Exploring the Universe: Measuring Distances and Understanding Cosmic Dimensions, Lab Reports of Astronomy

A lab exercise for students to understand measuring tools and techniques used in astronomy to determine distances to celestial objects. Students will explore everyday measuring tools, learn about parallax and stellar magnitudes, and calculate distances to stars like betelgeuse and deneb. The exercise also covers the sizes and distances of earth, the sun, and other objects in the solar system and beyond.

Typology: Lab Reports

2022/2023

Uploaded on 02/11/2024

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Distances)and)Models)
You r) Na me __ __ __ Ava)Piper________)
Objectives)of)this)lab)exercise:)
After&completing&this&exercise&you&should&-&
Understand)measuring)tools)
Learn)how)astronomers)are)able)to)determine)distances)to)celestial)objects)
Understand)the)vast)dimensions)of)the)universe)and)how)to)scale)those)dimensions)to)build)
a)model)
Part)I)–)Exploring)everyday)measuring)tools)[6)points])
Science)is)all)about)measuring.))One)of)the)most)important)parts)of)doing)astronomy)is)measuring)
distances,)angles,)and)luminosity)of)celestial)objects.))In)Astronomy)the)distances)are)huge)and)
unimaginable.)You)might)ask)yourself)the)question)“How)can)you)gather)information)about)an)
object)that)is)so)far)away)that)you)cannot)reach)it?))For)example,)how)do)we)know)if)a)star)is)far)
away,)but)very)bright,)or)close)to)Earth)and)relatively)dim?)Before)we)start)with)exploring)
astronomical)distances)you)will)investigate)how)you)measure)things)in)everyday)life,)and)what)tools)
you)can)use.)
1. List&at&least&10&tools&that&you&use&for&measuring&things&in&your&everyday&life.&&
Clock,&thermometer,&measuring&cup,&yardstick,&ruler,&bathroom&scale,&kitchen&scale,&
speedometer,&tape&measurer,&phone/Aitness&tracker&
2.&If&you&were&going&to&measure&the&area&of&your&room&what&kind&of&measuring&tools&might&you&
use?&
& I&would&use&a&tape&measurer&or&a&yardstick&to&measure&my&room.&
Part)II)–)Measuring)distant)objects)[24)points])
Parallax)as)explained)in)the)pre-lab)activity,)is)an)interesting)way)of)measuring)the)distance)of)an)
object)by)how)much)it)appears)to)move)when)viewed)against)a)much)more)distant)background)from)
one)location,)then)another)(the)distance)between)the)locations)is)called)the)baseline)).)
2. Print&a&paper&meter&stick&and&tape&it&to&your&arm&so&that&your&chin&can&rest&on&the&“0”&mark.&
With&your&other&hand&hold&a&pencil&or&pen&at&the&50&cm&mark.&Then&shut&Airst&one&eye,&then&the&
other&and&observe&how&the&pencil&moves&against&objects&in&the&background.&Describe&what&
happens&
& The&pencil&moves&more&towards&the&right&when&my&right&eye&is&closed&and&towards&the&left&
when&my&left&eye&is&closed.&
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Distances and Models

Your Name______Ava Piper________

Objectives of this lab exercise:

After completing this exercise you should -

  • (^) Understand measuring tools
  • (^) Learn how astronomers are able to determine distances to celestial objects
  • (^) Understand the vast dimensions of the universe and how to scale those dimensions to build a model

Part I – Exploring everyday measuring tools [6 points]

Science is all about measuring. One of the most important parts of doing astronomy is measuring distances, angles, and luminosity of celestial objects. In Astronomy the distances are huge and unimaginable. You might ask yourself the question “How can you gather information about an object that is so far away that you cannot reach it? For example, how do we know if a star is far away, but very bright, or close to Earth and relatively dim? Before we start with exploring astronomical distances you will investigate how you measure things in everyday life, and what tools you can use.

1. List at least 10 tools that you use for measuring things in your everyday life. Clock, thermometer, measuring cup, yardstick, ruler, bathroom scale, kitchen scale, speedometer, tape measurer, phone/Aitness tracker 2. If you were going to measure the area of your room what kind of measuring tools might you use? I would use a tape measurer or a yardstick to measure my room.

Part II – Measuring distant objects [24 points]

Parallax as explained in the pre-lab activity, is an interesting way of measuring the distance of an object by how much it appears to move when viewed against a much more distant background from one location, then another ( the distance between the locations is called the baseline ).

2. Print a paper meter stick and tape it to your arm so that your chin can rest on the “0” mark. With your other hand hold a pencil or pen at the 50 cm mark. Then shut Airst one eye, then the other and observe how the pencil moves against objects in the background. Describe what happens The pencil moves more towards the right when my right eye is closed and towards the left when my left eye is closed.

