05Lab_Magnitudes-and-Distances

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Montgomery College *

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101

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Astronomy

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Dec 6, 2023

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M ONTGOMERY C OLLEGE – R OCKVILLE A STRONOMY 101 ASTR101 Laboratory 5 - Magnitudes & Distances 1 Name: Millions of stars are scattered across the sky. Astronomers want to study these stars as carefully as possible. This means measuring everything we can possibly measure about them. Unfortunately, it's not easy to measure anything that's a septillion miles away! Astronomers use measurements of position, brightness, and color to deduce many other properties of the stars. We've already had practice using two methods to measure a star's position – the Altitude/Azimuth method and the Right Ascension/Declination method. Now it's time to look at a star’s brightness . Everyone agrees that stars come in different brightnesses – some are bright and some are dim. The brightness of a star as it appears in the sky is given by a number called its apparent magnitude , where smaller numbers mean brighter stars. Magnitudes can even be negative for very bright stars. Let’s explore this idea of magnitudes. Start Stellarium . Turn off the Atmosphere and Fog . Click on four stars randomly. For each star, when you've clicked on it and selected it, its Information will appear, as usual, in the upper left-hand corner of the screen. The star's “ Magnitude ” will be listed in the information below the star's name. This is the star's apparent magnitude . Enter the names and apparent magnitudes of your stars below. Click on both bright and dim stars to get a range of magnitudes, and then fill out the table below. Star Name Apparent Magnitude Sco 20 1.60 Antares 1.05 Cen 6 2.05 Sgr 3 1.75 1 Last edit Spring 2022. 1
ASTR101 L ABORATORY 5 Remember, there are two kinds of magnitudes – apparent magnitude , which is how bright the star appears to our eyes here on Earth, and absolute magnitude , which is how bright the star would be if it were 10 parsecs (32.6 light years) away. Let's examine more closely luminosity and distance . Luminosity is a measure of how much total light a star gives off every second. A star that looks dim to our eyes could be dim because it has a low luminosity, or because it is far away. Which one is it? If we could measure the star's distance, then we could answer that question. PART A Our first task is to measure a star's distance. The most accurate way to do this is to use parallax . Parallax is the word we use to describe how something appears to shift its position relative to the background when we look at it from two different angles. In the case of stars, those two angles are provided by looking at the star on two nights that are six months apart – that way we are seeing the star from two points on opposite sides of the Earth's orbit around the Sun. The figure below helps explain it: Unfortunately, the stars are all so far away that the amount they shift in the sky over the course of a year is very small – we're talking about arcseconds of angle (remember, one arcsecond is 1/3,600 of a single degree)! Astronomers have defined a distance, called a parsec , which is the distance a star has to be from Earth to shift its position by one arcsecond in the sky over the course of six months . 2
ASTR101 L ABORATORY 5 A parsec turns out to be 3.26 light years . To measure a star's distance, then, just observe that star for a year, and measure its parallax (in arc-seconds) during that time, and then you can use the following formula to calculate its distance: d = 1 p ( Eq. 1 ) Where d is the star's distance (in parsecs), and p is the star's parallax, in arcseconds. What the equation shows us is that the more a star appears to shift its position (in other words, the greater its parallax is), the closer it is! Let's calculate the distances to some stars. In Stellarium , search for the stars in Table 1 on the next page using the Search Window (or by simply pressing F3 ), and when you've selected them, look in the information given in the upper left-hand corner of the screen. The star’s parallax is listed near the bottom, and the distance (in light-years) is listed above that . For each star record its apparent magnitude in the column labeled “Apparent Magnitude”, its parallax in the column labeled “Parallax (Arcseconds)”, and its distance in the column labeled “Distance from Stellarium (light-years)”. You will fill in the first three columns of the table. Please read the following carefully: Stellarium will give you the parallax in units of milliarcseconds (mas). YOU MUST DIVIDE THIS NUMBER by 1000 to get it in arcseconds. Stellarium will give you an error bar for the parallax and the distance. You do not need to keep the number after the “±”. For example, for Sirius, Stellarium provides a parallax of 379.210±1.580 mas. You should enter 0.37921 into the table. (The row for Sirius has been completed for you as an example.) Table 1 Star Name Apparent Magnitude Parallax (arcsecon ds) Distance from Stellarium (light years) Distance (parsecs) Distance (light- years) Sirius -1.45 0.37921 8.60 2.64 8.60 Aldebaran .85 .04894 66.64 20.43 66.60 Betelgeuse .45 .00655 497.95 152.67 497.70 Proxima 11.00 .7685 4.24 1.30 4.24 Spica .95 .01306 249.74 76.57 249.61 3
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