Position

Location

As geologists, we are really only interested in our location in reference to the Earth. There are variations in Earth's orbit around the sun that influence the climate significantly. It might also be possible that changes in the position of our solar system within the galaxy can influence conditions on the Earth as well. As such, a geologist investigating the course of earth history would be interested in such things. However, they would refer to positioning co-ordinates as used by astronomers, and we will learn about those as well later.

Earth Referenced Co-ordinates
We need three co-ordinates to specify our location on (or in, or above) the Earth:

Latitude
Longitude
Elevation

While all of these seem simple enough in theory, each is complicated to one extent or another by the degree to which the shape of the Earth differs from that of a perfect sphere, and by the fact that different parts of the surface of the Earth are in motion relative to one another. The shape of the Earth is best approximated as an ellipsoid with a radius of 6357 km at the poles and 6378 km at the equator (an average of 6371 km). It might be even more accurate to describe the Earth as egg-shaped as its latitude of maximum radius is slightly south of the equator. All this being said, the Earth is close enough to a sphere for most purposes.

Lines

One concept that we must be clear on is the nature of lines drawn on the surface of the Earth. All straight lines drawn on the surface of a sphere look like circles when viewed from the right location (the point equidistant from all points on that line). There are two types circle on a sphere: Great Circles, which slice the sphere through its centre (the centre of the sphere and circle are the same) and Small Circles, which do not. Great circles are the equivalent of a straight line drawn on a flat surface in that the shortest distance between two points on the surface of a sphere is a segment of a great circle. Great circles also look straight when viewed from directly above any point on the line (see the equator and prime meridian lines in the blue and yellow diagrams below).

Co-ordinate Lines

	Latitude This is an angular measure that indicates the angle between a location and the equator. You know you are on the equator by the fact that when looking east, celestial objects rise up on a path perpendicular to the horizon. One's latitude also is indicated by the angle between the north star (Polaris) and the horizon. If Polaris is directly overhead, you are at the north pole (90 degrees latitude). If it is at the horizon, then you are on the equator. There are visible stars that are almost directly over the south pole that can be used to determine latitude south of the equator, but they are not part of easily recognisable constellations. The precise nature of this measurement is slightly complicated by the fact that the shape of the Earth is an ellipsoid rather than a sphere, but the difference is not usually important for the precision needed by geologists. All Latitude lines are small circles (except the equator) and are parallel to the equator. Thus, they are often called parallels. Check out this minutephysics video on the subject of Earth's poles. The poles that we are talking about in this context are the geographic poles.
	Longitude Longitude lines (called meridians) are great circles that pass through both the north and south geographic poles and intersect the equator and all other latitude lines at an angle of 90 degrees. Thus, it can be seen that any triangle drawn on the surface of the earth (or any sphere) must have interior angles that add up to more than 180 degrees. The fact that this is true for triangles on the earth is one of many indications that the earth is not a flat structure. Your longitude is the angle between the meridian that you are on and the meridian used as a reference datum. This reference longitude is called the prime meridian. The difficulty with defining a prime meridian is that there is no objective uniqueness to any partiular meridian the way that the equator is unique among all parallels. So, we had to pick one (or many, there was much disagreement). We eventually settled on the meridian going through Greenwich, England. The trickier issue is how to measure what meridian a particular location is on. This can be done with reference to the stars and a good clock. The earth rotates through 360 degrees every 24 hours (23 hours, 56 minutes, 6 seconds). This is a rate of roughly 15 degrees per hour. Set up a telescope at some location on the prime meridian on a perfectly vertical tripod and point it due south or north. We can make sure of this alignment by reference to the north star. When it is midnight in Greenwich, England, check to see which star is perfectly lined up with the centre of the telescope view. Anyone else can repeat this process anywhere else on the earth. If they see the same star centred in their telescope at midnight Greenwich time, then they also are on the prime meridian. If that star lines up with their telescope at 11 PM Greenwich time, they are on the meridian 15 degrees east of the prime meridian. If that star lines up at 2 AM Greenich time, then they are on the meridian 30 degrees west of prime.
	In summary, rather than use three distance co-ordinates x, y, z to describe a location on the earth we use two angles: longitude (an angle along the equator between your meridian and the prime meridian) and latitude (an angle along your meridian from the equator) as well as a distance along a line from your location to the centre of the earth. The diagram to the left makes some interesting points about direction which are not of much concern when one is worried about location on the earth, but become important when thinking about observations of objects in space. Examples: Up is a direction opposite of the direction to the centre of the earth. We don't often look in this direction. Usually we look at the sky in some compass direction (north, south, southeast, etc.) and up 20 to 40 degrees from the horizon. The only time we are likely to look straight up to the "top of the sky" (also called the Zenith - the opposite of which is the Nadir) is when we are lying on our back on the ground. If you are on the equator, then your view to the north is the same direction as the Zenith view for someone at the north pole. Your view of the Zenith is the same direction as the eastward view of someone 90 degrees of longitude to the west of you. When you are at the north pole every direction that you look is south.

