24 Experiment AS02: Eratosthenes 23 Eratosthenes Experiment AS02 Name Lab Section Objective

24 Experiment AS02: Eratosthenes


Eratosthenes Experiment AS02


Lab Section


To estimate the size of the Earth


View of the Horizon Sunglasses

Calculator Mat or blanket

Stopwatch or Timer App


The ancient Greeks not only knew the Earth was round, but they were able to measure its size. The first fairly accurate determination of Earth’s diameter was made about 2400 years ago by Eratosthenes (276–194 BCE), a Greek living in Alexandria, Egypt. Only about 50 years after Aristotle described evidence that supported the idea that the Earth was spherical, Eratosthenes figured out how to measure its circumference. Using shadows, geometry, and observations of the Sun the size of the Earth could be determined with surprising accuracy.

Eratosthenes was told that on the first day of summer at Syene, Egypt, sunlight struck the bottom of a well at noon. This meant that the Sun must be directly over the well. Otherwise, the well would have a shadow projected down it. At the same time and date in Alexandria, Eratosthenes observed the shadow of a column. He saw that the column produced a shadow. Therefore, the Sun was not directly overhead, but was slightly to the south. This slight angle made it so that the Sun’s rays made an angle equal to about 7°.

Because the Sun’s rays striking the two cities are parallel to one another, why would the two rays not make the same angle with Earth’s surface? Eratosthenes reasoned that the curvature of the Earth meant that “straight up” was not the same in the two cities. The measurement of the angle in Alexandria, allowed him to figure out the size of Earth.

If the angle of the Sun was different by 7° in Alexandria, the city must be 1/50 of Earth’s circumference north of Syene (7ׄ°/360° ≈ 1/50). Alexandria had been measured to be 5000 stadia north of Syene. (The stadium was a Greek unit of length, derived from the length of the racetrack in a stadium.) If the common Olympic stadium was used, this resulted in Eratosthenes’ estimates being 20% too large. However, according to another interpretation, he used a stadium equal to about 1/6 of a kilometer.

Part A: Ancient Measurements

If Alexandria is north of Syene by 1/50 of the circumference of the Earth, and this is equal to 5000 stadia, what is the total circumference of the Earth in stadia?

Circumference of the Earth

250,000 stadia

If the stadia used by Eratosthenes is equal to 1/6 of a kilometer, what is the circumference of the Earth in kilometers?

Circumference of the Earth

41,666.6 km

What is the circumference of the Earth by modern measurements? (Look it up!) How close was Eratosthenes’ estimate to modern measurements?

Modern Measurements

% Difference

40,075 km

3.97 %

Part B: Observations of the Sun

In this exercise, you will utilize basic concepts in trigonometry and geometry to derive the radius of the Earth. You will observe the Sun setting on the western horizon at two different markers and use a timer to time the difference between the two settings. Alternatively, if you are an early riser, you can do a similar measurement during sunrise from the eastern horizon. This exercise requires a relatively clear day and should be performed outdoors. It can be performed indoors if you have an unobstructed view of the horizon. You will need sunglasses, a mat or blanket to lay on, and a timer (stopwatch or an app on your phone).

As with any activity that involves being outside on a sunny day, please exercise common sense and never look directly at the midday Sun. This can cause serious eye damage. This exercise will require watching the sunrise or sunset five times, so you will need a full five days (or more, depending on weather conditions) to complete the exercise. Plan your time accordingly.

Record your standing height, in meters, in the data table below. For reference, 1-meter equals 39.37 inches.

Look up the local sunset (or sunrise) times. A great source is www.timeanddate.com. If you visit this site, go to the Sun & Moon tab towards the top and then search your city on the next page. The website will provide sunrise and sunset times for your area. You will need to begin this experiment a few minutes before sunset (or sunrise).

Write down your location (city/town), date, and local sunset (or sunrise) time in the table below.

Option 1: Sunset Instructions

Just before sunset, lie down on the ground (on a mat or blanket), put on sunglasses, and wait for sunset.

As the Sun sets, watch for the last visible edge of the Sun to go below the horizon, start your timer, and immediately stand up. (The Sun, or a portion of it, should be visible again.)

