lab 5 report docx filled out

The Parallax Experiment 11/13/2022 1. Replace the red text at the top of this page with your name and the date. 2. As you enter your work, please make sure that your answers stay red ( like this ). This will make them easier to see, and thus it will be easier for us to grade them accurately. To convert black text to red , highlight it and then click on the “ A ” symbol in the menu bar above, to the right of the “ B ”, “ I ”, and “ U ” symbols. Select the red square to turn your highlighted text red . 3. Delete these 3 initial instructions from this template as soon as you have followed them. Taking Parallax Measurements 1. Estimate the distance to the horizon, or to a distant landmark in line with your measuring device and your object at Position 1, by eye. I estimate the distance is 400 feet by eye Table 5.2: Direct Measurements of Distance Distances from observer to object, in inches, to the nearest half-inch. Position 1 Position 2 Position 3 120 240 360 (Distance from observer and apparatus to three foreground objects.) 2. Estimate the uncertainty in your measurement of the object's apparent shift. For example, do you think your recorded measurements could be off by ten degrees? One degree? One tenth of a degree? There is some uncertainty, so I would guess that the measurements could be off by about 4 degrees. Table 5.3: Parallax Measurements Record angles to the nearest tenth-degree, distances to the nearest half-inch.

Angle 1 ( ° ) 1 Angle 2 ( ° ) 2 2α ( ° ) 3 α ( ° ) r/d 4 d (in) 5 Trial 1 Posn. 1 87 80 7 3 .061 196.1 Posn. 2 86 85 2 5 .017 658.7 Posn. 3 87 86 1 .5 .008 1379.3 Trial 2 Posn. 1 90 80 10 5 .087 137.1 Posn. 2 90 85 5 2 .004 2745 Posn. 3 90 87 3 1 .026 457 Trial 3 Posn. 1 85 76 9 4.5 .078 152.5 Posn. 2 85 80 3 1.5 .026 457 Posn. 3 85 83 2 1 .017 685 Dependence of Parallax on Vantage Point Separation 3. What would happen if the vantage points were farther apart? We separated our vantage points by two feet, to simulate the two astronomical units by which the Earth shifts position over a six month period. What if we had used a separation of ten feet instead? How would you expect the angular shift of the object (the difference between Angle 1 and Angle 2) to change? The difference between the angle of something in the fixed background and the object would be greater than it is now. 4. By how many degrees did the object move using the more widely 1Landmark angle. 2Foreground object angle. 32 α = Angle 1 - Angle 2. 4r/d values can be looked up in Table 5.4. 5d = r / (r/d), where 2r is the vantage point separation (24 inches).

1 0 . If the differences are larger than 5σ, can you think of a reason why your measurements might have some additional error in them? We might call this a systematic error, if it is connected to a big approximation in our observational setup. Some of the deviations are larger than 5 but I think that’s because were using higher degrees and angles Table 5. 5 : Comparison of Average Distances Measured and parallax-derived distances from observer to object, in inches. For parallax distances record the average values (μ) of the three trials and the errors (σ) calculated with the plotting tool in this form: nn.n ± n.n Direct Distance Parallax Distance Position 1 120 123.2 ± 12.7 Position 2 240 148.6 ± 4.08 Position 3 360 255.8 ± 2.43 Distances on Earth and within the Solar System 1. We have just demonstrated how parallax works on a small scale, so now let us move to a larger playing field. Use the information in Table 5.4 to determine the angular shift (2α, in degrees) for Organ Summit, the highest peak in the Organ Mountains, if you observed it with a baseline 2 r of not 2 feet, but 300 feet, from NMSU. Organ Summit is located 12 miles from Las Cruces. (If you are working from another location, select a mountain, sky scraper, or other landmark at a similar distance to use in place of the Organ Summit.) There are 5,280 feet in a mile. If the baseline 2r = 300 feet, then r = 150 feet The distance to the object d = 12 miles = 63360 feet r/d = .00237 Finding the (r/d) value in Table 5.4, α = .15 degrees The observed angular shift 2α = .3 degrees