Practical Problems with Longitude
1) The earth's gravity is neither exactly the same strength everywhere, nor does it point always directly to the centre of the earth. This is because the Earth's composition is not uniform. If we don't correct for this as we set up of telescopes to measure longitude, our longitude lines are going to end up being rather wavy.

For simplicity of drawing, I have represented the earth as a flat plane in the diagram above. Each of the telescopes is being used to measure longitude. They are oriented using a plumb bob - a heavy weight on a string. The idea is that gravity causes the string to hang perfectly vertically (i.e., pointing to the centre of the earth). One a perfectly uniform, spherical planet this would be true. Telescope A is in the middle of a flat expanse of ground with uniform rock under it. As a result, the telescope is properly oriented in the vertical direction and an accurate determination of longitude will be made. Telescope B is east of some mountains. The extra gravity from the mountains' mass pulls the string westward out of vertical. However, knowing the mountains are there, the operator of the telescope can calculate a correction and properly orient the telescope. Telescope C has no topographic features nearby, but unknown to the telescope operator, there is a body of an extra dense mineral deposit to the east. The extra gravity from its excess mass causes the plumb bob to swing to the east. The resulting misalignment of the telescope causes the astronomer to think that stars are overhead when they are actually off to the west. They will thus think that they are further west than they actually are.

2) Reference Ellipsoids. It is difficult to draw nice straight lines along a fairly lumpy surface such as the Earth's. Thus, surveyors derive equations for nice, smooth mathematical ellipsoids that approximate the overall surface of the Earth. These mathematical models are called reference ellipsoids. They represent the earth as a smooth shape without features like mountains and valleys. The location of latitude and longitude lines are referenced to these ellipsoids.

Historically, each country adopted its own ellipsoid that best approximates the land surface for that country. In the modern age, the need for GPS to give sensible readings meant that every country uses the same ellipsoid, the one used by the US government (since they control the GPS satellites). This ellipsoid is called WGS84. This ellipsoid not only approximates the overall shape of the Earth fairly well, but also has its centre at the same point as the centre of mass of the Earth. This is a necessity for any ellipsoid used to control a system of orbiting satellites. This video by Tom Scott shows some of the issues involved with this ellipsoid. The trick with an ellipsoid is that vertical - perpendicular to the ground surface - is not always where a plumb bob would point (centre of the earth).

3) Plate Tectonics is a process by which rigid plates of rock are in a state of motion across the surface of the Earth with respect to each other. Thus, any longitude line fixed to the surface of the Earth will not stay in the same place relative to other places on the Earth.
The solution to this problem has been to have observing stations on all of the tectonic plates, each measuring its apparent longitude from fixed objects in space. The motion that each station experiences is averaged together with that of all the other stations to produce a reference longitude that stays in one place relative to the Earth while the tectonic plates move around under it. This means that most places on the earth show a changing latitude and longitude over time. Most countries have not seen fit to alter their maps yet, as their co-ordinate system has only changed by a few centimetres at most since the prime meridian was last defined.

Elevation: the last co-ordinate
This is the distance above or below some reference datum.
One could use the distance from the centre of the Earth as a datum, but this is very difficult to actually measure and since the Earth is not a sphere, the distance to the sufrace would not be constant even if the earth was a smooth shape.

Sea Level
This is a useful datum because the water in the ocean is self-levelling and it is significant to us since we like be on dry land rather than underwater. Sea level measurements have been recorded at tide monitoring stations for many decades. The defined value for sea level at any location on the earth is the 19-year average of hourly recordings of water level at the recording station. Stations performing this function are found all over the Earth.

