The Hertzsprung Russell Diagram. The Main Sequence
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1 The Hertzsprung Russell Diagram H R diagram plots stellar luminosity against surface temperature Luminosity ranges L. Temperature ranges by a factor of 10 increases to the left spectral sequence OBAFGKM puts hottest (blue) on left, coolest (red) on right Can compare properties of stars using this diagram The Main Sequence Stars are not uniformly distributed. Most stars lie in a welldefined band called the Main Sequence. Cool stars tend to be faint Hot stars tend to be bright Of the 80 closest stars, most are on the Main Sequence, including the Sun Dr. Kristin B. Whitson 1
2 Stellar Radii on the H-R Diagram Stellar radii vary on the Main Sequence dashed lines show constant stellar radius same R, different L and T radius-luminositytemperature relationship: L % T 4 Faint, red, cool, M-type stars 0.1 R called red dwarfs Bright, blue, hot, O-type stars ~ 10 or greater R called blue giants Luminosity on the Main Sequence 100 brightest stars All more luminous than Sun All are giants (red or blue). Giants are easy to detect Rare: O and B supergiants < 0.01% of all stars Blue giants = top left. Dwarfs are hard to detect Red Dwarfs (bottom right) probably most common: > 80% of all stars Dr. Kristin B. Whitson 2
3 White Dwarf Region White dwarfs do not lie on the Main Sequence: Very hot Dim Small Bottom left on H-R ~ 9% of all stars are white dwarfs Hard to detect Red giants to the top right of the Main Sequence. Cooler than Sun Luminosity range: 50 10,000 L R Red Giant Region Relatively rare: 1% of all stars. Dr. Kristin B. Whitson 3
4 The Hertzsprung Russell Diagram Hipparcos measured colors and luminosities of > 2,000,000 stars. Main sequence, red giant regions evident. few white dwarfs Overall distribution of stars in space: 90% main sequence, 9% white dwarfs, 1% red giants Presumably same ratio everywhere in the universe Sun is average by luminosity, temperature, radius Middle of H-R Luminosity Class Spectral line widths of main sequence, red giants, white dwarfs differ due to pressure and density of star Less dense atmosphere narrower lines Red giant main sequence white dwarf Luminosity classes designate the type of star by its spectral line width Correlates pressure of star with luminosity. Dr. Kristin B. Whitson 4
5 Standard Luminosity Classes Position of luminosity classes on the H-R Diagram Determination of the star s luminosity class reveals the kind of star (dwarf, giant, main sequence). Sun = G2V G2 spectral type V class luminosity Determining Luminosity from Stellar Spectra All stars of spectral class K2 have surface temperature ~ 4500 K and show the same spectral lines. Width of spectral lines reveal the luminosity class (K2Ib, K2V, etc.) Read luminosity directly from H-R diagram based on spectral and luminosity class Dr. Kristin B. Whitson 5
6 Distance Measurement Techniques Astronomical distances measured by techniques valid over certain ranges Radar ranging for solid objects < pc away Stellar parallax Distance determination by measuring apparent shift of star from two vantage points Objects 200 pc away Spectroscopic parallax Uses spectroscopy and luminosity classes to find distance Has nothing to do with parallax Useful for stars 10,000 pc away Spectroscopic Parallax Spectroscopic parallax is the application of the mathematical relationship between luminosity, apparent brightness, and distance Step 1: Measure the star s apparent magnitude and spectral class Apparent magnitude: amount of energy detected on a 1 m 2 surface in 1 second put it on the magnitude scale. Spectral class: match to spectral class OBAFGKM and luminosity class (I-V) Dr. Kristin B. Whitson 6
7 Spectroscopic Parallax Step 2: Use spectral / luminosity class to estimate luminosity from H-R diagram and correlate it with the absolute magnitude Step 3: Apply the distance/magnitude relationship distance apparent magnitude absolute magnitude = 5 log10 10 pc What is the distance to a star of apparent magnitude 10 and class A0V? How Do We Determine a Star s Mass? A star s mass is measured by observing its gravitational influence on a nearby body (another star or a nearby planet). If distance between two orbiting bodies is known use Newton s Laws to calculate their masses. Sir Isaac Newton ( ) and his law of universal gravitation Hit on the head by a falling apple OR Comparing the accelerations of the planets and the Moon. Dr. Kristin B. Whitson 7
