Observing the space we are in

Sun and Moon

If we observe outside of Earth, there are, between others, two Important objects around to be found:

The arrangement of these 3 bodies anomaly forms unique stage:

What causes the shade on the Moon, which we observe on daily basis?

Contrary to a popular belief, shade visible almost daily on Moon is caused not by Earth, but by Moon itself.

Earth and Sun and Moon in an animation of tidal waves

Geosynchronous and geostationary orbit

Since we can observe from Earth that Moon always changes its location on sky, we can be sure, that Moon is not on geosynchronous orbit. If it was on geosynchronous orbit, we'd see Moon above us still on the same place on the sky like geostationary satellites.
Geostationary satellites, used for telecommunications, are 35,768 km above sea level.
We do not call them geosynchronous but geostationary, because they use special location directly above the equator.
Like the Moon, man-made satellites do not require an engine to travel around Earth.

Global positioning system (GPS)

GPS started in 80's as a military project of USA, later it was decided that usage will be allowed to public as well.
For its purposes, it needs at least 3 to 4 satellites visible on sky. The principle of GPS stands on measuring distances from known position (satellites) and computing unknown position (GPS receiver).
Location of unknown point in 2D (above) and in 3D (below)

In 3D space, we need 3 distances from known points to locate our unknown position:

Satellites have built-in clocks with a very high precision and are synchronized. Handheld GPS receiver
doesn't have such precise clock because of lowering production costs. It
has only oscillator, which can measure time distances.
GPS receiver does not know the current time, is not synchronized with GPS satellites, but can measure time distances between events. When message (signal use frequency of around 1.5 GHz) is sent from satellite, message will be received by handheld GPS, and the distance of satellite is still unknown. Only relative distance against other satellites are known.
Because of such limitation, typically 4th satellite is requested to compute all variables.

Today there are around 30 GPS satellites cruising. Their altitude 20,200 km is lower to altitude of the geostationary orbit. Therefore, they cruise faster (they run around Earth 2 times per a day), so they appear to move when being observed from Earth. We can typically track around 10 satellites every time and the number changes during the day.

GPS satellites around Earth

Limitations of GPS

The handheld GPS shows coordinates with precision of thousands of minute (1.8 m). But holding the receiver in hand reveals that even such digit is not stable and is far from being exact. The device itself computed that error is around 14 m. The systematic error of handheld GPS receivers is in meters.

GPS is in use for upgrading current networks now. However, because of factors written above, classic geodetic equipment are still basic need for surveying engineer.

Improved concept of GPS for geodetic surveying

Differential GPS positioning (DGPS)

The classic concept of GPS stands on receiving signal from satellites
. Satellites are sending messages containing their positions and other informations. GPS receiver records time when message arrives from each satellite. Then computer in GPS receiver calculates its position. This is how typicall handheld GPS works
and systematic error is typically counted in metres or tens of metres. Horizontal positions are being found with better accuracy than altitudes.

There is a number of reasons behind systematic error. Only some of them are named here:

  • Orbit errors ("winds", gravitational pulls, ...)
  • Satellite geometry
  • Atmospheric interference (humidity, temperature, pressure, ionized air)
Sources of errors: A. Multipath interference, B. Satellite and receiver clock errors, C. Orbit errors, D. Satellite geometry, E. Atmospheric interference, F. Restrictions on accuracy for civilian usage.
These errors are
expected to be very similar in particular area in time, they are
mostly binded to given location. For that reasons, some areas/countries are rich in so called base stations. The exact coordinates of base station are known.
Base stations are meant to continuosly monitor and evaluate these errors and provide a correction to GPS receivers around. Improved GPS receiver is able to listen to radio signal sent from base station, read and apply correction. If there is no base station available around, we can establish our own.
Error detected on Base station is applied by GPS receiver as an correction:
1—Observed positions
2—Because the exact position of base station is known (sometimes located at benchmark), error can be calculated
3—GPS receiver listens radio signal from base station, reads and applies correction then

Real time kinematics (RTK)

The classic concept of GPS has some limits in measuring the time when the message from GPS satellite has arrived. Much better accuracy can be obtained, if not the message timing, but phase of carrier wave is evaluated. The signal/message sent from satellite is of frequency of 1.023 MHz. But the carrier wave has a frequency of 1575.42 MHz.
Signal is modulated on carrier wave. If the receiver can analyse carrier wave, precision can be much improved.
Thus even better than centimeter accuracy can be achieved by GPS receiver working in duo with base station.
Both base station and geodetic GPS receiver are equipped with RTK.

Improvised GPS

Having knowledge of speed of sound can become in some cases useful as well. The speed is 1,236 km/h or 343 m/s. In other words, in 1 second sound travels roughly 3 km and that is information worth remembering.

Geographic coordination system

Radius of Earth is 6,378 km. It can be computed (2πr) that circumference (eg. length of the equator) is around 40,000 km.

Arrows point to longitudes and to latitudes

We use a degree of longitude (West or East), latitude (North or South) together with altitude to describe locations on Earth.