When the Sun sets completely again, stop your timer. Convert this time to hours and record in the table below. (1 hour = 60 minutes = 3600 seconds.)

Option 2: Sunrise Instructions

Just before sunrise, put on your sunglasses, stand on your mat or blanket, and wait for sunrise.

As soon as you see the first edge of the Sun appear, start your timer, and immediately lie down on the mat. (The Sun should no longer be visible.)

When you again see the edge of the Sun begin to rise over the horizon, stop your timer. Convert this time to hours and record in the table below. (1 hour = 60 minutes = 3600 seconds.)

You have now measured the time it took the Earth to rotate by an angle θ. The Earth takes 24 hours to rotate 360°. During the time you measured with your timer, the Earth rotated by θ°. Therefore:


The angle θ forms a right triangle with its adjacent sides R and R+h, such that R+h is the hypotenuse. In this exercise, R is the radius of the Earth, and h is your standing height. A trigonometric property of θ is


If we solve this equation for R, which takes a few algebraic steps, we have


Use this equation, and your value for θ, to calculate the radius of the Earth. Your answer should be in meters. Record this in the table below.

Repeat this process for a total of five measurements. (Five different days of sunrises or sunsets. Keep in mind there is one sunrise and one sunset each day.)

How Long Should Your Measurement Take – Sample Calculation

Let’s take a moment to make sure that whatever time we record on our stopwatches for the parts above make sense. Should your measurement take a minute? A second? 30 seconds? To do this we will start with the last equation from the previous page, assume a height for our example student, use the known radius of the Earth, and work backwards.

Let’s assume your height is 5’9”. If we convert this to meters (which can quickly be done with a Google search if you don’t have the conversion factor conveniently at hand), we find our height as

Equation (3) on the previous page allows us to find the radius of the Earth based on someone’s height and the angle which the Earth rotates in a certain amount of time. Since we know the radius of the Earth (6.378 x106 m), we can rearrange this equation and solve for the angle θ. There are a few steps to solve this, and the final result is


Since we know both R and h, we can solve for θ. This value for θ can be used in equation (2). Below, is equation (2) solved for the time (in hours) that would elapse.


However, this gives our estimate in hours. To convert to second, just multiply your answer in equation (5) by 3600 (that’s the number of seconds in one hour).

To reiterate the sample calculation process, enter the value for R (6.378 x106 m) and h (1.75 m) into equation (4) and solve for θ. Put this value in equation (5) and solve for T. Finally, multiply your value for T by 3600 seconds.

Sample Calculation Estimate

Sample Calculation Estimate

3.67 hours

13,212 seconds

You now have an estimate for how long your measurements should take. This will give you an idea if your measurements make sense while doing this experiment. If you record measurements that are much shorter or way longer than your estimate, you should evaluate how you did the experiment and try again.





Time of Sunset/Sunrise

Time Elapsed (hours)


Salisbury, Md


6:01am sunrise


Salisbury, Md


8:16pm sunset


Salisbury, Md


6:03am sunrise


Salisbury, Md


8:14pm sunset


Salisbury, Md


6:05am sunrise



Time Elapsed (hours)

Θ (°)

R (m)






Average value of R


Calculate the percent error between your result of R and the accepted value you looked up earlier.

Modern Measurements

% Difference



Artificial intelligence applications There are numerous, real-world applications of AI systems today.

Artificial intelligence applications

There are numerous, real-world applications of AI systems today. Below are some of the most common examples:

Speech Recognition: It is also known as automatic speech recognition (ASR), computer speech recognition, or speech-to-text, and it is a capability which uses natural language processing (NLP) to process human speech into a written format. Many mobile devices incorporate speech recognition into their systems to conduct voice search—e.g. Siri—or provide more accessibility around texting. 

Customer Service:  Online chatbots are replacing human agents along the customer journey. They answer frequently asked questions (FAQs) around topics, like shipping, or provide personalized advice, cross-selling products or suggesting sizes for users, changing the way we think about customer engagement across websites and social media platforms. Examples include messaging bots on e-commerce sites with virtual agents, messaging apps, such as Slack and Facebook Messenger, and tasks usually done by virtual assistants and voice assistants.

