🌍 The Fundamental Challenge
The Earth is approximately spherical — yet every map you've ever used is flat. This seemingly simple transformation introduces distortions that affect how we perceive area, shape, distance, and direction.
In this module, you'll learn how geodesy (the science of measuring Earth) and map projections work together to solve this ancient problem — and why every projection is a compromise.
📐 Core Concepts
Geodesy
The science of accurately measuring and representing the Earth's shape, gravitational field, and rotation. Modern geodesy relies on satellites, GPS, and precise mathematical models.
Datum
A mathematical model of the Earth used as a reference for coordinates. Common datums include WGS84 (used by GPS), NAD83 (North America), and NAVD88 (vertical datum).
Map Projection
A systematic transformation of the Earth's 3D surface onto a 2D plane. Every projection preserves some properties (area, shape, distance, direction) while distorting others.
Coordinate System
Geographic coordinates use latitude/longitude on a sphere. Projected coordinates (like UTM or State Plane) use X/Y on a flat surface with units in meters or feet.
🔬 Interactive: Projection Distortion Explorer
Compare how different projection families distort the Earth. Each projection preserves certain properties while sacrificing others.
⚖️ Interactive: The True Size of Countries
Most of us grew up with Mercator-projection maps. Click on countries to compare their apparent size (on Mercator) vs. their true area.
Greenland vs. Africa
Greenland's true area is only about 7% of Africa's size — yet on a Mercator map, they appear roughly equal. Africa could fit the US, China, India, and most of Europe inside it!
📖 Case Study from History: Eratosthenes Measures the Earth (240 BCE)
Over 2,200 years ago, the Greek mathematician Eratosthenes calculated Earth's circumference with remarkable accuracy using just a stick, a well, and the shadow of the sun.
He observed that at noon on the summer solstice, the sun shone directly into a well in Syene (modern Aswan, Egypt), while in Alexandria, a vertical stick cast a shadow. By measuring the shadow's angle (~7.2°) and knowing the distance between the cities (~5,000 stadia), he estimated the Earth's circumference to within 2% of its actual value.
Why this matters: This ancient technique demonstrates the core of geodesy — using geometric principles to understand our planet's shape.
🔬 Lab Assignment: Alaska vs. Texas — Does Projection Matter?
In this lab, you will:
- Load the US States boundary layer in ArcGIS Pro
- Compare the apparent size of Alaska and Texas in Web Mercator
- Reproject both states to an Albers Equal-Area Conic projection
- Calculate the true area of each state using the
Calculate Geometrytool - Answer: How many times larger is Alaska than Texas really?
Deliverable: Submit a map layout showing both projections side-by-side with calculated areas.
Download Lab Data →📚 Required Readings
- ESRI - Understanding Map Projections (PDF)
- Dana (1994) - Coordinate Systems Overview
- Web Tool - TheTrueSize.com (Interactive Mercator comparison)
✅ Module Quiz: Projections & Coordinate Systems
Test your understanding of datums, projections, and coordinate systems.
- What is the difference between a datum and a projection?
- Why does the Mercator projection distort area near the poles?
- Which projection would you use for a thematic map of Africa? Why?