Distances and Magnitudes of Stars Credit: Developed by Beth Bell and Neal Sumerlin, Lynchburg College (Virginia) Data from Internet Stellar Database: http://www.stellar-database.com/ Introduction If we were to construct a scale model of the Earth and its moon, we could choose a child's kickball to represent the Earth, and a tennis ball to represent its moon. This is a scale of 1 inch = 1000 miles, as the Earth has a diameter of roughly 8000 miles and the moon a diameter of roughly 2000 miles. The average distance of the moon from the Earth is 240,000 miles, or 240 inches on our scale-20 feet. Most people are surprised to find the tennis ball moon so far away from the kickball Earth, but these two astronomical objects are actually relatively close to each other. They are so close, in fact, that it is possible to depict both their correct relative sizes and their correct relative distance. That is not possible with stars. To illustrate, let's use the same child's kickball to represent our sun, and change the scale to 1 inch = 100,000 miles. The nearest star to us is one of the three stars comprising the Alpha Centauri system, 4.4 light years away. A light year is the distance light travels in one year, equivalent to 5.88 trillion miles. Sparing you all the calculation, on our scale, the nearest star to our kickball sun would be about 4000 miles away! Clearly, we cannot represent both the correct relative distances and the correct relative sizes of the stars the way we can for the Earth and the moon. So we'll just limit ourselves to the relative distances. The stars are distributed around our sun in 3-dimensional space, of course. We will use a Cartesian (X,Y,Z) coordinate system to locate our stars. We have set up the sun in the middle of the room, and it provides a reference point by its location at (0,0,0). The X direction is the width of the room and the Y direction is its length. The Z coordinate runs from floor to ceiling, with negative Z being below the sun and positive Z being above it. See below for X and Y coordinates. +Y -X +X -Y Front of Room
A. Nearest Stars Let s begin with the 20 stars that are nearest to us. THE nearest is the Sun, also called Sol. Here are the others, with their coordinates and some other information, listed in increasing order of distance from us.
More about spectral type and luminosity later: for now, let s just focus on location. Using a scale of 1 light year = 10 cm, set up your star at the appropriate location relative to the sun. Your instructor will assign you one or more stars from the table. Once you and the rest of the class have your stars set up, answer the following questions. Q1: Use your ruler to measure the straight-line distance between the sun and your star(s). How does your value compare to the value listed in the table (scaled down)? Q2: Does there seem to be any particular pattern to the arrangement of the stars in space, or do they look pretty random? Some stars are found in multiple systems, where there are two or more stars that are gravitationally bound to each other, and are presumed to have formed at the same time. For example, Alpha Centauri is a triple system, and the three stars (A, B, and C) are listed from top to bottom in the spectral type and luminosity columns. Q3: How many of these twenty star systems are multiples? The spectral type of a star is an indication of its temperature. Going from the hottest to the coolest spectral type, they are: O, B, A, F, G, K, M. That is, a G star is hotter than a K star. Within each letter, there are subclasses that run from 0 (hottest) to 9 (coolest). Thus, a G2 star is hotter than a G5 star. Q4: How many stars of each main spectral class (O, B, A, etc.) are there?
Q5: How many of these stars are more luminous than the sun? Q6: The nearest stars to the sun should be a fairly representative sample of all stars. What general statement can you make about the temperature and the luminosity of a typical, average star? B. Brightest Stars Most of the twenty nearest stars are not visible to the naked eye. However, all of the twenty brightest stars are visible (why is that? You don t have to write down why, just think about it). We ll take down all the stars we ve set up, leaving Sol in place as our reference point. These two tables list the twenty brightest stars in decreasing order of their brightness.
Your instructor will assign stars to you as before, but we will use a different scale this time, where 100 light years = 10 cm. Q7: Does this distribution of stars differ from that of the nearest stars? How? Q8: Is there any relationship between this group of stars to a star s luminosity and distance? What is it? Why do you think this relationship exists in this group of stars? Q9: How many stars of each main spectral class (O, B, A, etc.) are there? What differences do you see here between the 20 nearest stars and the 20 brightest? Q10: How many of these bright stars are more luminous than the sun? Q11: What general statements can you make about the stars visible to you in the night sky, as compared to all the stars there are?
C. Apparent and Absolute Magnitudes of Stars Adapted from Lecture-Tutorials for Introductory Astronomy, CAPER Team (2002) Q12: Which value, apparent magnitude or absolute magnitude, a) Tells us how bright an object will appear from Earth? b) Tells us about the object s actual luminosity? Consider the following debate between two students: Student 1: I think that stars with the greatest luminosity also have a large apparent magnitude and a large absolute magnitude (large here meaning a positive number, let s say > 5). Student 2: I don t think that apparent or absolute magnitudes have anything to do with it, because they are not related to the luminosity of a star. The luminosity of a star just depends on how much light the star gives off. Q13: Do you agree or disagree with either or both of the student statements? Explain your reasoning for each. Q14: Star Y appears much brighter than Star Z (it has a smaller number for its apparent magnitude) when viewed from Earth, but is found to actually give off much less light. Assign a set of possible values for the apparent and absolute magnitudes of these stars that would be consistent with the information given in the previous statement. Q15: The star Rigel has an apparent magnitude of 0.1 and is located about 250 parsecs away from Earth. Which of the following is the most likely absolute magnitude for Rigel? Explain your answer. a. -6.9 b. 0.1 c. 7.1 Q16: Refer to the following table for questions 16a d. a. Which star appears brighter from Earth: Star C or Star D? Explain your reasoning. b. Which star is more luminous: A or D? Explain. Star Apparent Magnitude A 1 1 B 1 2 C 5 4 D 4 4 c. How would the apparent and absolute magnitudes of Star A change if it were located at a distance of 40 parsecs? Explain. d. Rank the objects (from farthest to closest) in order of their distances from Earth. Explain your reasoning for your ranking. Absolute Magnitude Q17: Another star, Star F is known to have an apparent magnitude of -26 (about) and an absolute magnitude of 5 (about). Where might this star be located? What is the name of this star? Explain your reasoning.