Computer Vision: This AI technology enables computers and systems to derive meaningful information from digital images, videos and other visual inputs, and based on those inputs, it can take action. This ability to provide recommendations distinguishes it from image recognition tasks. Powered by convolutional neural networks, computer vision has applications within photo tagging in social media, radiology imaging in healthcare, and self-driving cars within the automotive industry.  

Recommendation Engines: Using past consumption behavior data, AI algorithms can help to discover data trends that can be used to develop more effective cross-selling strategies. This is used to make relevant add-on recommendations to customers during the checkout process for online retailers.

Automated stock trading: Designed to optimize stock portfolios, AI-driven high-frequency trading platforms make thousands or even millions of trades per day without human intervention.[supanova_question]

Name: Nikia S. Greene Degree Program: Health Services Administration, AAS MyCred Link:

Name: Nikia S. Greene Degree Program: Health Services Administration, AAS

MyCred Link: http://mycred.com/p/7281474488/NikiaGreene

CAPS265 – Articulation Worksheet

Program/institutional outcome

Course name

(where outcome was met)

Brief description of the course portfolio project, including summary of how outcome was met

Demonstrate an understanding of patient/client/customer service needs within the continuum of health and human services environments.

Organizational Behaviors & Leadership

I did a report of GRANTS. My main objective was to put across the importance of learning CPR and first aid because these two are the main life saving strategies. CPR assists in maintaining blood flow to the brain and heart while first aid ensures a client is stable before presenting them to a healthcare provider.

Demonstrate ethical and legal communication techniques specific to the health and human services environments.

Ethics in Health & Human Services

I did a detailed case note for a client. The case involved observing the client, confirming that the issue is there and developing strategies of solving the issue.

Use current technology from clinical, financial, and operational systems to support decision-making processes.

Health Information Systems

I did a report that explained the importance of having a information system in a healthcare facility. The information system is an important technology in healthcare facilities at aid in clinical, financial and operational activities within the facility.

Function as a team member to support the goals and objectives of an integrated health care system.

Career Development II, Theory and Practice

I was involved in a project where I played the role of a leader. The project was to demonstrate how a team leader should integrate their leadership skills to meet the objectives of the organization.

Analyze and apply contemporary knowledge and skill sets to perform diverse administrative responsibilities in health and human services environments.

Funding Health and Human Service Organizations

I did a report of creating a healthcare program on wellness that would help clients clear their minds and relieve fatigue. I encouraged clients to visit healthcare professionals more often as a way of adopting healthy behaviors.

Utilize appropriate current technology and resources to locate and evaluate information needed to accomplish a goal, and then communicate findings in visual, written and/or oral formats.

Research and Writing

I did a report on communication as a case manager in mental health. The report emphasized the importance of communication in improving mental health of clients. The communication report aimed at demonstrating how information is crucial in using strategies that help accomplish organizational goals. Information depend mostly on technology, thus in my report I showcased various technological resources that can make communication more effective.

Transfer knowledge, skills and behaviors acquired through formal and informal learning and life experiences to new situations.

Career Development III

I did a research paper of how various cultural practices are a determinant of health in today’s world. Various cultural factors influence the state of health of the general population. Through the research paper I was able to acquire formal learning experiences that were important in coping in new situations.

Employ strategies for reflection on learning and practice in order to adjust learning processes for continual improvement.

College Mathematics

I completed a presentation of loan budgeting. The presentation gave reason why it is important to lend students loan other than offering them financial aid.

Follow established methods of inquiry and mathematical reasoning to form conclusions and make decisions.

College Mathematics

I presented a PowerPoint presentation of the important of students’ loan over financial aid. The PowerPoint demonstrated how mathematics can be used to make decisions. From the analysis of student loans and financial aid, I managed to conclude that students issued with loans are better than those who receive financial aid.

Participate in social, academic, and professional communities for individual growth and to function as a citizen of a multicultural world.

Career Development I

I prepared a speech about myself in regards to skills and competence that would allow me to express myself better. The personal speech allowed me to interact with the social world in expressing my professional achievements and how it benefit the multicultural world.[supanova_question]

Select a recently published article regarding the Six Sigma continuous improvement strategy.

