What are the results you can record with a radio telescope? In this article you can see spectra, cross-scans and radio maps you can record with SPIDER radio telescopes. When we record a picture of an Universe object, we usually use a digital camera that has many pixels (typically several millions). This way, when we record the picture, the light we receive “lighten” many pixel at the same time and each pixel records light coming from different sky areas. But, when we use radio telescopes, we record the signal from a single area of the sky (only large professional radio telescopes may have more LNA units), just as if our camera had only one pixel.
If the instrument is equipped with a precise automatic pointing and tracking system, and you have the coordinates of Universe radio sources in the sky (as in our SPIDER radio telescopes), you can point the antenna to the correct direction, and then record the radiation flux coming from the object itself. This is relates to the power of the signal emitted by the radio source. The type of data obtained depends on the receiver characteristics and by the fact that the measure could be calibrated or not. That’s why, in general, the first result you get radio telescopes pointing the sky is a number.
Results of radio telescope: on the left, radio telescopes record the radio waves coming from a specific area of the sky. On the right, radio telescopes can also record cross-section of the radio source to study.
Another result type that can be obtained with radio telescopes is a cross-scan. This technique consist in pointing the radio telescope to the selected target and command data acquisition by moving the antenna in azimuth and elevation, this way creating a cross section centred on the target with the antenna tracking system, with a faster speed than sidereal rate. We can thus record a curve of values and, if the radio source is perfectly centred, the resulting central peak has a direct correlation with the radio emission coming from the source. This type of result is very interesting since it allows to evaluate also antenna parameters such as the resolution capabilities of the antenna and is also used to verify performance of radio telescope.
The results of radio telescopes: Cross-Scan the Sun recorded by SPIDER 300A radio telescope.
By using a specially designed receiver and backend, like our SPIDER radio telescopes, the captured signal coming from a precise area of the sky may be sampled with a digitiser. This way the radio telescope is able to detect also the spectrum of the target. This is particularly interesting when the user wants to detect particular emission lines like the neutral Hydrogen line emitted by the Milky Way.
The results of radio telescopes: spectrum of Cassiopea A showing the neutral Hydrogen line at 1420 MHz, captured with SPIDER 300A radio telescope.
If the radio telescope has a precise tracking and automatic pointing system, we can record a radio map of the object that we want to study. This allows us to record an image of the object radio emission. In order to do so, the radio telescope is continuously moved by scanning the desired sky area and recording the radio emission which comes from each pixel that compose our image. Some pixels will record a different quantity of radio waves from the adjacent ones and each number is then associated with a color, this way generating a radio image of the object! Our SPIDER radio telescopes allow the user, in a very simple way, to obtain these results with a compact radio telescope by using the RadioUniversePRO software. In the image below, you can see a radio map of the Cassiopea A supernova remnant recorded with SPIDER 300A radio telescope.
The results of radio telescopes: radio map of Cassiopea A recorded with SPIDER 300A radio telescope. Each pixel corresponds to a numerical value proportional to the intensity of the radio emission coming from a precise sky area.
Radio interferometry is an advanced technique, developed by professional radio astronomers, that allows to use many smaller antennas instead of a too large one. In fact, when we think of a radio telescope, we imagine an instrument of enormous dimensions, equipped with a very large parabolic antenna that collects radio waves coming from space. By using many compact radio telescopes, radio interferometry improves results in radio astronomy research and allows the use of more affordable radio telescopes. For example, by using this technique the Event Horizon Telescope (an international collaboration of multiple radio telescopes from all over the world) recorded, in April 2019, the first radio map of a black hole inside the M87 galaxy, with an incredible resolution of 25 microarcseconds!
Radio interferometry: basics
When we look at a point source, such as a star, with a telescope, a point image will not form on the focal plane since the circular aperture of the instrument causes diffracted rays to generate a particular “pattern” on the focal plane, first explained by George Airy in 1835 with his “wave theory of light”: this pattern consists of concentric light regions alternating with dark ones. These rings, increasingly weaker as you move away from the center of the pattern, are the product of diffraction and have a peak in the central area, called “Airy disk”.
Introduction to radio interferometry: The diffraction pattern for a stellar type object shows the peak called “Airy disc” in the center
The optical resolving power of a telescope is related to the size of the Airy disk which depends on the wavelength λ of the observed radiation and the diameter D of the instrument. Using the approximation for small angles, Airy’s disc has an angular size given by the equation θ ≈1.22 λ/D: the larger the diameter of the instrument, the greater the theoretical resolution. If we now assume to observe a celestial object formed by 2 or more stars arranged very close to each other, Airy’s discs will overlap on the focal plane of the telescope, therefore it will be possible to “resolve” each of the stars only if the peaks the centers of each pattern won’t be added destructively, that is when their focal plane distance is no shorter than the radius of Airy’s disc (this rule known as Rayleigh’s condition).
