astronomy

Earth-centered, Earth-fixed coordinate system

Earth-centered, Earth-fixed coordinate system is a astronomy topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Earth-centered, Earth-fixed coordinate system rather than just read about it. In short: The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, atmosphere, and surrounding outer space) as X, Y, and Z measurements from its center of mass. Its most common use is in tracking the orbits of satellites and in satellite navig…

Key takeaways

Earth-centered, Earth-fixed coordinate system belongs to astronomy; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Earth-centered, Earth-fixed coordinate system to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Earth-centered, Earth-fixed coordinate system from memory before moving on to harder problems.

Reference excerpt

The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, atmosphere, and surrounding outer space) as X, Y, and Z measurements from its center of mass. Its most common use is in tracking the orbits of satellites and in satellite navigation systems for measuring locations on the surface of the Earth, but it is also used in applications such as tracking crustal motion. The distance from a given point of interest to the center of Earth is called the geocentric distance, R = X 2 + Y 2 + Z 2 {\displaystyle R={\sqrt {X^{2}+Y^{2}+Z^{2}}}} , which is a generalization of the geocentric radius, R0, not restricted to points on the reference ellipsoid surface. The geocentric altitude is a type of altitude defined as the difference between the two aforementioned quantities: h′ = R − R0; it is not to be confused for the geodetic altitude. Conversions between ECEF and geodetic coordinates (latitude and longitude) are discussed at geographic coordinate conversion.

Structure As with any spatial reference system, ECEF consists of an abstract coordinate system (in this case, a conventional three-dimensional right-handed system), and a geodetic datum that binds the coordinate system to actual locations on the Earth. The ECEF that is used for the Global Positioning System (GPS) is the geocentric WGS 84, which currently includes its own ellipsoid definition. Other local datums such as NAD 83 may also be used. Due to differences between datums, the ECEF coordinates for a location will be different for different datums, although the differences between most modern datums is relatively small, within a few meters. The ECEF coordinate system has the following parameters:

The origin at the center of the chosen ellipsoid. In WGS 84, this is center of mass of the Earth. The Z axis is the line between the North and South Poles, with positive values increasing northward. In WGS 84, this is the international reference pole (IRP), which does not exactly coincide with the Earth's rotational axis The slight "wobbling" of the rotational axis is known as polar motion, and can actually be measured against an ECEF. The X axis is in the plane of the equator, passing through the origin and extending from 180° longitude (negative) to the prime meridian (positive); in WGS 84, this is the IERS Reference Meridian. The Y axis is also in the plane of the equator, passing through extending from 90°W longitude (negative) to 90°E longitude (positive) An example is the NGS data for a brass disk near Donner Summit, in California. Given the dimensions of the ellipsoid, the conversion from lat/lon/height-above-ellipsoid coordinates to X-Y-Z is straightforward—calculate the X-Y-Z for the given lat-lon on the surface of the ellipsoid and add the X-Y-Z vector that is perpendicular to the ellipsoid there and has length equal to the point's height above the ellipsoid. The reverse conversion is harder: given X-Y-Z can immediately get longitude, but no closed formula for latitude and height exists. See "Geodetic system." Using Bowring's formula in 1976 Survey Review the first iteration gives latitude correct within 10-11 degree as long as the point is within 10,000 meters above or 5,000 meters below the ellipsoid.

In astronomy

Geocentric coordinates can be used for locating astronomical objects in the Solar System in three dimensions along the Cartesian X, Y, and Z axes. They are differentiated from topocentric coordinates, which use the observer's location as the reference point for bearings in altitude and azimuth. For nearby stars, astronomers use heliocentric coordinates, with the center of the Sun as the origin. The plane of reference can be aligned with the Earth's celestial equator, the ecliptic, or the Milky Way's galactic equator. These 3D celestial coordinate systems add actual distance as the Z axis to the equatorial, ecliptic, and galactic coordinate systems used in spherical astronomy.

See also Earth-centered inertial (ECI) Geodetic system International Terrestrial Reference System and Frame (ITRS) Orbital state vectors Planetary coordinate system

References

External links ECEF datum transformation Archived March 22, 2007, at the Wayback Machine Notes on converting ECEF coordinates to WGS-84 datum Datum Transformations of GPS Positions Application Note Archived September 27, 2007, at the Wayback Machine Clearer notes on converting ECEF coordinates to WGS-84 datum geodetic datum overview orientation of the coordinate system and additional information GeographicLib includes a utility CartConvert which converts between geodetic and geocentric (ECEF) or local Cartesian (ENU) coordinates. This provides accurate results for all inputs including points close to the center of the Earth. EPSG:4978 Archived April 13, 2015, at the Wayback Machine

Illustrations

Worked examples

Example 1 — a first encounter with Earth-centered, Earth-fixed coordinate system

Start with the simplest possible case. Write down what Earth-centered, Earth-fixed coordinate system claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Earth-centered, Earth-fixed coordinate system before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Earth-centered, Earth-fixed coordinate system ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Earth-centered, Earth-fixed coordinate system

In research: Earth-centered, Earth-fixed coordinate system appears in astronomy research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Earth-centered, Earth-fixed coordinate system in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Earth-centered, Earth-fixed coordinate system is common in secondary-school and first-year university syllabi. It links to neighbouring topics Astronomical coordinate systems, Global Positioning System, so understanding it makes those chapters shorter.
In everyday life: Look for Earth-centered, Earth-fixed coordinate system outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Earth-centered, Earth-fixed coordinate system in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Earth-centered, Earth-fixed coordinate system means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Earth-centered, Earth-fixed coordinate system out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Earth-centered, Earth-fixed coordinate system in simple terms?

Why does Earth-centered, Earth-fixed coordinate system matter?

Because it connects several astronomy ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Earth-centered, Earth-fixed coordinate system?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Earth-centered, Earth-fixed coordinate system.