Topic: The shape and size of Earth

Target group

First‑grade student of high school and technical school (basic programme)

Core curriculum

II. Earth in the Universe: Earth as a planet, consequences of Earth's movements, celestial bodies, Solar System, construction of the Universe. Pupil:

1) characterizes the Earth as a planet of the Solar System;

The general aim of education:

Learn the shape and size of Earth.

Criteria of success

• explain the method to determine Earth’s size, used by Eratosthenes;

• calculate the circumference of the planet using the above method;

• explain the concept of a spheroid and a geoid;

• explain the relation between Earth’s shape and its rotation.

Teaching aids

• computers with internet access;

• globes or world maps (at least 5‑6 per class);

• multimedia resources available under “The shape and size of Earth” in the e‑textbook;

• interactive whiteboard/blackboard, marker/chalk.

Methods / forms of work

• the problem‑solving methods: structured interview, discussion;

• the demonstrating method: presentation;

• programmed learning: via computer, e‑textbook;

• practical learning: practical classes;

• forms of work: individual work; work in groups; collective work.

Lesson plan overview (Process)

Introduction

1. Before class, the teacher asks students to become familiar with the method to determine Earth’s size, used by Eratosthenes, described under “The shape and size of Earth”.

2. During the introduction, the teacher defines the purpose of the lesson, informing students about its planned course.

3. The teacher then writes the topic of the lesson on a traditional board or an interactive whiteboard. The students write it in their notebooks.

Realization

1. A short recalling of the method to determine Earth’s size, used by Eratosthenes. The teacher explains the pictures in the illustration attached under “The shape and size of Earth” and describes the calculations that were used to determine Earth’s circumference.

2. Work in groups.

• By using a globe or a world map, each group compares the angle of the direction of the sunrays in Aswan at noon on the day of the June solstice, with the direction of the sunrays in Kiev or another European city close to the same meridian as Aswan, on the same day and at the same time.

• After that, the students measure the distance between these two places, e.g. via Google Maps. The teacher monitors the situation in class, helping students struggling with the task.

• Following the calculations of Eratosthenes, students calculate Earth's circumference based on data obtained for Aswan and the selected European city.

3. Discussion on the whole class forum, during which the correct way of performing the exercise and the reasons for the discrepancies between the groups are discussed. Groups that performed the task incorrectly write down the correct method.

4. A short description of Earth’s shape. The teacher shows pictures in the abstract and the animation explaining the influence of centrifugal force on the shape of a rotating celestial body.

5. Individual work - the students perform the interactive exercise: Identify true statements and Match the effect to its cause. The purpose of the exercises is to check, to what extent students have learned about the size and shape of Earth.

Summary

A short summary of the lesson to systematize and solidify information, clarify any ambiguities and complete the notes.

The following terms and recordings will be used during this lesson

Terms

Texts and recordings

The Earth’s shape and size

Upon thousands of years of perceiving the Earth as a flat object, people finally concluded (as a result of many observations, calculations and reasoning attempts) that our planet is a sphere or a solid closely resembling a sphere. The first successful attempt to determine the Earth’s size was completed by Eratosthenes, a philosopher, a geographer, an astronomer and a mathematician of Greek origin, living most of his life in Egypt. He compared lengths of shadows cast at noon during the summer solstice in two Egyptian locations which, as he had presumed, lied on the same meridian: Syene (modern Aswan, south Egypt) and Alexandria (at the shore of the Mediterranean Sea). When sun rays lit the bottom of a deep well in Aswan (which means they were perpendicular to the Earth’s surface), in Alexandria they fell under the angle of 7.2 degrees (which is 7.2/360 or 1/50 of a full angle). Eratosthenes measured that the distance between these locations was about 800 km (497 mi) (in modern units of length). He concluded that the Earth’s circumference should be 50 times that which was about 40,000 km (24,855 mi). This is astonishingly close to modern measurements of the Earth’s circumference according to which it measures 40,075.017 km (24,901 mi), and the average radius is 6,371.0 km (3959 mi).

The Earth is not an ideal sphere. The Earth’s rotation around its own axis results in a centrifugal force which acts the strongest on the equator and makes the Earth’s radius, measured from its centre to the equator (ca. 6,378 km / 3963 mi), to be greater than the radius measured from its centre to the pole (ca. 6,357 km / 3950 mi). Such a solid is called a rotational ellipsoid Due to the fact that land elevates from the ocean level, the Earth’s shape is neither an ideal sphere nor it is an ideal rotational ellipsoid. This is a shape typical exclusively for our planet, with no equivalent in geometric solids, and therefore called a geoid.