3. Move the pencil closer, to the 25 cm mark. What happens to the motion of the pencil now when you Airst close one eye and then the other? Can you quantify the difference? Is the motion apparently twice as much as it was before? Five times as much? Write your answers below. The motion of the pencil was more signiAicant when I moved it to 25 cm. I’d say the motion of _the pencil is twice as much as it was when it was at 50 cm.

  1. Now move the pencil to about the 100 cm end of the paper meter stick or as far as it can get_ from your eyes. Again quantify the motion compared to when the pencil was at the 50 cm position. _At 100 cm, the shift of the pencil increased signiAicantly and was noticeable.
  2. The pencil at 50 cm is shown below. Explain how the drawing would change for the 100 cm_ and 25 cm situations. In particular describe how the parallax angle, the angle between the two sight lines, changes as the distance of the pencil from the eyes changes. Does the angle double when the distance doubles? To perform this task use the insert shapes feature in your word program and draw the appropriate lines in the Aigure below. Use different colors for the two cases. Pencil 50 cm from eyes. Distant object or eyes^ wall

25cm 100cm

  1. α-Cygni (Deneb) is the upper left star in the Summer Triangle (see photo below) and the main star in the Swan. Its apparent magnitude is 1.25 and the distance to Deneb is 993 parsec. Calculate the absolute magnitude for Deneb. What does this tell you about the nature of Deneb? 993 = 10 ^ (1.25 - M +5)/

Part IV – How big is the universe?

Realm of the Earth and Moon [30 points]

We will begin by shrinking the Earth to a two – inch diameter circle, then scaling other objects close to earth to see how they compare.

Earth has a diameter of approximately 12756 km. We will use the metric system measurements for all astronomical objects today. Since one inch is 2.54 cm, it would be more consistent with the metric system to think of this a 5 cm universe. However, since the United States still doesn’t use the metric standard, most of us are used to thinking in terms of inches and feet and have a better idea of what an inch is (about the length of your thumb from top joint to tip) than what a cm is. Now do the math. In this realm 2 inches = 12756 km and the Moon is 3475 km in diameter, so how many inches in diameter would it be in our two inch Earth/Moon system? or, putting in the numbers

so inches (the km units cancel).

In other words the moon’s diameter is about .54 inches, or about ¼ the diameter of the Earth. Do the same process to calculate the distance the Moon is from Earth. In this case x is the distance of Moon from Earth in the model, but you will now need to use the fact that the Moon is about 384403 km away from Earth on average when measuring from the centers of Earth and Moon. Now we have: Doing the math we get x = 2 (384403/12756) or 60 inches. Since 1 foot = 12 inches that is about 5 feet away. Other sizes and distances In this model, where the Earth is 2 inches across, the Sun is about 18 feet in diameter (imagine a round, glowing mini-van!) and is 1800 feet, or about 6 football Uields away from Earth

Realm of the Sun

The next stage of this exercise is to shrink the Sun down to a 2 inch diameter. The Sun is approximate 1400000 km in diameter. Write this number in scientiUic notation.

  1. Sun’s diameter in scientiAic notation: 1.4x10^ We use the same routine to calculate Earth’s size in this model: Size of ear th in 2 − inch model Size of ear th in kilometers = size of Moon in 2 − inch model Size of Moon in kilometers 2 in 12756 km = x 3475 km x = 2 ( 3475 12756 ) 2 inches 12756 km = x 384403 km
  • (^) Distance to Farthest Galaxies Observed by Hubble Telescope - 4 miles (6.5 km). In the Hubble image of the "Ultra Deep Field" almost all the fuzzy spots of light are distant galaxies. Because light takes time to travel through space, we see the farthest of these not as they are now, but as they were 12 billion years ago.
  • (^) Size of the Whole Universe? - No one knows...it could be inUinite.
  • (^) Light Travel Time - It would take 100,000 years for a beam of light to cross our galaxy and 2. million years for light to travel from the Andromeda Galaxy to us.

Conclusion questions [Grade points: 15]

1. The absolute magnitude, M, is deAined as the apparent magnitude a star would have if it were placed 10 parsecs from the Sun. But wouldn’t it be more correct to measure this distance from the Earth? Does it make a difference whether we measure this distance from the Sun or from the Earth? _The answer is yes given how far distant the two places are from one another.

  1. Explain how this exercise has impacted your thinking about the size and importance of Earth_ in the universe. _Completing the exercise has altered my perspective on the size and importance of Earth. This exercise emphasized just how tiny our planet appears. It is easy to underestimate the true extent of our planet’s insigniAicance.
  2. Given what you have learned in the 2-inch universe exercise, what do you think the likelihood is of interstellar travel by humans in spaceships? Explain your reasoning. I think navigating the immense distances could be difAicult because our current capabilities do not travel to such vast distances._