Cosmic distance ladder
Under distance measurement, distance measurement or length measurement is the measurement of the distance between two points in space by direct or indirect comparison with a unit of length such as the meter. The range of possible lengths begins with the so-called Planck length of some meters. This is the smallest length, in which the space can be divided. The physically relevant range starts at meters, the size of the elementary particles, and extends to meters. It spans so orders of magnitude. The result is that a very large number of different methods is necessary to measure distances.
The following diagram gives an overview of the unit 's resolutions, provides examples of the size ranges and assigns the respective measurement principles.
- 2.1 Distance measurement in everyday life 2.1.1 traveled pathes
- 2.1.2 Land Surveying
- 2.1.3 Flight Distances
- 2.1.4 underwater and in the earth
- 2.5.1 Distance of the Moon
- 2.5.2 radar measurements
Measurement principles
Direct measurement
The most direct form of distance measurement is the so-called direct measurement. This refers to the direct comparison of the distance to be determined with a scale. This type of measurement is only possible in a limited wavelength range, as standards of comparison can not be made in any size. The smallest scales are produced using lithographic methods and are only a few micrometers in size. They can be used under a microscope such as a normal tape or be automated using optical devices read (see glass scale ). The longest scales are made of flexible steel tape in lengths up to 100 meters.
All these standards are on a length standard (formerly the standard meter, today the definition of the meter using the light - runtime ) returned. This process is known as calibration. The definition of the meter enables the global comparison of length measurements.
Technically computing the direct distance measurement is treated as a slope distance that still requires measuring its slope or the angle of elevation for their conversion into a horizontal line.
The following are some methods of direct distance measurement and briefly explained.
Interferometry
Interferometry with coherent waves is very precise for the measurement of changes in length. The accuracy depends mainly on the used wavelength. In practice, light and radio waves are used. In order to measure distances with an interferometer and, inter alia, the phase shift method, the white light or the conoscopic holography can be used. Interferometry is a direct measurement, since the distance to be determined is compared with the wavelength of the light used. The wavelength is linked to the International System of Units.
Confocal distance measurement
The confocal technology is used in various technical configurations to determine very small distances in the nanometer to millimeter range. It is based on the effect of depth discrimination: A Confocal provides a signal that is the greater the closer the test object is located at the focal plane of the optics. The confocal technique is a direct measurement, since it shifts the object or look at the gauge length and the displacement with a reference scale.
Indirect measurement
The direct measurement can not be used in many cases. Already in determining the distance between two islands from the mainland, it fails because the two points are not accessible simultaneously. Universal and usually more convenient to use are indirect methods.
All indirect methods have in common that they do not measure the distance itself, but a dependent of her size - for example, the run-time measurement of a signal or echo ( laser, radar ), the direction of a bearing or the brightness of a star. Indirectly, all changes in the distance to be measured, such as by Doppler effect (see also approaching ). Indirect measurements must be calibrated by comparison with known standards, so that comparability is ensured with other measurements.
Hodometrie
The Hodometrie, often referred to by the English as odometry, is a very simple and old method of indirect position measurement, which can be used also limited for distance measurement. The revolutions of the wheel are counted with a known circumference, which is rolled on the measuring section. The number of rotations multiplied by the circumference results in the measured distance. This method is for example used for odometer of cars or measuring wheels in the measurement in everyday life. ( See also: curvimeter, equipment for measuring winding routes in Maps)
Inertial
Inertial navigation is based on the fact that a movement that is not uniform, is always associated with an acceleration of the moving object. Integrating all accelerations, which has experienced an object, direction dependent on the time you speed time and distance equal speed acceleration can it according to the simple formula equal times times times the distance traveled calculated ( two-time numerical integration ). This method is uses in vehicles and aircraft of all types, to allow environment -independent distance measurement. However, add up over time and the measurement error, which is why the position must be adjusted on a regular basis with information from other sources.