Introduction to radio interferometry: Rayleigh’s condition explains how an instrument “resolves” two apparently close stars due to the overlap of their diffraction patterns on the focal plane
This applies not only to optical telescopes but also to radio telescopes which, due to the longer wavelength they record to “observe” the sky, have a much lower resolution capability than the optical ones, given the same diameter. For example, in order to match the resolution of Hubble Space Telescope (2.4 meters in diameter), ALMA, one of the most modern radio telescopes recording millimeter radio waves, would need a 5 km diameter parabolic antenna.
Michelson’s interferometer is based on the interference properties of light: a beam of electromagnetic waves coming from the same source (in the case of a radio telescope, from a celestial object) is divided into 2 parts on different paths and subsequently reconverted. If the 2 paths have different lengths or move through different materials, there is a phase shift in their optical path. We will obtain maximum light intensity when the angle θ formed by the direction of the star with respect to the optical axis of the instrument is such that the difference between the paths of the 2 beams is an integer number of wavelengths (with respect to the center of the passband). If the angular dimensions of the star are small compared to the space between 2 adjacent interference maxima, the image of the star will be crossed by a clear pattern of alternating dark and light bands, known as interference fringes. Conversely, if the angular dimensions of the star are comparable to the spacing between the maxima, the image will be the result of the superposition of a series of patterns along the star, where the maxima and the minima of the fringes do not coincide and the amplitude of the fringe will be attenuated, as shown in figure below (b). Thanks to this technique, in 1920 Albert Michelson and Francis Pease created the first “stellar interferometer” and by using it they measured that the diameter of the Betelgeuse star was equal to the Mars orbit.
Introduction to radio interferometry: Michelson-Pease stellar interferometer used to measure diameter of Betelgeuse star for the first time in 1920
The first radio interferometer dates back to 1946 when it was used by Ryle and Vonberg for the study of radio emissions from space that a few years earlier had been first discovered by Jansky, Reber and others. This interferometer was formed by an “array” (a group) of 2 dipole antennas operating at 175 MHz frequency and having a baseline D (distance between the antennas) varying between 17 and 240 meters.
Introduction to radio interferometry: Ryle and Vonberg interferometer
It was a so-called “transit interferometer”, a diffused type in the 50s and 60s of the last century, that needed antennas to be pointed to the local meridian, at a certain elevation, and wait for the earth’s rotation to move the object along the Right Ascension. If θ is the zenithal angle of the object to be observed and is different from zero, the electromagnetic waves will reach antenna B first (see figure above) and subsequently antenna A with a delay τ=(D/c) sinθ, where c is the speed of light. The detector of the receiver, integrated over time, will generate a response proportional to the square sum of the voltages of the 2 signals similar to the trace in picture below.
Introduction to radio interferometry: response generated by transit interferometer detector, during the passage of two strong radio sources at the meridian, around 16:30 and 19:30 respectively.
Modern radio interferometry
The countless technological advances of recent years have led to a large use of interferometry in radio astronomy. Just think of the large networks of professional radio telescopes that form the VLBI, Very Long Baseline Interferometry, which has been operating since the late 1970s by connecting several instruments distributed in several parts of the world, with the aim of creating a single large instrument with an equivalent diameter of thousands of kilometers. Among the most sensitive and performing networks in the world there is the EVN, Europe VLBI Network, which uses the largest European radio telescopes for periods of a few weeks a year.
Introduction to radio interferometry: the antennas of the EVN network do not only include instruments in Europe.
Among the most famous networks we also remember the VLBA, Very Long Baseline Array, which uses 25 radio telescopes located along the American continent; ALMA, an array of antennas that rises on the Chilean plateau at 5000 meters above sea level and that since 2013 observes the sky in wavelengths from 0.3 to 9.6 mm; LOFAR, an interferometer managed by ASTRON in the Netherlands capable of mapping the universe at frequencies between 10 and 240 MHz; SKA, the Square Kilometer Array, an ambitious project currently under construction that will see the creation of 2 arrays ensuring constant coverage of frequencies from 50 MHz to 14 GHz.
Introduction to radio interferometry: the ALMA interferometer in the Chilean Andes observes the sky at millimeter wavelengths. Credit: ALMA (ESO/NAOJ/NRAO)
Radio interferometry with small instruments?
Although some experiments of amateur radio interferometry date back to the 80s of the last century, it was with the advent of the Sat TV systems at the end of the last century that we a progressive increase in amateur experiments, however always by few electronics experts.
Introduction to radio interferometry: an amateur interferometer in the 1990s, consisting of two satellite TV antennas (by radio astronomer Goliardo Tommassetti).
Introduction to radio interferometry: 3 SPIDER 500A radio telescopes installed at Sharjah Academy for Astronomy, Space Sciences & Technology
The difficulties in the realization of an interferometer project are many: first of all the antennas that compose the array must have very high mechanical precision, with a mount for radio sources pointing and tracking ff the large antennas equipped with a precision similar to the one of an optical telescope. SPIDER radio telescopes are in fact equipped with ultra-low backlash alt-az mounts and with encoders capable of reading few arc seconds errors. They are also equipped with an specially designed feed for 21cm wavelength, with double polarization, connected to very low noise LNAs that amplify the signal before it reaches the receiver. For the operation of the interferometer, PrimaLuceLab is developing a device that transforms the radio frequency output from the LNA into an optical signal over fiber, even at distances in kilometers. This eliminates the normal coaxial cables and therefore the losses in the signal between antennas and receivers.
