Understanding Stellar Mass: Determining the Mass of Stars and Binary Systems
Determining the mass of stars poses challenges for astronomers, who utilize the gravitational fields produced by stars. Heavier stars exert stronger gravitational forces, which can be studied through the interaction with orbiting objects. Binary stars, which orbit around a common center of mass, provide key insights. By analyzing the mass ratio, orbital distance, and period, astronomers can calculate individual and total stellar masses. Different types of binary systems—visual, spectroscopic, and eclipsing—offer diverse methods for mass determination and understanding star behavior.
Understanding Stellar Mass: Determining the Mass of Stars and Binary Systems
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Presentation Transcript
Determining the Mass of Stars • It is difficult to determine the mass of stars. • Astronomers use the gravitational field produced by a star to determine its mass... Heavier stars have a greater gravitational field. • Astronomers study how objects, like another star, behave as they pass through the gravitational field.
Binary Stars • Binary stars are pairs of stars that orbit each other. • The gravitational attraction between two stars pulls them toward each other. • They rotate around a fixed point between them called the center of mass… think about a seesaw.
Center of Mass • If the stars are the same mass, the center of mass will be exactly in the middle. • If they are different masses, the center of mass will be closer to the heavier star.
Mass Ratio • Ratio of Masses • The heavier star has a smaller orbit because it is closer to the COM. • MA / MB = rB / rA • This approach only tells you how much larger one is than the other.
Mass, Orbital Distance, & Period • Recall Newton’s Universal Law of Gravitation & Kepler’s 3rd Law… • MA + MB = r3 / T2 • R is measured in AU and is the distance • T is measure in years and is the time for one orbit (Period)
Solar Masses • The majority of the mass in our solar system is the Sun so the total mass is thought of as 1 solar mass. • In other systems, the solar mass is not always 1.
Example • A binary system has a period of 32 years and an average separation of 16 AU. What is the total mass? • 163 / 322 = 4 solar masses • Suppose Star A is 12 AU from the COM and B is 4 AU away. Find the individual masses. • MA / MB = 12:4 or 3:1 • The masses must add up to 4 and have a ratio of 3:1… • Star B = 3 • Star A = 1 (larger period)
Not Always So Easy… • Many binary stars orbit each other in an elliptical pattern. • Many orbits are also tipped at an unknown angle. • The distance to the stars must be known so the size of the orbits can be estimated.
Types of Binary Star Systems • Visual • Spectroscopic • Eclipsing
Visual Binary System • Both stars are separately visible through a telescope • That means the size of the orbit must be large • Nice Diagram on pg. 202 • Other Images http://www.google.com/search?q=visual+binary+star+system&hl=en&prmd=imvns&source=lnms&tbm=isch&ei=kgYrT_r0IImw2QXKt9niDg&sa=X&oi=mode_link&ct=mode&cd=2&ved=0CAwQ_AUoAQ&biw=1280&bih=595
Spectroscopic Binary System • The two stars appear to be a single point of light through a telescope. • Spectral analysis shows red shift and blue shift as the stars orbit each other. • Nice Diagram on pg. 203
Eclipsing Binary Systems • The two stars cannot be distinguished when looking through a telescope. • Astronomers analyze a light curve and see a difference in brightness over time. • This shows that the two stars are passing in front of each other and block some of the light. • Nice Diagram on pg. 205 • http://www.google.com/search?q=visual+binary+star+system&hl=en&prmd=imvns&source=lnms&tbm=isch&ei=kgYrT_r0IImw2QXKt9niDg&sa=X&oi=mode_link&ct=mode&cd=2&ved=0CAwQ_AUoAQ&biw=1280&bih=595#hl=en&tbm=isch&sa=1&q=eclipsing+binary+system&oq=eclipsing+binary+system&aq=0S&aqi=g-S2g-mS1&aql=&gs_sm=c&gs_upl=9328l11172l0l14672l9l9l0l0l0l0l63l561l9l9l0&bav=on.2,or.r_gc.r_pw.,cf.osb&fp=fa3fe87ccfc37441&biw=1280&bih=595