Triangulation
In the triple angulation or triangulation is aiming for this measurement point of at least two different points of a known distance using a theodolite or other protractor. The object point P and the two positions (1 and 2) form a triangle, the base length, and the base angle, and is known. Thus one can calculate all other variables in the triangle. The base length forms the scale of triangulation. The three angles of the triangle give the method the name of ' triangulation '.
In a reversal of this process, the end points of a highly accurate reference path, a so-called base bar from a point can be targeted. The base bar thus forms the base length of an isosceles triangle.
Since ancient times, the triangulation was used for land surveying and is down to technical innovations still used today for it. Additions are methods of optical metrology as the fringe projection and photogrammetry, which have opened up other applications.
The measurement process itself uses direct ( optical ) or indirect ( harmful ) angle measurements, metrological each phase as comparisons ( ambiguous ) realized at a known length of the measurement base. The spatial position of each of two base angles of the distance from the known length can be calculated. Also, distance sensors use the principle of triangulation ( see laser triangulation or distance measurement ( optical) ). A simple variant of estimating distances without technical aids is the thumb jump.
Trilateration
Trilateration is a triangulation similar method also uses three variables of a triangle to the description, namely the sides. This can in turn calculate all other sizes that define the triangle.
The measurement process itself uses direct ( optical ) or indirect ( harmful ) distance measurements ( unique) realized by measurement in each case as delay measurements or additionally by phase comparisons ( ambiguous ). From the spatial position of two points can be calculated on the basis of geometrical relations in the triangle their distance. The method primarily serves the spatial location of measurement points to determine each other on the basis of simple distance measurements quickly and with reasonable accuracy.
For determining the position of an unknown point in three dimensional space known four points are required which meet in an area of three known points, and meet along a trajectory two known points. Can be selected on the basis of constraints between multiple mathematically correct solutions that can reduce the number of usable constraints the number of required known points.
Trilateration is the basis of the distance measurement, for example in systems of satellite navigation or Global Navigation Satellite Systems. In the sense of classical geodesy trilateration is not an independent measurement method, however, probably in satellite geodesy (see also Satellite Laser Ranging and SECOR ).
Transit time measurement
The transit time measurement is based on that electromagnetic and acoustic waves propagate with a finite, known speed. One sends a signal to a measurement object, by which it is reflected, and measures the time it needs for the round trip, it can be from the propagation time and the propagation speed of the signal is the group velocity of the wave, the object distance calculate:
The measurements are influenced by the environment. A medium penetrated the speed of light is reduced in relation to the speed of light in vacuum. Are the material properties depending on temperature or anisotropic tensors are disturbed Delay measurements of changes in the parameters or orientation. For example, the sound velocity is highly temperature-dependent, electromagnetic waves are deflected by the electrically conductive layers of the atmosphere.
Particularly problematic is the determination of the gangplank: Only direct walkways provide direct distance. All detours through secondary reflectors provide longer run times and thus false measurement data.
Examples:
- Bats and ultrasonic distance sensors or measuring devices use ultrasonic signals to determine the distance of obstacles and prey.
- The echo sounder and sonar use sound signals in the water for depth measurement under ships for distance measurement under water ( submarines) and for locating shoals of fish.
- Radar systems use electromagnetic waves in the radio wavelength range for distance measurement. A distinction is made between pulse devices for large and continuous wave radars for short distances. See, eg, distance measuring equipment, satellite navigation (eg GPS ), Time Domain Reflectometry
- Even light is suitable for this procedure, refer Satellite Laser Ranging, LIDAR, laser gun, distance measurement (optical).
Chromatic confocal distance measurement
The chromatic confocal distance measurement uses the dispersion of white, ie, spectrally broadband light in an optical system for determining the distance between target and sensor. Measuring serve different due to the dispersion in the focus lens focal lengths for different spectral components of the light sensor.
