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Astronomy Unit 2B

by: Emily Mason

Astronomy Unit 2B Astronomy 1020

Emily Mason

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This is a study guide covering all the material for Unit 2B as seen on blackboard.
Stellar Astronomy
Dr. Flower
Study Guide
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This 9 page Study Guide was uploaded by Emily Mason on Monday February 22, 2016. The Study Guide belongs to Astronomy 1020 at Clemson University taught by Dr. Flower in Winter 2016. Since its upload, it has received 161 views.


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Date Created: 02/22/16
Astronomy Unit 2B Temperatures and Abundances:  Collecting the light from a star without dispersing it into its individual wavelengths allows us to determine distances and luminosities  Dispersing starlight into a spectrum (wavelengths) allows us to determine surface temperature and abundances of chemical elements making up the atmosphere of a star.  Astronomers can determine the chemical compositions of stars from their spectra from identifying the chemical elements responsible for the absorption lines of their spectra  Temperature Classification of Stars: o Based on the appearance of absorption lines. Each letter represents a temperature range: O, B, A, F, G, K, M, or L stars Hottest-----------------------------------Coolest  Why stars can have the same chemical composition but their spectra can look very different? o The spectra look different because temperature determines the supply of photons passing through a star's atmosphere, where the atoms that can absorb reside. o The energy of the photons determines which atoms can absorb or not. o Too much energy results in no absorption because of ionization. o Too little energy results in no absorption due to there not being enough energy to cause transitions. Luminosity of Stars  Luminosity determines a star’s lifetime  Luminosity is a star’s wattage (how much energy a star is emitting per second)  We can find a stars luminosity without using distance; we use the Sun’s Magnitude (-26.5), the Sun’s luminosity(3.8 x ???????? ), and the Star’s apparent magnitude. o To do this, we must line the stars up at the same distance of 10 pc o We see this taking place and in the examples of the Stellar Lineup below Stellar Lineup Drawing A depicts all the Drawing B shows four stars stars at 10 pc, the red line. at different distances from Next to the stars are the Sun and their apparent their absolute magnitudes magnitudes. (5.0, 6.0, 0.0, etc.) (-26.8, 2.5, 1.2, etc.)  Compare the magnitude of star 1 in Drawing B with star 1 in Drawing A. Since star 1 moves from about 5pc in Drawing B to 10pc in Drawing A, the magnitude becomes larger, making the star fainter.  Compare the magnitude of star 2 in drawing B with star 2 in Drawing A. Since star 2 moves closer from 15pc in Drawing B to 10pc in Drawing A, its magnitude becomes smaller, making the star brighter.  Example: How to find how much brighter a star is to another: ***Recall from Unit 1B, the difference in magnitudes corresponds to a brightness factor of 2.512*** o Compare Star 2 and the Sun in Drawing A o We see Star 2 is brighter since its magnitude is smaller. o Subtract the magnitude of Star 2 and magnitude of the Sun: Magnitude of the Sun (5) minus magnitude of Star 2 (0) equals 5 o To determine how much brighter Star 2 is, square the brightness factor (2.512) by the number you have just calculated through subtraction (5) 5  Your calculation should look like this: 2.512  This comes out to be about 100 o Therefore, in this example, Star 2 has a luminosity 100 times greater than the Sun. Radii of Stars (HR Diagram)  These are HR Diagrams, which shows how radii vary.  The dashed lines, running diagonally from the upper left to the lower right, represent the radius of are lines of the Sun’s constant radius.  Stars with plotted radii are names and represented with a ‘+’  The green circles show radii of different sizes, to represent how the radius changes.  The radius increases from left to right in the HR diagram, and diagonally from lower left to upper right.  The largest stars are in the upper right of the diagram, and the smallest stars are in the lower left.  Key for graph on the right: a= spectral type (coolest to hottest from right to left), b= decreasing absolute magnitude, d= decreasing radius, e= main sequence (top left are the hottest and faintest stars, bottom right the faintest and coolest), A= where white dwarfs are located, C= where to find a supergiant, D= low mass main sequence star, E= low giant star How to Calculate the Radius Use the equation: Ratio of luminosities between the star and Ratio of radii between the sun the star and the sun Ratio of temperature between the star and the sun Example:  Calculate the radius of a star with:  Ratios needed: ***Even if these ratios weren’t given to us, we could still figure them out. We know the temperature of the sun (5800K), and we can simply rearrange the equation given to us for the luminosity of the star ( ), and solve for the luminosity of the sun, resulting in these same ratios.  Next, insert the ratios into the blue equation for the radius  Reduce and solve for Double Stars  Binary/Double Stars- two stars that orbit each other.  