How to Measure Earth?

Summary

In 245 BC, Eratosthenes accurately calculated Earth's circumference using simple tools like a vertical stick and the angle of the noonday sun. Dave Cederberg from Purdue University's Saturday Morning Astrophysics Heritage teaches viewers how to replicate this experiment. By measuring a stick's shadow at solar noon and comparing it with another location's shadow, one can estimate Earth's size. The video offers various methods to ensure the stick's verticality and measure the shadow accurately, encouraging participation in the Eratosthenes project and sharing of results.

Takeaways

• 📅 In 245 BC, Eratosthenes calculated the Earth's circumference with remarkable accuracy.
• 📍 The experiment took place in Northern Egypt, specifically in Alexandria.
• 🎓 Eratosthenes was a polymath known for his contributions to mathematics, music, philosophy, and geography.
• 🌐 The method involved using a vertical stick, a measuring tool, and the position of the sun at solar noon.
• 📏 To replicate the experiment, one needs a vertical stick, a measuring tape or meter stick, and the sun's position at solar noon.
• ☀️ Solar noon is the time when the sun is at its highest point in the sky, which can be determined with a Google search.
• 🔍 The experiment requires aligning the pole vertically and measuring the shadow's length at solar noon.
• 📏 The shadow's length is measured from the pole's edge to the shadow's outer edge, with precision to the nearest 0.1 centimeter.
• 🔄 Various methods are shown to ensure the pole is vertical, including using a bubble level, a photographic tripod, a string and weight, or a cardboard structure.
• 📊 The experiment requires data from two locations to calculate the Earth's circumference, with additional data available for comparison.
• 🔗 The video description contains a link to resources for the complete lesson, teacher materials, and a study guide for the Eratosthenes project.

Q & A

Who was the mathematician, musician, philosopher, and geographer that calculated the circumference of the Earth in 245 BC?

The mathematician, musician, philosopher, and geographer who calculated the circumference of the Earth in 245 BC was Eratosthenes.

What tools did Eratosthenes use to calculate the Earth's circumference?

Eratosthenes used a vertical stick, a measuring tape or meter stick, and the Noonday Sun to calculate the Earth's circumference.

How did the shadow's length and the Noonday Sun help Eratosthenes in his calculations?

The shadow's length and the Noonday Sun helped Eratosthenes by allowing him to compare the angles of the sun's rays in different locations, which he used to calculate the Earth's circumference.

What is solar noon and why is it important for this experiment?

Solar noon is when the sun is at its highest point in the sky, which is important for the experiment because it provides the most accurate shadow length measurements for calculating the Earth's circumference.

How can one determine the exact time of solar noon at their location?

One can determine the exact time of solar noon at their location with a simple Google search.

What is required to ensure the pole used in the experiment is vertical?

To ensure the pole is vertical, one can use a bubble level, a photographic tripod with a string, a wooden dowel with a hook and string, or a cardboard structure with a vertical stick.

How should the length of the shadow be measured during the experiment?

The length of the shadow should be measured from the edge of the pole to the outside edge of the shadow, to the nearest 0.1 centimeter.

Why is it necessary to have two locations to complete the calculations in this experiment?

Having two locations is necessary to compare the shadow lengths and the angles of the sun's rays, which is crucial for calculating the Earth's circumference.

What resources are provided for those who want to participate in the Eratosthenes project experiment?

Participants in the Eratosthenes project experiment are provided with a link to a complete written lesson, teacher resources, a data study guide, and photos of others doing the experiment.

How can one share their results and ask questions about the Eratosthenes project experiment?

One can share their results and ask questions by contacting the organizers through the provided link in the video description.

Outlines

00:00

🌏 Eratosthenes' Experiment on Earth's Circumference

In 245 BC, Eratosthenes, a mathematician, musician, philosopher, and geographer from Northern Egypt, calculated the Earth's circumference with remarkable accuracy. He used a simple method involving a vertical stick, a measuring tool, and observations of the Noonday Sun. Dave Cederberg from Purdue University's Saturday Morning Astrophysics Heritage introduces a way to replicate Eratosthenes' experiment. To perform this, one needs a vertical stick, a measuring tape or meter stick, and the Noonday Sun. The experiment involves measuring the shadow cast by the stick at solar noon, the time when the sun is at its highest point in the sky. Solar noon can be determined with a Google search. The stick must be aligned vertically, and the shadow's length must be measured accurately. The video provides multiple methods to ensure the stick's vertical alignment and to measure the shadow. The experiment can be completed with the help of a link provided in the video description, which offers a complete lesson, teacher resources, and a data study guide.

Keywords

💡Eratosthenes

Eratosthenes was a Greek mathematician, poet, geographer, and astronomer who is renowned for calculating the circumference of the Earth. In the video, he is central to the theme as his method of calculating Earth's circumference is the historical context for the experiment being demonstrated. The script describes how Eratosthenes used the shadow cast by a vertical stick at solar noon to determine the Earth's size, which is a key part of the educational content.

💡Circumference

Circumference refers to the distance around a closed curve or the perimeter of a circle or any other round shape. In the video, the main experiment revolves around calculating the Earth's circumference, which is a fundamental concept in geography and astronomy. The script explains how Eratosthenes used shadows to estimate this value, showcasing the practical application of this term.

💡Vertical Stick

A vertical stick is a straight object that is positioned perpendicular to the ground. In the context of the video, a vertical stick is essential for the experiment as it casts a shadow at solar noon, which is then used to calculate the Earth's circumference. The script provides various methods to ensure the stick is vertical, highlighting its importance in the measurement process.

💡Noonday Sun

Noonday Sun refers to the position of the sun when it is at its highest point in the sky, typically around midday. The video script emphasizes the importance of taking measurements at solar noon because the sun's position is crucial for casting accurate shadows. This term is integral to the timing of the experiment and the accuracy of the results.

