I need help with this multipart question

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1 ANGLE HAS BEEN EXAGGERATE 8 = 2. Love ane The concept of scale is an important one in many aspects of life. The scale of a map tells us what linear unit of measure in centimeters, milli- meters or inches on the map corresponds to an actual unit of length in kilometers or miles on the surface of the earth. In astronomy when using photographs of celestial objects, however, we must relate the angular separation in the sky to linear distances on a photograph. The diagram at the right illustrates how in the photograph depends on the enlargement. Thus the scale of a particular photograph must be given or derived to convert linear measurements back into an- gle size. The scale of a photograph indicates the equivalency between a given length on the photographic plate to a corresponding angular size. It is usually expressed as 1 cm or mm. angle in degrees, minutes or seconds. Since the two stars are 1° apart. on the sky, and appear 1 cm apart on plate 1, the scale for this photograph must be 1 cm = 1°. However, since hic Pa the two stars on plate 2 appear 2 cm apart, the scale for this photograph must be 2 cm = 1°, or 1 cm = 14° the angular separation as seen from earth between two stars appears as a linear distance on a photograph. Notice that the linear dis- tance between the stars <-STARS- TELESCOPE Photographi Plate 1 QUESTIONS: The apparent angular size of the sun is ½°. This is about the apparent size of a dime at distance of 4 meters. Convert the apparent size of the sun to units of minutes and then seconds. Zum minutes (') seconds (") Refer to the concepts in the introduction and use the scale for each astronomical photograph shown to make the measure- 6 ments required in each case for completing parts a- e. a. In the photograph below, determine the angular distance between stars A and B by first measuring the linear separation and then converting it to the equivalent angular separation. cm (Mount Stromlo Observatory) Scale: 0.6° = 1 cm b. In the photograph above, estimate and mark the end of the comet's tail. What is the angular length of the comet as you have marked it? c. On the photograph below, what is the angular diameter of the galaxy along the line indicated on the photograph? (Hale Observatories) Scale: 4' 1 cm d. If the angular diameter of the moon is about the same as that of the sun (°) calculate the scale of the photograph below in terms of 1 mm how many degrees. (Lick Observatory)
e. If the sun is about 400X larger than the moon, why do they have the same apparent angular size? IV. Graphical Representation Very often scientific observations are diffi- cult to analyze as data or numbers in a table. By presenting data in the form of a graph, it is often much easier to find relationships among the physical properties being plotted. In simplest terms a graph is a visual representation of numer- ical information. A common type of graph you will encounter is illustrated below. It is a grid formed by two intersecting number lines on which are plotted two quantities. The point of intersection of the two number lines is called the origin, and the lines are called coordinate axes. Every point on the plane, or grid, can be reached by a pair of numbers, one indicating the X value (horizontal) and the other the Y value (vertical). Two points, A and B, have been illustrated on the graph. 10 Y Axis 1. 8 6 4 2 0 B 2 4 x Axis A 6 8 10 Origin From a graphic representation it is generally easy to find the comparative relation between physical properties. When comparing properties in graphs we must clearly understand the use of the terms difference and how many times. The term difference requires a subtraction. For example, the difference between 6 and 2 is 6-2-4, where 6 is 4 units larger than 2. The term how many times requires a division of the smaller quantity into the larger. For example, to determine how many times larger 6 is than 2, we setup the ratio 6/2 E 3. Thus 6 is 3 times as large as 2, or 2 fits into 6, 3 times. QUESTIONS: On the graph at the top of the page plot the data in the table below the graph. The table shows the velocity, v, that is measured for gal- axies moving away from us, and the observed distance, d, to the galaxy. The graph can be used to investigate if there is any relationship 7 to 10,000 2. 8,000 6.000 V (km/sec) 4,000 2,000 2 Origin - velocity v (km/sec) 790 1600 2200 3100 3600 20 40 60 d(Megapersecs) distance d (Mpc) 10 25 30 40 50 80 100 velocity v (km/sec) 4900 5400 5900 6800 7500 120 distance d (Mpc) 65 70 80 90 100 between these two observed properties of galaxies. The vertical axis is labeled v (veloc- ity), and the horizontal axis d (distance). Thus, the graph would be titled the relation- ship between velocity and distance of gal- axies. When an experiment provides a set of points such as those plotted for question one, we generally assume, if data were available. between the points, all the points would form a line defining a mathematical relation or equation. Unfortunately, in the real world there are always errors associated with any measurement making the curve appear much more complicated than it probably is. Thus, we usually don't connect all the points, but instead, look for a simple smooth line that comes close to all the points. Complete parts a- e. a. In the graph of question one see if a straight line is a reasonable fit to the plot- ted points. If it is, draw the single straight line that comes closest to most of the points. b. Two simple types of mathematical relations are the direct relation and the indirect or inverse relation. In a direct relation as one quantity increases the other quantity increases. In the inverse relation as one quantity increases the other quantity decreases. Which kind of relation is repre-
sented by the data in the graph? c. Usually one texts the validity of the fit of a line to data by checking if the curve is within the error associated with each measurement. Test your straight line fit for the 2200, 5400, and 7500 km/sec data points by assuming there is a 10% error, in both the velocity and distance measure- ments. EXAMPLE The first point in the data table is v 790 km/sec: 79 km/sec and d 10 Mpc + 1 Mpe. Thus we have drawn a box on the graph bracketing v 711 km/sec to 869 km/sec and d- 9 Mpc to 11 Mpe. Similarly, draw the boxes for your test. points using the appropriate error boxes. Does your line fall within the boxes de- fining the errors? Explain. d. If from spectrum analysis it has been deter- mined that a galaxy has a recessional velocity of about 6350 km/sec, then how far away is it? e. From the graph, what is true about the more distant galaxies as compared to closer galaxies? Explain. Luminosity (solar units) 10⁰ 10⁰ 10¹ 10 10² 10¹ 10⁰ 10¹- 10²- D 3. The graph below is a plot of the amount of energy radiated (luminosity) by a star in units of the sun's luminosity, Le versus the surface temperature, T, in degrees Kelvin. The graph is greatly simplified compared to what is really observed in nature. Notice that the temperature variable has been plotted so that is increases toward the left. This is a peculiar convention whose origin lies in the historical aspects of star studies. a. Is the relation between luminosity and temperature a direct or inverse relation? b. Which letter indicates the hottest star? c. Which letter indicates the most luminous star? d. How hot is star B? e. How hot is star A? f. What is the temperature difference in "K between star B and A? g. About how many times brighter is star C than star A? h. If the sun has a temperature of 6000°K and a luminosity of 1 Le which letter repre- sents the sun on the graph? i. On the graph, plot a white dwarf star which has a temperature 7000° K more than the sun, and a luminosity of 10 times the sun. C K B A 15,000 13,000 11,000 9,000 7,000 5,000 3,000 Temperature ( Kelvin)