8 (a) An object at rest will remain at rest (b) An object in motion stays in motion in a straight line at constant speed (c) Unless an external force acts on it. Newton s First Law of Motion Also called the Law of Inertia Inertia: the tendency of an object to resist a change in its state of motion to stay at rest to maintain state of motion in a straight line Newton s First Law of Motion The ball is guided around the metal rim. When the ball leaves the rim, which path (1, 2, or 3) will the ball follow? Earth s inertia causes it to travel in a straight line Sun s gravitational force pulls Earth toward it Result: Earth travels in a curved path. How fast? Dr. Kristin B. Whitson 8
9 Newton s Laws of Motion An object s inertia is directly related to its mass More mass Harder to move Less mass Easier to tackle Can change directions faster Force: a quantity capable of producing motion Unless an external force acts refers to the net force If an object s velocity changes it undergoes an acceleration. Speeds up Slows down Changes direction Newton s Second Law of Motion Newton realized to produce an acceleration, a force must be acting. Acceleration produced by a force on an object is directly proportional to the magnitude of the force Greater net force = greater acceleration Acceleration is inversely proportional to the mass of the object Greater mass = smaller acceleration F a = F = ma m Dr. Kristin B. Whitson 9
10 The 2 nd Law of Motion and Gravity If you know initial conditions and forces, can determine object s state of motion by F = ma. In astronomy, force is most always gravity. On Earth, acceleration due to Earth s gravity is ~9.8 m/s 2 everywhere, at all times, and on everything directed toward center of Earth On the Moon, acceleration due to Moon s gravity is ~ 1.6 m/s 2 (1/6 th of Earth) Force of gravity is less because Moon s mass is less It would take less force to put an object into orbit Newton s Law of Universal Gravitation Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them G: universal gravitational constant valid throughout the universe G = 6.67 x N. m 2 /kg 2 Dr. Kristin B. Whitson 10
11 Newton s Law of Universal Gravitation At locations equidistant from Sun s center, gravitational force due to Sun is the same and directed toward the Sun Gm 1 m 2 F = r 2 If m 1 or m 2 increases and distance stays the same: force increases The strength of the Sun s gravitational pull decreases in proportion to the square of the distance from the Sun Force of gravity can never equal zero, no matter the distance. Newton s Third Law of Motion When object A exerts a force on object B, object B exerts an equal and opposite force on object A. For every action there is an equal and opposite reaction. A B Gravity: if student jumps off a table, she accelerates toward Earth. Newton s third law states that BOTH the student and Earth accelerate toward each other. Student: small mass, large acceleration (m 1 a 1 ) Earth: huge mass, very small acceleration (-m 2 a 2 ) m 1 a 1 = -m 2 a 2 : forces are equal and opposite Dr. Kristin B. Whitson 11
12 Newton s Third Law of Motion Mutual gravitational attraction of Sun and planets is what keeps the planets moving in stable elliptical orbits. Gravitational pull of Earth Gravitational pull of Sun Why does the Sun dominate the interaction? 3 rd law: Forces on Sun/Earth are equal 2 nd law: F = ma or a = F/m Acceleration is inversely proportional to its mass Sun accelerates 300,000X less because it is 300,000X more massive than Earth Measuring Mass using Orbital Motion All masses are calculated in astronomy using only the speed of something orbiting the object (measure circumference and time), and the path of the orbit (for the radius) Consider the case of extreme difference in mass (Sun-planet): Force required to keep an object moving in a circle is centripetal force, given by: mv F = 2 r Equate with universal law of gravitation: F = m p v 2 r = Gm p m s r 2 = F v 2 r = v 2 = Gm s r 2 GM s r M = rv 2 G Dr. Kristin B. Whitson 12
13 Weighing the Sun The Earth orbits the Sun at ~30 km/s at a distance of 150,000,000 km. What is the mass of the Sun? Dr. Kristin B. Whitson 13
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