💡Shadow

A shadow is a dark area where light is blocked by an opaque object. In the video, the length of the shadow cast by a vertical stick at solar noon is measured to determine the Earth's circumference. The script describes how the shadow's length changes with the sun's angle and the location, which is a key factor in the experiment.

💡Measuring Tape

A measuring tape is a flexible ruler used to measure length or distance. In the video, a measuring tape or meter stick is necessary to accurately measure the shadow's length, which is a critical step in Eratosthenes' experiment. The script mentions the need for precision in measurement, illustrating the importance of this tool.

💡Solar Noon

Solar noon is the moment when the sun reaches its highest point in the sky, which varies by location. The video script instructs viewers to measure the shadow at solar noon for accuracy. This term is crucial for timing the experiment correctly and is used to ensure that the sun's position is optimal for casting a precise shadow.

💡Geography

Geography is the study of Earth's landscapes, peoples, places, and environments. The video's theme of calculating the Earth's circumference falls under the domain of geography. The script connects the historical method of Eratosthenes with modern educational practices, demonstrating the relevance of geography in understanding our planet.

💡Astronomy

Astronomy is the scientific study of celestial objects, space, and the physical universe as a whole. The video's focus on the sun's position and its relation to shadows is an application of astronomical principles. The script uses astronomy to explain the scientific basis behind the experiment, linking it to broader astronomical concepts.

💡Experiment

An experiment is a scientific procedure undertaken to make a discovery, test a hypothesis, or demonstrate a known fact. The video script outlines an experiment based on Eratosthenes' method to calculate the Earth's circumference. This term is central to the video's educational purpose, as it encourages viewers to engage in hands-on learning.

💡Educational Content

Educational content refers to material designed to inform or instruct, often in an academic or skill-building context. The video script is rich with educational content, providing a historical lesson on Eratosthenes and a practical guide to performing his experiment. This term encapsulates the video's goal of teaching viewers about both the scientific method and specific geographical concepts.

Highlights

In 245 BC, Eratosthenes calculated the Earth's circumference with surprising accuracy using a simple method.

The method involves using a vertical stick, a measuring tape, and the Noonday Sun to measure shadows.

Dave Cederberg from Purdue University explains how to replicate Eratosthenes' experiment.

The experiment requires a vertical stick, a measuring tape, and the measurement of a shadow at solar noon.

Solar noon is when the sun is at its highest point in the sky, which can be determined with a Google search.

The pole must be aligned vertically, which can be achieved with a bubble level or other methods shown.

The length of the shadow cast by the pole is measured at solar noon.

Multiple ways to ensure the pole is vertical are demonstrated, including using a tripod and a string.

The shadow's length is measured from the edge of the pole to the outside edge of the shadow.

The measurement should be taken to the nearest 0.1 centimeter for accuracy.

Two locations are needed to complete the calculations for the Earth's circumference.

The video provides a link to other locations for comparison and to complete the calculations.

A complete written lesson, teacher resources, and a data study guide are available for the experiment.

The video encourages viewers to share their results and questions, and to send photos of their experiments.

Transcripts

the year 245 BC the place Northern Egypt

a curious mathematician musician

philosopher and geographer calculated

the circumference of the earth to

surprising accuracy armed with a

vertical stick a meter stick or

measuring tape and the Noonday Sun you

can do it too

hi this is Dave cederberg from Purdue

Saturday morning astrophysics Heritage

the knees in the great city of

Alexandria Egypt learned that the shadow

cast by an object in the Noonday sun was

longer or shorter than the shadow cast

in a more Northern or Southern location

based on the comparative difference

between the angles of the sun's rays and

the distance between the two locations

eratosthenes found a way to calculate

the circumference of the Earth

I'm going to show you how to repeat

eratosthenese experiment and you can do

it for yourself

in order to do this experiment you will

need some sort of vertical stick or pull

you'll need a measuring tape or meter

stick a way to measure the length of the

Shadow and you'll need the Noonday Sun

you will need to know the length of the

pole and the length of the shadow that

it casts you'll want to take your

measurement at exactly solar noon now

solar noon is when the sun is at its

highest point in the sky you can figure

out solar noon at your location with a

simple Google search

at solar noon you want to align the pole

exactly vertically we'll show you

multiple ways to do this on this pole we

have a little bubble level on the top so

we can tell when it's perpendicular to

the ground you need a level surface on

the ground and at the right time solar

noon measure the length of the Shadow

[Music]

from the edge of the pole to the outside

edge of the Shadow and in this case we

have about 39.5 centimeters measure the

length to the nearest 0.1 centimeter

we'll show you another way to create a

vertical pull we have a photographic

tripod I have a wooden dowel with the

hole drilled through it and a string to

hang it from the handle of the tripod we

want to make sure that it just barely

touches the ground hangs vertical and

then we can measure the shadow

here's yet another way to create a

vertical pole we have a wooden dowel rod

a hook a string and a weight

when the string hangs parallel to the

rod we know that it's vertical we're

using gravity

and we can then measure the shadow

all right and here's still another way

we've taken some cardboard squares or

triangles glued them together to make a

corner and glued a vertical stick in the

corner if I set this down on level

ground it'll be vertical and I can

measure the shadow

just like your attached the knees you

will need two locations to complete your

calculations

you have your own data once you record

your data and upload it we'll provide

you a link to other locations that you

can use to compare and complete your

calculations there is a link in the

description of the video to give you

access to the complete written lesson

teacher resources data study guide and

photos of others doing the experiment we

hope you have fun with our eratosthenes

project experiment share your results

let us know if you have any questions

and send us photos if you can