# LEARNING ASTRONOMY BY DOING ASTRONOMY ACTIVITY 1 MATHEMATICAL

LEARNING ASTRONOMY BY DOING ASTRONOMY ACTIVITY 1 – MATHEMATICAL AND SCIENTIFIC METHODS STEP 7 – COMBINE SCALING, SMALLANGLE FORMULA, SCIENTIFIC NOTATION, AND MEASUREMENT UNCERTAINTIES Let’s get started!

Here are two spiral galaxies that look similar and thus could be similar in actual size. However, the galaxy on the right has a smaller angular size. If these images were taken on identical telescopes, identical set ups, and identical cameras and detectors, then the galaxy on the right must be farther away from us.

Where do you start?

Each image in Figure 1. 5 is 600 arcsec on a side. Using the ruler in Figure 1. 6, measure the length of the white line in one of the images and calculate the scale for all of the images. We get the angular size of the image from knowing about our telescope and our detector. The number of arc seconds per pixel depends on the focal length of the telescope and the size of each pixel of the detector. Stay tuned for more! Your measurements will be different than the ones we made here!

Round off your answers! You don’t need more than 1 decimal place here. One would be justified to say that 5 cm = 600 arc seconds to make the calculations even easier.

It would have been completely alright if you noticed that this galaxy filled up most of the image, and so was approximately 600 arc seconds in angular size. For demonstration purposes, we have done a separate measurement and came up with 5. 5 cm.

Activity 1 uses a value of 600 arc seconds for the angular size of the example galaxy. We have changed the number to our measurement here of 649 arc seconds to give you another example of what to do.

27. The angular size of a galaxy is inversely proportional to its distance from us. How much farther away from us is the farthest galaxy compared to the nearest? _____ USE RATIOS! SO much easier than using actual distances, especially since we do not at this point in the activity KNOW any actual distances. Go to the next slide.

Galaxy A (left) Angular size: 0. 0031 radians Galaxy B (right) Angular size: 0. 0024 radians Relative distances: Galaxy B is about 1. 3 times farther away than Galaxy A. How can we get ACTUAL distances?

is the angular size in radians for each galaxy 100, 000 light years s

Your turn: 28. Distance to galaxy A______ light years; B______ light years; and C______ light years. 29. Which galaxy has the most uncertainty in your measurement of its angular diameter? ____ Which one has the least? _____ Explain your answer, using the appropriate techniques we have covered in this activity. You should now have enough foundation to finish all of Activity 1 as well as being prepared for the calculations in the rest of the activities for this quarter. Our use of mathematics – the language of the Universe – has revealed a universe that is unimaginably large and complex, and ultimately the most fascinating thing we might ever study!

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