1.5: Size and Shape

Figure \(\PageIndex{1}\): Taking readings from a GPS atop the US capitol building. (Courtesy NOAA. Source)

Shape of the earth

Humans have always been curious of the shape of the earth. In many ancient cultures like Egyptians and Babylonians it was believed that the earth was flat. By 5th century B.C.E. Greek thinkers like Pythagoras and Aristotle provided evidence of the sphericity of the earth. Greeks and Egyptian scholars observed from the way the sun's shadow worked on different places and they believed that it would be possible only if the earth was a sphere. However, it was not until the Middle Ages that people were convinced of the spherical shape of the earth. 

Proofs of the earth's sphericity

Measurement of the earth's circumference : Around 240 B.C. Eratosthenes used the angles of shadows cast by the sun in different cities and calculated the earth's circumference accurately proving that the earth cannot be flat 

Circumnavigation : In the 16th century, Ferdinand Magellan was the first to circumnavigate the earth and proved that it was possible to continuously travel around the world something that would be impossible if the world was flat. 

Ships appear mast first : When observed from the harbor, the mast (highest point of the superstructure of the ship) appear before the rest of the ship and the hull. This happens because of the curvature of the earth. If the earth were flat then all of the ship would be seen at the same time. 

Horizon: From high vantage points like mountains and high buildings the horizon appears curved due to the earth's spherical shape 

View of constellations : Due to the sphericity of the earth as one travels north or south, different stars are visible, even the angle of the North Star changes. 

Lunar eclipse : During a lunar eclipse as the earth passes between the moon and the sun, the shadow cast by the earth on the moon is circular proving that the earth is a sphere. Only a sphere can cast a circular shadow. 

Sunrise and sunset : Different places on the earth along different meridians have sunrise and sunsets at different times since the earth is a sphere. If the earth were flat then all places on the earth would have sunrise and sunset at the same time. 

Images : Images of the earth from the moon or space clearly show that the earth is spherical in shape.

Oblate spheroid

Those involved in the study of measuring the Earth, called geodesists, don't know exactly what the true shape of the Earth is. We often describe it as a sphere but it's more like an oblate spheroid. That is, Earth is wider in the middle and flatter at the poles than a perfect sphere. From pole-to-pole the distance is 12,713.6 km. The equatorial diameter Earth is about 7926 miles (12,756 km) while the polar diameter is 7900 miles (12,714 km). The equatorial circumference is approximately 24,900 miles (40,075 km). The equatorial bulge is due to the centrifugal force exerted on the Earth by its rotation.

Figure \(\PageIndex{2}\): Oblate spheroid

On December 26^th, 2004 subduction occurred between the India and Burma plates off the coast of Indonesia making for a slightly more compact Earth. The shift in Earth's crust resulted in a magnitude 9 earthquake and large tsunami that devastated South Asia. Interestingly, Earth became slightly more round and the North Pole shifted by about 2.5 cm (an inch) in the direction of 145 degrees East longitude (Science Daily, 2005).

From the top of Mt. Everest at 29,029 feet (8848 m) in the Himalayas, to the depths of the Mariana Trench in the Pacific at 36,198 feet (11,033 meters) below sea level, Earth has a total relief of about 12 miles. Though this seems to be a great distance, it's a mere blip when compared to the diameter of Earth.

Geoid

The true shape of the earth is not sphere or oblate spheroid but it is geoid. This shape is determined by the earth's gravity and rotation. If the earth were to be covered entirely by water with no wind or tides, the water would settle into a shape where the gravity is level. This level surface is geoid. Some areas of the earth have dense mountain ranges while some have deep mountain trenches which have led to a shape that is not perfectly uniform. It can thus be concluded that even though the earth looks like a sphere from space, precise measurements reveal that the true shape of the earth which is defined by its gravitational field is slightly irregular. The earth's true shape is an unique shape called geoid. 

Suggested Reading : https://www.nasa.gov/earth/how-do-we...rt-episode-53/