Capacitive distance measurement
The distance between two conductive parts can be determined from the capacitance between them. For this purpose, the parts must be isolated from each other; they are included in the capacity measurement, an electrical oscillating circuit or a ring oscillator whose frequency is sensitively dependent on the capacity. Application can be found at the focus position control of laser - cutting machines, for position control in nanopositioning systems and for measuring force.
Parallax
For the determination of distances that go beyond the scale of the solar system, various Parallaxenmethoden be used. The word " parallax " is here used in the sense of " distance ". A distinction is made between the following:
Trigonometric parallax
The trigonometric parallax is the change in direction of view to an object against the sky background, which is caused by the annual motion of the earth around the sun. The trigonometric parallax is thus based on the triangulation, its base length is the diameter of Earth's orbit. Moreover, also referred to as the daily parallax, which is caused by the rotation of the earth. The farther away an object is, the smaller the parallax. From it, the distance can be calculated directly:
The first parallax of a star could be carried out in 1838 by Friedrich Wilhelm Bessel for the star 61 Cygni. He determined a value of about 0.3 arc seconds and thus a distance of about 3.3 pc. Proxima Centauri, the star that is closest to the Earth, has a parallax of 0.762 arcseconds, which corresponds to a distance of about 1.31 pc. Usually leaves the trigonometric parallax up to distances of about 100 pc determined. With modern methods parallaxes are today but also already been measured by a few milliarcseconds. Between 1989 and 1993, the satellite Hipparcos has about 100,000 stars up to a brightness of 9 mag determined and measured its parallax. He reached this an error of only 0.001 arcseconds. The date (2005) the smallest parallax could be determined for the pulsar PSR B1508 55 with a radio telescope: it amounted to 0,415 milliarcseconds ( = 0.000415 arcsec ) - equivalent to a distance of 2,400 pc or about 7,800 light years.
Spectroscopic parallax
In the spectroscopic or photometric parallax is not examined the direction of the light as the trigonometric parallax, but its quality. In addition to the temperature of a star, the intensity of the incoming light with us naturally also depends on the distance, which makes it possible to measure the distance. Of course, the brightness of a star that can be directly observed, only the so-called apparent magnitude m. A very bright star which is far away, and a very nearby star, but only dimly lit can both appear to us equally bright. Therefore, it is necessary to define the absolute magnitude M: it corresponds to the apparent magnitude, which would have an object if it would be exactly 10 pc from Earth. Following relationship exists between apparent and absolute brightness:
Where the distance r must be specified in parsecs. If the absolute brightness of an object is known, the distance immediately from the measured apparent brightness can be calculated. The absolute magnitude can be determined by comparing spectra. The spectrum of the object is used with a known distance as a measure - that is, the spectroscopic parallax builds directly on the trigonometric parallax.
Dynamic parallax
The dynamic parallax is used to determine the distance of visual double stars. For this, the train speed, which can be determined spectroscopically to be known; from the apparent distance of the two stars and the orbital period of stars around their center of mass, you can now calculate the distance.
Redshift
The distance determination using the redshift of the light is applied at very distant objects such as galaxies or quasars. For this distance, there is no alternative measurement methods. For the redshift of known spectral lines must be identified in the spectrum of a galaxy and its exact wavelength to be measured. The distance can be calculated by means of the Hubble constant using the following formula:
The frequency shift and the vacuum speed of light are.
Application of distance measurement
For each distance range appropriate means of measurement are needed. The following is an overview of the various applications of the distance measurement is given.
Distance measurement in everyday life
The direct measurement is the most common method of distance measurement in everyday life. It compares the distance to be measured with a multiple of the length standard. This is done not usually with a replica of the standard meter shown on the right, but with an inexpensive and handy folding ruler, tape measure or ruler. With these measuring means longer distances can be determined by repeatedly sets the standard succession. This will of course also increases the measurement error. For very small lengths in everyday life of 0.1 millimeters to 200 millimeters using mechanical precision measuring instruments such as calipers or micrometers. In inaccessible places such as between machine parts also deformable wax strips, called Plastigauges can be used.
