Chapter 9: The Family of Stars

9-1 Measuring the distance to Stars The Surveyor’s Method: The distance between A and B is the baseline. The surveyor’s site a tree or boat from points A and B and determine an angle. Knowing two angles of the large triangle and the length of the side between them, the surveyors can then find the distance across the river by using trigonometry. Or once the surveyors have the base line and the angles of A and B, they can draw a similar triangle on a smaller scale to determine the distance.

9-1 Measuring the distance to stars The Astronomer’s Method: To find the distance to a star, you must use an extremely long baseline- the diameter of Earth’s orbit= 2AU. If you take a photograph of a nearby star and then wait 6 months to take another photograph of the star. (The second photo is taken at a distance of 2AU) When you examine the two photos, you will notice that the star is not in the same position. This is called parallax (the apparent change in the position of an object due to change in the location of the observer)

9-1 Measuring the distance to stars Distance to a star with a parallax uses the formula d= 1/p, p is the stellar parallax and is measured in seconds of arc and d is measured in a distance unit invented by astronomers

9-1 Measuring the distance to stars Proper Motion: Take pictures of the sky on two date separated by 10 or more years, you will notice that the stars in the photographs have moved slightly. This motion, expressed in units of seconds of arc per year is the proper motion. Stars with small/ zero proper motion are distant while stars with large proper motion are closer.

9-2 Intrinsic Brightness The scale of apparent magnitudes only tells you how bright stars look. Intrinsic means “belonging to the thing”- when astronomers refer to the intrinsic brightness of a star, they mean a measure of the total amount of light the star emits.

9-2 Intrinsic Brightness Brightness and Distance: The farther objects look fainter than nearer stars

9-2 Intrinsic Brightness Absolute Visual Magnitude If you knew the distance to a star, you could use the inverse square relation to calculate the brightness the star would have at some standard distance Astronomers take 10 pc as the standard distance ad refer to the intrinsic brightness of the star as its Absolute Visual Magnitude (Mv)

9-2 Intrinsic Brightness Calculating Absolute Visual Magnitude The magnitude-distance formula relates the apparent magnitude mv, the absolute magnitude Mv, and the distance d in parseces: mv-Mv=-5+5 log 10(d) The magnitude-difference mv – Mv is known as the distance modulus, a measure of how far away the star is. The larger the distance modulus, the more distant the star

9-2 Intrinsic Brightness Luminosity: the total amount of energy the star radiates in 1 second. (not just visible light, but all wavelengths) To find a stars Luminosity, you begin with its absolute visual magnitude, correct it a bit, and compare the star with the sun. The correction you must make, adjusts for the radiation emitted at wavelengths humans cannot see. Adding the proper correction to the absolute visual magnitude changes it into the absolute bolometric magnitude (the absolute magnitude the star would have if you could see all wavelengths)

9-3 The Diameter of stars You can find the diameter of star by knowing it’s temperature and luminosities. Luminosity, Radius and Temperature Two factors affect a star’s luminosity: surface area and temperature Ex. Birthday candle vs a candle that is 12 feet tall Astronomers use the equation : L = 4 p R2 s T4 to determine the size of a star.

9-3 The Diameter of stars The H-R Diagram: Hertzsprung- Russell (H-R) Diagram- named after its originators Ejnar Hertzsprung and Henry Norris Russell- sorts stars according to their sizes.

9-3 The Diameter of stars Main sequence stars- run from the upper left to the lower right of the HR diagram. It includes roughly 90% of all normal stars. Giants, Super Giants and Dwarfs Giants: lie at the right above the main sequence stars. They are cool, but more luminous because they are 10-100 times larger than the sun. Super Giants: lie near the top of the H-R Diagram and are 10-1000 times larger than the sun Dwarfs: at the bottom of the H-R diagram they have low luminosity because they are very small Red: small and cool White: small and hot

9-4 The Masses of Stars Binary stars: pairs of stars that orbit each other and used to find the masses of stars

9-4 The Masses of Stars Binary Stars in General: Orbital motion is used to study the masses of binary stars. When two stars orbit each other, their mutual gravitation pulls them away from straight-line paths and makes them follow closed orbits around a point between the stars. Each star in a binary system moves in its own orbit around the system’s center of mass. The more more massive star is closer to the center of the mass, while the less massive star is farther away. The smaller the orbits, the stronger the gravitational pull. Binary systems are common, more than half of all stars are members of binary systems.

9-4 The masses of Stars Calculation the Masses of Binary Stars Scientists use the equation MA+ MB= a3/p2 M= the masses of the stars a= the average distance between the two stars p= their orbital period.

9-4 The Masses of Stars Visual Binary Systems The two stars are separately visible in the telescope, which indicates that the stars have large orbits. The stars will also have long orbital period, some take hundreds or even thousands of years to complete.

9-4 The masses of stars Spectroscopic Binary Systems Binary systems that are extremely close together, look like one point with a telescope, but looking at a spectrum of the light show spectral lines with Doppler shifts

9-4 The Masses of stars Eclipsing Binary Systems Two stars whose orbit is lie in a plane that is nearly edge-on to Earth. When on star crosses in front of the other it blocks some of the light of the star that is behind. From Earth, the two stars are not visible separately, and the system looks like single point. When one star moves in front of the other, part of the light is blocked and the total light decreases. The resulting variation in the brightness of the system is shown on a graph versus time, known as a light curve.