The Effect of Gravity
It was once thought that the surface of the ocean ought to be roughly parallel to the surface of the ellipsoid if the ellipsoid was chosen carefully, but with the advent of accurate elevation mapping from space it has been found that the ocean surface is irregular, just like the land surface.
Once again, Minutephysics does a good job summarizing the issues: gravity and sealevel.

Topography affects gravity since mountains have extra mass piled up and valleys have less. Water is attracted by gravity and so will pile up higher around mountains and flow away from valleys.
There are zones of more dense rock and less dense rock underground that cause much the same effect.
The Earth's gravity is uneven on a regional scale as well. We know this from satellite measurements (low-earth-orbit satellites are affected by gravity variations, rising when it is weak and dropping when it is strong).

The Geoid
The surface that the sea would settle at in the absence of any short-term effects like wind and air pressure differences, is what geodetic scientists call the Geoid, or the Earth Geodetic Model (EGM96). It is a mathematical construct, like the ellipsoid, but much less regular.

The Geoid is a product of all the effects related to gravity. The difference between it and the ellipsoid is as much as 100 m below and nearly 90 metres above.

In spite if this apparent "topography," the geoid is the real surface of equal gravitational potential energy. If the ocean were made solid, you would walk along it and not feel like you were going up hill or down, because really, you are not. If a marble were rolled along this surface, it would roll from Sri Lanka to Indonesia (200 m up in terms of the ellipsoid) without slowing down (negating friction) since it would not be gaining any gravitational potential energy.

GPS
Remember that GPS satellites use the ellipsoid as their datum. Thus, early GPS readouts would show you as 100 m underwater when you were on the beach in Sri Lanka. Modern GPS receivers access a Geoid database to calculate a realistic height above sea level. Please read this link on GPS, the Geoid, and Sea Level. Take particular note of how equalizing gravity would affect coastlines on page 2 and how melting of the polar ice caps would affect coastlines on page 3.

Other Effects on Sea Level
Global sea level can be affected by a number of things.

Glacial ice: as ice melts, more water enters the oceans and sea level rises. This is a concern at the moment and we will address it later in the course.
Warming the oceans also raises sea level since water expands when it gets warmer.
Plate tectonics. Where plates separate from each other tall ocean ridges are found under the oceans. They rise high above the ocean floor because the rocks are still warm, thus have a low density, and do not sink as much into the mantle as older rocks away from the spreading ridge. During times when tectonic plates are moving quickly, these ridges rise farther and take up more space in the ocean basins. As a result, the water level in the oceans increases without actually having any more liquid water present.
Long-term weather patterns, particularly the trade winds, can push water towards one side of an ocean basin resulting in a semi-permanent increase in sea level there and a lowering on the other side of the basin. This is particularly significant in the equatorial Pacific where warm water is piled up around Indonesia. The extra height in the sea level amounts to about 0.5 m. When the winds fail, this warm water sloshes back across the Pacific and results in a weather event that we call El Nino.
Short term weather events with abnormally high or low air pressure can cause large changes in local sea level. In severe hurricanes the water level can rise by more than 10 metres from the reduction in air pressure.

Moving Around on the Earth

A map is a projection of the surface of the earth (or some part of it) onto a 2D surface. The conceptually simplest way to do this is to imagine wrapping a sheet of paper around a globe and shining a light at the exact centre of the globe so that the features on the surface of the globe cast shadows onto the paper. This would produce a Mercator map on the paper. If you interested in the subject of maps, check out this summary

Remember that all straight lines on the surface of a sphere are great circles.
The shortest distance between two points on a sphere is a segment of the great circle that passes through both of them. Viewed from above the midpoint of the line segment, this great circle really would look like a straight line. On a Mercator map, however, these paths seldom look anything like straight. To see why this is so, consider the following path from point A to point B viewed both on a perspective view of a globe and a mercator map.

The great circle path (the blue line) is the shortest path from A to B and it looks like that on the perspective view of a globe.
In order to show a globe on a flat map, the surface of the Earth is stretched out towards the poles. This distorts angles, distances, and areas. It stretches the path line between two points as well. There are lots of ways to manage this stretching. On a Mercator map, the math behind the stretching is such that a straight line is actually a path of constant true compass heading (the orange line on the diagram). Even on the perspective view of the globe it is easy to see that the orange path crosses each meridian at roughly the same angle. This is handy for navigating if you want the simplicity of holding a constant heading, but it ends up being a much longer path. A great circle path usually cuts across each longitude line at a different angle, so to follow it you must continually change your heading but your journey is shorter.