Traveled pathes
The distance measurement on distances driven mainly by using an odometer, the determined by counting the revolutions of the wheel track. Such odometer are common in motor vehicles and bicycles. Although the method implies inaccuracies of up to a few percent of the distance (for example of worn automobile tires having a slightly smaller diameter than a new ); for simple calculations for navigation or the fuel consumption, it is sufficient, however. More precise measurements allows a so-called Peiselerrad. For simple geodesic measurements, the Hodometrie is practiced with a measuring wheel. For walkers there are pedometer (step counter). More recently spread in the motor vehicle, with walkers and cyclists GPS - based navigation systems that can measure and record the distances. Special systems can also measure altitude profiles and record what may be for hikers, cyclists and mountain bikers of interest. Also, hang gliders, gliders and paragliders use such systems.
The steeper the distance traveled, the greater the deviation between the actual and displayed by the GPS system track is ( for the latter we find the name of pseudo- distance, a German synonym has probably not yet been established ).
To this end, a numerical example with the Pythagorean Theorem
The distance b is 4 units of length; the distance a is 3 LE. Then c is 5 LE long. The distance c is a steep mountain pass. A navigation system claims of road users have completed only 4 LE: the used by him for computational purposes map is flat, that is, it ignores the periods height differences, and thus the resulting Wegverlängerungen ( in the numerical example: 5 LE instead of 4 LE).
Land Surveying
At distances of a few kilometers, as you have to determine in the national survey, one resorts to the geodesic triangulation. This determines the accuracy of the angle measurement and the length of the benchmark index on the achievable measurement accuracy. A triangulation, a relative accuracy of one millionth ( 0, 000 001 ) of the measured length possess. A survey of Germany, the south is about 1000 kilometers long from north would thus have an error of about one meter. Additionally, however, the standard error has to be taken into account, which is introduced through the reference scale.
Triangulatorische distance sensors operate on the principle of laser triangulation, often a light emitting diode is used as a beam source with low requirements here.
Flight Distances
With radar waves distances between a few centimeters to several million kilometers can be measured, which is why they are often used in aviation. The antenna emits short pulses at a frequency of a few gigahertz ( Hertz) and measures the time until the receipt of the signal reflected from the object. In addition to the distance can be measured even the speed and direction of the object.
Instead of radio waves are also different types of optical distance measurement used. There are flashing lights, lasers and light emitting diodes are used. Examples are cloud height measurement using reflected signals flash a flash lamp, laser gun and LIDAR and laser triangulation, which works with low requirements with a light-emitting diode.
Underwater and in the earth
Distances under water is usually determined by sound waves, for example, a sonar or sonar. For seismic surveying within the earth is used, inter alia, pneumatic impulse sound sources or explosives and determines the running times to several microphones.
Photography
In photography, it is necessary to adjust the lens used on the correct distance to the subject. There exists a variety of approaches, the technical implementation of this problem. For the determination of the minimum focusing distance of optical rangefinders are frequently used. Many are built directly into the viewfinder or be reflected in the viewfinder.
Micro - and nanometer range
The visible world is limited by the wavelength of light. Things that are less than about half the light wavelength of about 0.5 micrometers, are not directly observable. Up to this limit, you can make very good direct measurements but still. For this we use measuring microscope for vertical measurements or measuring eyepieces for lateral measurements and microscopic scales, so-called stage micrometer, which is compared directly with the object size.
The optical distance measurement offers many different methods to one micron and even significantly below are practical in the field. The phase shift method permits distance measurements to a hundredth of the wavelength of light and is used in white light interferometers or interferometer.
Atoms and elementary particles
Atoms and elementary particles fill the space below one nanometer ( meters). The size of atoms and elementary particles determine the physicist by means of scattering experiments or sophisticated instruments such as atomic force microscopes. But when it comes to small changes in length, even with very large reference distances, so can be refined methods of interferometry, as has happened in the GEO600 experiment, so an accuracy of only meters at a reference distance of 600 meters to the most accurate measuring instruments the world belongs.
