Overview

Not only is the Universe unfathomably large, it also contains things which are unfathomably small. In this lab, we will explore the scale of things from the Planck Length to the Observable Universe.

Science Question

Where do humans fall on the cosmic distance scale?

Materials

• One long hallway or outdoor space (at least 50 m)
• Accompanying pictures of the 27 scale objects scales_Lab1
• A calculator
• A 50 m measuring tape

Math

If we put all of these things on a normal scale together, the small things would all end up on top of each other. Instead, we will use what is called a “logarithmic scale” to represent sizes. A log (logarithmic) scale is when you count how many zeros it takes to write out a number instead of the number itself. For example, the city of Tacoma is about 10,000 meters across. On the log scale, we would count how many zeros are between the first digit (1) and the decimal. There are four zeros there, so we could write the diameter of Tacoma as “10^4 meters”. It’s the four that we are really interested in there.

Let’s do another example. The average cell in your body is about 0.00001 m across. For numbers smaller than one, we count how many times you have to move the decimal to get to the end: 5. Then we write this number as 10^-5 meters. If the number is smaller than one, it gets a negative sign when we write it as an exponent.

This is how we will organize our scale. At one end of the soccer field, we will put the smallest possible thing (10^-35 m), and at the other end, the largest possible thing (10^26 m). Then, we will use math to calculate where everything in between goes.

Example

One end of the hallway (0 meters) corresponds to the Planck Length (10^-35 meters). The other end (50 m) corresponds to the size of the observable universe (10^26 m). Let’s use this equation to find out where the human red blood cell (10^-5 m) goes:

(X + 35)/61 * 50 = L

X is the exponent of the number we are interested in: -5. -35 is the exponent of the “lower bound” of our range of numbers, and 61 is the difference between the upper and lower bounds (26 – -31 = 61). The 50 corresponds to the length of the hallway or other space.

(-5 + 35)/61 * 50 = 27.8 meters

Starting from the “0 meters” side of the field, we know that the location of the size of the human cell must be at 13.9 meters.

Activity

Your group will be given 4-7 different items along the cosmic distance scale listed below. Use the equation above to calculate where along the soccer field they should go.

Items

1. Planck Length (10^-35 m): The theoretical smallest length anything can be.
2. Quark (10^-18 m): a subatomic particle which is believed to be the fundamental building blocks of protons and neutrons.
3. Proton (10^-15 m): one of the constituents of atoms. Has a positive charge to balance out the negative charge of the electron. Usually found with neutrons.
4. Atom (10^-11 m): The fundamental unit of matter which makes up 4% of things in the Universe.
5. Amino Acid (10^-10 m): A simple molecule known as the “building blocks of life”. Amino acids come together to form proteins, the basis of cells.
6. Protein (10^-9 m): A large a versatile type of molecule which serves a wide range of roles in the cell
7. Virus (10^-7 m): The smallest organism. Carries DNA to infect other organisms but is not technically considered to be “alive”
8. Bacteria (10^-6 m): A single-celled organism
9. Red blood cell (10^-5 m): Some of the smallest cells in your body which make up your blood
10. Hair (10^-4 m): The stuff that grows out of your head
11. Blood vessel (10^-2 m): Carries blood around your body, delivering oxygen and removing waste materials from your cells
12. Apple (10^-1 m): A fruit
13. Human (10^0 m): You and I
14.  Soccer Field (10^2 m): What we are doing this activity on if it’s not cold + raining
15. City of Tacoma (10^4 m): The city where Tacoma Community College is located
16. United States (10^6 m): The country we live in
17. Diameter of Earth (10^7 m): The planet we live on
18. The Sun (10^8 m): The star our planet orbits
19. Solar System (10^10 m): The sun and all of its planets, including Earth
20. Biggest Star in the Milky Way (10^12 m): UY Scuti is the biggest star yet found
21.  Globular Cluster (10^18 m): An old group of gravitationally bound stars (100,000 – 1,000,000 stars)
22. Dwarf Galaxy (10^19 m): A small galaxy which is often found orbiting another. The Milky Way has two major dwarf galaxies.
23. The Milky Way (10^20 m): The galaxy we live in
24. The Local Group (10^22 m): The cluster of galaxies the Milky Way belongs to
25. Virgo Supercluster (10^23 m): The supercluster of galaxies the Local Group belongs to
26. Hercules-Corona Borealis Great Wall (10^25): The largest structure of galaxy superclusters in the observable universe
27.  The observable universe (10^26 m): The universe as far as we can see.

Questions

1. Where do humans fall on the cosmic distance scale?
2. How many times larger is a virus than an atom?
3. Roughly how many apples could stretch across the United States?
4. How many of our Sun could fit inside UY Scuti?
5. Based on their sizes, how many quarks do you think it takes to make up a proton
6. How much bigger is the Hercules-Corona Borealis Great Wall than the Planck Length?