The result of all of this is that the direction to another place is not necessarily the direction that you start walking to get there. For example, Shanghai China is due west of Dallas Texas. They are at the same latitude. However, if you were going to walk from Dallas to Shanghai (or fly there) the most direct (shortest) straight-line path starts off from Dallas going northwest towards Vancouver. It is only at the midpoint of the journey over the east coast of Alaska that you would be moving west.

A Roughly Spherical Earth

My understanding is that educated people have understood the Earth to be roughly spherical since more than 2000 years ago. However, there are two recent developments, starting in the late 19th century (1800s) which relate to this issue. One was a populist notion that people in the past had predominantly believed that the Earth was a flat plane. Some individuals went so far as to forge supposedly ancient artwork depicting the idea of a flat Earth. This notion may have had something to do with a need that people often have to feel that new, technologically advanced societies must be somehow distinct and better than those of the "more primitive past." The other development that took place around this time was the appearance of individuals and groups who purported to genuinely believe that the Earth really is a flat disk. This group seems to arise out of the conflict between the science of biological evolution and European/North American religious dogma. These individuals show a general distrust of scientific "authority." The nature of the Earth serves as a useful focus for this conflict. The arguments involved are interesting as an exploration of how scientific arguments work. Most flat-earth arguments address one aspect of the science at a time whereas good scientific theories must work in all relevant situations. I will leave it to you to investigate the phenomenon of flat earth belief, if you wish. Explanations as to the fallacies involved are easy to find.

The Coriolis effect is a feature of a rotating planet that most people have heard of although it is not readily apparent at human scales of motion with all the other forces acting at a local level. An air mass in the absence of wind generally moves east along with the rotation speed of the ground below it unless generating a very high wind speed (see why isn't it faster to fly west.). If this air mass was to be pushed away from the equator it would move toward the earth's rotation axis where it would encounter a ground surface moving eastward less fast. The air mass, still moving with its original eastward speed, would be moving faster to the east than the ground under it and so would be deflected eastward from its north/south path until friction with the ground reduced its speed down to the speed of the ground surface (see Coriolis Effect). Some might argue that we would see the same effect on a rotating disk which is true, although I think that there would be subtle differences.

One phenomenon that requires the nature of the earth to be a rotating spheroid is the Eötvös effect. Our weight is mostly a function of gravity, but the Earth's rotation also has an influence. In the frame of reference of the Earth, its rotation produces an apparent upward force in the same way that a car taking a corner produces an apparent outward force pushing you against the side of the car. In the case of the Earth's rotation, the apparent force is upward against gravity. In the diagram below, the accelerations associated with gravity and the outward spin force are used instead of the forces themselves.

What we see is that for a person standing on the equator the gravitational acceleration downward is always 9.79 m/s/s. The rotational speed of the Earth produces an apparent upward acceleration of 0.0335 m/s/s. This is only 0.35% of the acceleration due to gravity. Thus, a 70 kg person standing on the equator would feel the equivalent of 240 g less heavy due to the Earth's spin.

The important effect, however, is what happens when you move east or west. While moving east one is adding to the Earth's rotation speed and this will increase the upward apparent acceleration, making you feel less heavy. The opposite would occur if you travelled west. The diagram shows the Eötvös effect, as it is called, for a person moving at 10 m/s which is fast for a bicycle, much less a person walking. However, it is a reasonable speed for a ship, where the effect was first seen. The change in apparent upward acceleration is only 0.0015 m/s/s, which is only enough to make a 70 kg person weigh about 11 g heavier or lighter, but this is an easily measurable amount.

For us, the importance of this effect is that the Eötvös effect would only occur if the Earth was a roatating spheroid.

Both the Coriolis and Eötvös effects have been known for more than a hundred years. I am told that long-distance sharpshooters must account for both effects, but I have no first-hand knowledge that this is true. For me, the fact that parallel lines on the earth's surface eventually intersect or that triangles drawn on the earth's surface have interior angles that add up to more than 180 degrees is convincing enough evidence that the earth is a spheroid.