masses, and separation of the stars in the system. This lab focuses on double-lined spectroscopic binary NSVS01031772.  The blue star is brighter than the yellow star in the binary system represented in Figure 1.   Figure 1b is the secondary eclipse and Figure 1c is the primary eclipse. The primary eclipse causes a greater decrease in brightness, represented by the larger peak in the light wave curve and the secondary eclipse represents the smaller peak in the light wave curve ( Figure 1d) . Observing these stars through the Clay telescope and using data from the paper  rvcurve.pdf (harvard.edu)  will allow us to determine the mass, separation, radius, and period of these stars.                      ...

The sun is a little less than halfway through its lifetime and in about 5 million years it will become a white dwarf. Currently it is on the main sequence when stars undergo nuclear fusion and convert Hydrogen into Helium. When there is no more hydrogen in the sun's core to be converted, the force of gravity will cause it to collapse until his is balanced out by some outward force due to pressure. One possible outward force is the force due to degeneracy pressure. White dwarfs are very dense so the fermions in the sun's core do not have space between them. They cannot occupy the same quantum state as their neighbors so they must constantly be in motion to avoid other fermions. The Broglie wavelength $\lambda $ is when the space between the particles is on the order of the particles themselves. $\lambda $ is related to the momentum p of the particle by the formula: $\lambda= \frac{h}{p}$ where h is the Planck constant, $h = 6.6 \times 10^{27} erg s$ (a) For a stellar core of a ...

The virial theorem, maybe better described as bound body energetics, requires that an object has an inward central force $r^{-a}$ such as a gravitational force or an electromagnetic force. The theorem also requires a constant moment of inertia on average so that the object maintains its rough shape over whatever timescale is relevant. Most structures can be virialized such as Earth, the sun, and the galaxy. For virialized structures we can say that Kinetic energy (K)$= \frac{-1}{2}$ Potential Energy (U) Worksheet 8.1 #1 For a planet of mass m orbiting a star of mass M, at a distance a, start with the Virial Theorem and derive Kepler’s Third Law of motion. Assume that m is much less than M  $U_g = \frac{-GmM}{a}$ $K=\frac {U_g}{2}=\frac{-GmM}{2a}$=$\frac {1}{2} mv_p^2$ $v_p= \frac{2 \pi a}{T}= (\frac{GM}{a})^{\frac{1}{2}}$ $\frac{4 \pi ^2 a^2}{T^2}= \frac{GM}{a}$ $T^2=\frac{4 \pi ^2a^3}{GM}$ #2 Consider a spherical distribution of particles, each with a mass $m_i$ and a total (coll...

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...