Solar system
For very large, extends beyond our earth distances astronomy has developed a great wealth of measurement methods, some of which are tailored to very specific applications:
Distance of the moon
The moon takes in the distance measurement among the celestial bodies in our solar system a special position.
Since the first moon landing in 1969, a highly accurate distance determination is possible. From the crew of Apollo 11 at that time was an array of retroreflectors, the so-called lunar laser ranging Retroreflector array, situated on the lunar surface in Mare Tranquillitatis (see image ). This makes it possible to determine the distance of the moon to within a few centimeters. For this purpose, a laser beam emitted from the surface (see picture), which is directed exactly to the reflector on the lunar surface. Through its structure, the laser beam is thrown back exactly to the transmitter. Normally come from the transmitted signal a few photons, sometimes only one back which can be detected therein. From the time that elapses between the transmission and the return of the reflected signal, the distance can then be determined exactly.
In addition to the reflector the Apollo 11 mission later four more laser mirrors were installed on the lunar surface: Two by NASA during the Apollo 14 mission (1971 north of the crater Fra Mauro ) and the Apollo 15 mission (1971 east to the Hadley Rille ); additionally contained the two Soviet Lunokhod Moon vehicles per a laser reflector, but unlike Lunokhod 2, which was stationed in 1973 during the unmanned lunar mission Luna 21 in the lunar crater Le Monnier, was from the reflector of Lunokhod 1 in the unmanned Luna -17 Mission will receive after completing the activities 1970/1971 in the Mare Imbrium decades no more laser echo. In March 2010, Luna 17 and Lunokhod 1 was finally discovered on recordings of the probe Lunar Reconnaissance Orbiter. Thus, a calculation of the Park position was possible: 38.2473 ° N; 325.002 ° E for Luna 17 and 38.32507 ° N; 324.9949 ° E for Lunokhod 1 After recalculating the park position, the reflector could be used again. On April 22, 2010 Laser measurements were successfully carried out by the Apache Point Observatory.
By continuing for more than 35 years, measurements not only the moon distance could be determined very accurately, but also insights in many other fields were won. It could be found, for example, that the moon by about 3.8 cm per year from Earth. This is due to the tide friction, which reduces the angular momentum of the earth. The precise measurement of the distance and the numerical value of the gravitational constant could be calculated very accurately. Since the beginning of the measurements, the thus determined values differ only by a factor of. The validity of the general theory of relativity could be confirmed by the exact distance measurements. 2003 APOLLO (Apache Point Observatory Lunar Laser -ranging Operation) was founded: With the 3.5 -meter telescope at the Apache Point Observatory in New Mexico since 2006, is the accuracy of the data collected so far in the millimeter range.
Radar measurements
For the inner planets, Mercury, Venus and Mars and the asteroids astronomers can use active run-time measurements. They rely on a sophisticated radar distance measurement. For more distant objects, the failed but because the signal propagation time is too long and the reflected energy is too small.
The Milky Way
At distances that extend beyond our solar system, initially helps a method that is commonly used in land surveying: Triangulation, which is called in astronomy as a Trigonometric parallax. With their distances to meter are determined. This is sufficient to measure the distance of the adjacent regions of the Milky Way.
The galaxies and the universe
For distances over 1 zeta meter ( about 100 000 light- years), beyond our Milky Way Astronomers use the photometric parallax. In order to calibrate these methods are so-called " standard candles " used. These are stars with a known absolute brightness, from which then can be determined by measuring the apparent brightness determine the distance. The absolute brightness is known, for example in the Cepheids, because in them the so-called period-luminosity relationship.
The distance of globular clusters can be determined by their color and brightness and the color-magnitude diagram.
Finally, to measure the expansion of the universe, the redshift of the galaxies is determined. It provides a range is detected up to around meters.