Map projections

As you probably have noticed, we usually use plane map while surface described is sphere.
There are several projections concepts, none of them is perfect, each of them is only better for its dedicated scope of a projected area.
We may see on the picture of the globe above that we can draw what appear to be a triangle with three right angles, 3 × 90° = 270°. Since on paper triangles always have 180°, one must bear in mind that map projection is a simplification of surface described. The error becomes noticeable when depicting lengths of 1,000 km (error around 1:1,000), meaningful when lengths are around 2,000 km (error 1:200) and grows fast then.
Earth surface projection and map projections examples
The shortest way is not being projected as a straight line

Geoid and ellipsoid

For many purposes Earth can be simplified to be viewed as a sphere. Two terms are connected with this topic: Geoid and ellipsoid:

Geoid, reference ellipsoid and Earth surface


The mass is not distributed homogenously.
There are number of reason why weight is not distributed ideally. If we observe these anomalities we can find out that there are distances ±100 m from ellipsoid. Plumb-bob is always pointing perpendicular to Geoid surface and deflection against ellipsoid of up to tens of seconds can be found.
1—The angle between normal to the Geoid and the normal to the ellipsoid is known as the deflection of the vertical (the angle is exaggerated to illustrate it). Vertical deflections are caused by Geoid undulations and amount to 10" (flat areas) or 20-50" (steep mountain slopes)
2—The Geoid, exaggerated to illustrate the complexity of its surface
3—Deviations (undulations) between the Geoid and the WGS84 ellipsoid

Sea level

The Geoid is used to describe heights. Ocean's water level is registered at coastal places over several years.

Every nation or group of nations have established their mean sea level points.

The Geoid is used to describe heights. In order to establish the Geoid as reference for heights, the ocean's water level is registered at coastal places over several years. The resulting water level represents an approximation to the Geoid and is called the mean sea level.

Every nation or group of nations have established those mean sea level points, which are normally located close to the area of concern. For the Netherlands and Germany, the local mean sea level is realized through the Amsterdam tide-gauge (zero height). From that sea level height of other points can be found by geodetic levelling. The sea level at particular area is affected by ocean currents and climate.

Obviously, there are several realizations of local mean sea levels (also called local vertical datums) in the world. They are parallel to the Geoid but for other reasons offset by up to a couple of meters.

Care must be taken when using heights from another local vertical datum. This might be the case in the border area of adjacent nations. An example, the tide gauge (zero height) of the Netherlands differs -2.34 metres from the tide gauge (zero height) of the neighbouring country Belgium (figure below). Even within a country, heights may differ depending on to which tide gauge, mean sea level point, they are related. An example, the mean sea level from the Atlantic to the Pacific coast of the USA increases by 0.6 to 0.7 m.

Fragment of a topographic map showing the border area of Belgium and the Netherlands. The heights in both countries refer to different tide gauges (zero heights). As a result, height contours (represented by brown lines) are abruptly ending at the border.

GPS and heights

GPS is able to work in both systems
: either heights are refered to ellipsoid or Geoid. Therefore it might be possible that later all maps will be converted to global vertical datum.
Height h above the reference ellipsoid and height H above the Geoid for two points on the Earth surface. The ellipsoidal height is measured orthogonal to the ellipsoid. The orthometric height is measured orthogonal to the Geoid.


  • The most convenient geometric reference is the oblate ellipsoid
  • For small scale mapping purposes a sphere may be used (the global horizontal datum)
  • For local areas local ellipsoid is being used (the local horizontal datum)

Above was defined a physical surface as a reference to measure heights. Since we project horizontal coordinates onto a mapping plane, the reference surface for horizontal coordinates requires a mathematical definition and description. The most convenient geometric reference is the oblate ellipsoid, though for small scale mapping purposes a sphere may be used. Global horizontal datums, such as the ITRF2000 or WGS84, are also called geocentric datums because they are geocentrically positioned with respect to the centre of mass of the Earth.

The sphere compared to the ellipsoid

Local and global ellipsoids

Local ellipsoids have been established to fit the Geoid (mean sea level) well over an area of local interest, which in the past was never larger than a continent. This meant that the differences between the Geoid and the reference ellipsoid could effectively be ignored, allowing accurate maps to be drawn in area near the datum (figure below).

The Geoid, a globally best fitting ellipsoid for it, and a regionally best fitting ellipsoid for it, for a chosen region
Several hundred local horizontal datums exist in the world. The reason is obvious: Different local ellipsoids with varying position and orientation had to be adopted to best fit the local mean sea level in different countries or regions. These datums are improved through the time. So we can meet local datums for different years and different locations.
For example Indian 1960, Australian Datum 1966, South American datum 1969, Hong Kong 1963.

Magnetic pole

We are used to use a magnetic compass to find directions. However using a compass is a bit tricky:

In short, using the magnetic compass for geodetic purposes is very limited and not recommended. Surveying engineer should use fixed points instead.
If the compass is used anyway, one has to fix measurement by means of diagrams for magnetic declinations.
Magnetic and geographic pole. Magnetic pole has no static location. 400 years on picture.

Map of the World

It is expected that who has an university degree, has also some general knowledge. Anyone who has passed university has to be confident to find at least all G-20 members on the map and some other important locations as well.

Note: reload the page if you change screen size. The interactive map may not work correctly on some browsers/resolutions.

Click to open high resolution map (3.5 MB)

List of chapters