2. What about an object farther out in the solar system? Consider our near neighbor, planet Mars. At its closest approach, Mars comes to within 0.4 A.U. of the Earth. (Remember that an A.U. is the average distance between the Earth and the Sun, or 1.5 × 10 8 kilometers.) L et us assume we have two telescopes in neighboring states, and calculate the ratio r/d for Mars for a baseline of 2 ,000 kilometers. If the baseline 2r = 2,000 kilometers, then r = 1000 kilometers The distance to the object d = 0.4 A.U.= 6E7 kilometers r/d = .0000166 Can we find this (r/d) value in Table 5.4? (No) We can say that α < .1 degrees 3. Create a linear plot with r/d values on the x -axis and α values on the y - axis, and then check the slope of a line fit through the values, for α = 0 ° to 80° (the complete table) and then trimming the table to contain only the points for which α is less than or equal to 2 ° . Include a copy of both plots in your lab report (making sure to label the axes, and to add titles). Is a straight line a good fit to either set of data (for α ≤ 80 ° , or just up to 2 ° )? What is the slope, in the linear region? Are you now comfortable using this approximation to shift between α and r/d ? Replace this text , and include PNG-format images of two plots. Distances to Stars, and the Parsec 4 . (a) If a star has a parallax angle of 0.25'', what is its distance in parsecs? For a star with parallax angle α (in arcseconds) located a distance d (in parsecs) aways from us, d = 1 / α = 4 parsecs (b) If a star is 5 parsecs away from Earth, what is its parallax angle in arcseconds? For a star with parallax angle α (in arcseconds) located a distance d (in

d = 1 / α =.12 parsecs. 4. Astronomers like Tycho Brahe made careful naked eye observations of stars in the late 1600's, hoping to find evidence of semi-annual parallax shifts for those which were nearby and so weigh in on the growing debate over whether or not the Earth was in motion around the Sun. If the nearest stars (located 1.3 or more parsecs from Earth) were 100 times closer th a n they are now known to be, or if the resolving power of the human eye (0.02 degrees) was improved by a factor of 100, could he have observed such shifts? Explain your answer. The angular shift of the nearest is star is α = 1 / d = .008 arcseconds. The smallest change in angle we can see is r = 0.02 degrees = 50 arcseconds. We ( cannot ) observe the angular shift of the nearest star by eye. If the stars were 100 times closer, α would increase to 100 × α = .8 arcseconds. Or if our eyes were 100 times better, r would decrease to r / 100 = .5 arcseconds. In either case, we (could not) observe the shift by eye. Summary (300 to 500 words) I think the goal of this lab was to figure out how to calculate parallax and what it does to the objects we are look at. Astronomers use parallax to determine the distances to nearby stars. The parallax method works for the stars that an observer can see from their eye vantage point. Parallax is an apparent vision method to observe the displacement or change of the object from earth. The parallax method does not work for every star in the galaxy. Some stars in our galaxy are too far, dim, or small to see with the naked eye. We also only used this method in a way that suits out classroom lab so I would be curious to see how professional astronomers use this method to measure things on a larger scale. We can find the parallax of a star from earth when we can see and know the distance of that star from earth. It is so important for astronomers to determine the distance to the stars because it has helps them find relationships with other stars and planets. I do think there is always a way to tie things back into a safety concern too. So if scientist can keep track of stars distance then we will know if there is

any danger to earth or not. By finding the distance, we can also find out the color and brightness of those stars. Stars are always changing, so it is good to keep tabs on them. One way to keep up with them is to find the distance or Parallax of that star. Since stars are always changing, we can see how much they are changing and maybe learn why. Maybe learn why some are dimmer than others are or why there are more stars in one area of the galaxy. This was an interesting lab because it shows us that we can find out some things about stars ourselves and we do not need a fancy NASA space station to figure it out. Extra Credit Replace this text.