Writing Assignment Help Select a recently published article regarding the Six Sigma continuous improvement strategy. Summarize article and offer your analysis and opinion of the information presented per the rubric below. Points will also be awarded for in-class discussion on the 1st night of class.

Six Sigma Green Belt – Article Summary

If the answer is no to the following question, you will receive a zero on this assignment.

The article chosen is related to the topic of Six Sigma, is at least one page in length, and is dated between January 1, 2013 and the present.

Yes____ No_____





Summary of the article

8 points

All main ideas from the article are included and specific ____ (4 pts.)

Clear examples and facts from the article are presented to support the main ideas ___ (4 pts.)

Analysis and Opinion

12 points

A statement of your opinion of the articles main points is included along with a statement describing how the article relates to the assigned reading.___(4 pts.)

Key ideas he/she agreed with and/or disagreed with are presented ___ (4 pts.)

Presented findings of the summary and the analysis/opinion to the class at assigned time ____ (4 pts.)


3 points

Article title, author, and electronic link are stated at top of summary ___ (1 pts.)

The document is word processed in Times New Roman, 12 point font ____ (2 pts.)


2 points

The text is written with no errors in grammar (.5 pt.) ____

The text is written with no errors in punctuation (.5pt.)___

The text has no spelling errors. (1 pt.) ____ [supanova_question]

Review Box 6.1 in Chapter 6 of your textbook, which offers

Review Box 6.1 in Chapter 6 of your textbook, which offers evidence supporting the importance of social worker and client relationships in social work practice. Generate a list of the most important things a social worker can do to be effective in a relationship. Discuss how they might achieve these elements with their clients.

Hint: Your discussion should include references to theory, evidence-based practice and interventions, and include concepts from the textbook, articles and videos assigned in this module. Be sure to review scholarly literature in developing your primary posting.[supanova_question]


1. Article title:  


Permalink: http://ezproxy.columbiacollege.bc.ca/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=143576390&site=eds-live

State the author’s main claim in one sentence in your own words:  the author’s main claim in this article is about the analyses and solutions of the employment crisis that people face during covid.

Briefly explain why you think this article is helpful to your paper.:  this article is helpful to me because this relates to my topic about the negative effects of covid with its solutions and analyses about the employment crisis during the pandemic.
Mental health solutions for domestic violence victims amid COVID-19: a review of the literature.

Author(s):      Ioan, Cindrea

Magazine or newspaper title:  studies in business and economics

Publication date:  April 2020

2. Article title: 

Mental health solutions for domestic violence victims amid COVID-19: a review of the literature.


Author(s):   Su, Zhaohui; McDonnell, Dean; Roth, Stephanie; Li, Quanlei; Šegalo, Sabina; Shi, Feng; Wagers, Shelly
Magazine or newspaper title: globalization and health
Publication date:  6/28/2021       
State the author’s main claim in one sentence in your own words: authors’ main idea in this article is about mental health issues faced by people due to domestic violence and the increasing rate of mortality due to covid and the solutions to cope with this violence and mental issues.
Briefly explain why you think this article is helpful to your paper: I think this article is helpful for me because it clearly explains the negative health effects of covid with its possible solutions.

3. Article title:      

Reported health and social consequences of the COVID-19 pandemic on vulnerable populations and implemented solutions in six West African countries: A media content analysis

Author(s):  Saalim, Khalida; Sakyi, Kwame S.; Fatema-Tuz-Zohra; Morrison, Emily; Owusu, Prince; Dalglish, Sarah L.; Kanyangarara, Mufaro.
Magazine or newspaper title:  PLoS ONE. 
Publication date:    6/16/2021     

State the author’s main claim in one sentence in your own words: the main claim of authors in this article is about the consequences of covid 19 on the population of different countries with the solution of those problems and the analysis of media about this pandemic.

Briefly explain why you think this article is helpful to your paper: this article is useful to me to use in my research because it is related to the question asked by the instructor for the research paper and it explains the solutions of covid 19 effects on different countries and the analysis done by the media by taking into consideration, all the effects of this pandemic on different 6 African countries.[supanova_question]