We describe this orbit using 2 main parameters: 1. The Semi major axis (a)- distance from center to the point on the orbit along longest diameter (equals half of the longest axis) - this is the size or "radius" of an orbit 2. Eccentricity- the shape of the orbit (value of 0 for a circle and approaching 1 for a very flat orbit) o Also important is the orbital period (time once around) and the velocity in orbit  The masses of the orbiting stars control the periods and velocities through the force of gravity  If you observe two of the parameters, it is possible to extract the value of the masses of the stars Gravity and Orbits  Force of gravity between two masses separated by a distance d  F= G(m1Xm2/d^2) G is the gravitational constant  Newton’s 2 nd law: F= mass x acceleration  Smaller mass experiences greater acceleration (faster motion)  Stars orbit around each other—motion prevents collision  Relative orbits- the motion of the brighter star is ignored o Astronomers make continuous measurements of the position of the fainter star relative to the brighter o Relative orbits don’t provide enough info to determine individual masses (only the sum of the masses are known)  Absolute orbits- individual orbits of the two stars about the center of mass of the system o If the masses of the two stars are the same, the center of mass is exactly between them (same distance away) o If one star is more massive, the center of mass shifts closer to the more massive star o The more massive star has the small orbit (stars orbit about the center of mass) Binary Star Orbits  Binary stars: pairs of stars that orbit about each other  Gravitationally bound to each other  Their orbits are the result of their interaction through the gravitational force  High masses, strong gravitational forces Must have high orbital velocities to maintain their orbits Leads to short orbital periods  Periods and velocities are related to orbital sizes, or semimajor axes o The radius of the orbit equals the semimajor axes, a o The orbital period, P, is the circumference of the orbit divided by the orbital velocity o P= 2pia/v  Types of Binary Systems: o Visual binary stars- visible as two individual stars - A= Alpha Centauri A and B= Alpha Centauri B - Over 70,000 visual binaries - Orbital periods range from 2 to many thousands of years o Astrometric binaries- close enough to earth that astronomers deduce their binary nature from the motion of the visible companion about the center of mass of the pair - Change of position of the visible star of the astronomic pair gives away the presence of the unseen companion - Can distinguish binaries from single stars through Doppler shifts (shift will vary if a star is orbiting another0 o Spectroscopic binaries- binaries detected through variations in their spectra - Orbital period is the time it takes for the observed spectral lines to cycle through the red and blue variations - Radial velocity curve shows the periodicity of the orbital motion o Eclipsing binaries - Primary minimum: hotter star is eclipsed, greater decrease in light. Times between 1 and 2 and 3 and 4 measures the size of the cool star - Secondary minimum: cooler star is eclipsed, less of a decrease in light. Times from 1 to 3 measures the size of the hot star - Light curve: light variation in eclipsing binaries is plotted against time Radial Velocity Curve  Velocity of the system through space: o The dashed line that cuts through the wave-like line (km/s)  Orbital velocity of stars: o Where the wave-like line hits the dashed line or how much time is spent on the positive side of the dashed line (km/s)  Points where star is moving toward or away from us: o Towards: when the velocity(wave-like line) is under the dashed line o Away: when the velocity (wave-like line) is above the dashed line Mass-Luminosity Relation:  The main sequence is a progression in mass as well as in temperature and luminosity  Faint, cool main sequence stars have low masses  Bright, hot main sequence stars have high masses  There are deviations though ex: white dwarfs are underluminous rd Kepler’s 3 Law:  Relates the semimajor axis to mass  Allows astronomers to determine masses of stars  Two gravitationally interacting objects are needed for us to determine the mass of one or both  Evidence of stellar mass is in the effects of the gravitational interaction between stars  M + A = a Bp 3 2  The a= the semimajor axis in AU  The p= orbital period in years  The final answer should be in solar mass units, M☉-- But now we only have the sum of the masses  Use Absolute Orbit to get the distances o Plot the location of both stars relative to a more distant background Newton’s Laws: 1. Constant speed in straight line unless unbalanced force acts o Force- any push or pull o Frictional force slows the object o Collisional force changes direction and speed of the object 2. Force= mass x acceleration o Acceleration- any change in speed/direction o If F is the same, m and a inversely correlated 3. Action-Reaction Newton on Planetary Motion:  Newton’s 1 law tells us that a force acts on planets—makes the planets circle the sun  This force is called gravity  Newton’s 3 law tells us why the sun is the center of the solar system— Sun feels force from planets (action-reaction) o Sun and planets experience acceleration but the sun is more massive o Sun’s acceleration is very small, planets move not Sun o Sun is at center of planetary motion  Law of Gravity o F= (mass of sun x mass of planet)/ distance 2 o Force decreases with the square of distance Kepler’s Laws of Planetary Motion: 1. Orbits are ellipses/ sun at one focus 2. Planets move faster closer to the sun o Perihelion- closest to sun o Aphelion- farthest from sun 3. P a= 3 o P= orbital period in years o The a= semimajor axis in AU  Shape of ellipse= eccentricity= e= F/A


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