Introduction to radio interferometry: interferometer scheme with 3 antennas, every instrument has its own rack with receiver, backend, timing synchronization device, data storage and host.
In the control room, on the other end of the optical fiber, the signal will be transformed in the RF band and connected to the receiver (one for each antenna). To maintain adequate time consistency, a synchronization device will also be developed for the timing of radio telescopes and for the acquisition system. Then, signal will be digitized by means of an extremely performing backend and which will save the data on disk for subsequent processing. Finally, signals from each antenna will be sent to the digital correlator that, based on the Fourier transform, will perform the calculations necessary for the signal correlation and will output the visibility functions for each baseline of the antennas array.
Introduction to radio interferometry: Radio2Space backends, one for every SPIDER radio telescope, controlled by RadioUniversePRO software.
Thanks to the radio interferometry technique, we are developing an affordable interferometer system to simultaneously use many radio telescopes and obtain high resolution radio maps of radio sources in the Universe. The system will be configurable with a variable number of antennas and it will also allow the user to increase their performance by installing more antennas in a later moment. Thanks to this system, universities, scientific museums, planetariums, research institutes but also groups of amateurs will have at their disposal a scientific instrument, ready to use but very powerful, that up to yesterday was available only to professional researchers.
Radio astronomy is a fascinating science and it studies the Universe by detecting radio emission from many objects like the Sun, the Milky way, planets, galaxies and nebulas. In this presentation Filippo Bradaschia, PrimaLuceLab president and co-founder, gives an overview on radio astronomy history and basic physics. Then he introduces the most important radio sources in the Universe and the SPIDER affordable radio telescopes developed by PrimaLuceLab with Radio2Space brand. These instruments allow any school, university, museum or science institute to make real radio astronomy with powerful but affordable, compact and easy to use radio telescopes.
By today, radio astronomy can be performed not only by professional radio astronomers. In fact PrimaLuceLab builds complete radio telescopes ready for use for educational (schools, universities, science museums) and research (science institutes, space agencies) markets at an affordable price. This way you no longer need to study how to build a radio telescope but you can use a certified and powerful instrument, and focus your attention in getting data and make real radio astronomy!
SPIDER radio telescopes by PrimaLuceLab
SPIDER radio telescopes are turnkey systems composed of the antenna, mount, pier, receiver and software, ready to capture radio waves coming from space. Antenna diameters range from 2.3 to 5 meters with different types of mounts, also weatherproof in order to allow the radio telescope to be installed in the field without the need of a protection structure. Every SPIDER radio telescope is designed to be remotely operated from a control room where the H142-One 1420 MHz receiver with computer and RadioUniversePRO software are installed.
If you want to know more about our SPIDER radio telescopes, you can click here and discover all the available models. In order to allow everyone start his project, PrimaLuceLab also offers design, shipment, installation and training services. Thanks to our team specialized in radio telescopes, we can support you from design to shipment, from installation to on-site training. If you want to know more about our services, please click here.
The Sun is one of the strongest radio sources in the sky: if the part of the Sun emits more in the visible wavelengths is called photosphere, the radio frequencies born in the chromosphere and in the corona, the solar atmosphere. The solar surface has a temperature of about 6000K, and even if the gas at this temperature emits more wavelengths in the frequencies of visible and ultraviolet light, because of its proximity we can also record the radio emission.
The radio Sun: radio image of the Sun recorded by VLA. The brightest regions are part of corona nearby but beyond sunspots. Courtesy (NRAO/AUI)
The Sun emits radio waves since it’s hot hot (it is said that it is a thermal source and then emits radio waves more at high frequencies) but there is a strong emission even at lower frequencies (in the field of non-thermal sources) for the mechanism of synchrotron radiation which derives from the movement of high speed electrons around the magnetic field.
If we analyze the flux density (in simplified terms, the amount of radio waves arriving from the Sun) emitted as a function of frequency, we can highlight a second peculiarity: at wavelengths greater than 1 cm the curve is divided into two cases identified as “quiet Sun” and “disturbed Sun”. The first is defined from normal Sun activity while the second depends on the sunspots activity.
The radio Sun: sun spectrum from ultraviolet to radio waves (from “Radio Astronomy, J. D. Kraus”)
In reference to “quiet Sun” emission , the solar disk has a different diameter in function of study frequency.
At very low frequencies (below 0.1 GHz) and therefore at very long wavelengths (> 3m) the solar disk appears much bigger and brighter in the center, and its brightness gradually decreases and vanishes after several solar radii.
For frequencies between 0.1 GHz and 3 GHz, the Sun is still larger than its optical counterpart and a radio peak intensity near the edge called limb brightening is noticeable.
For frequencies above 3 GHz the Sun appears similar (though still greater in size) to its visible counterpart and its brightness is uniform.
From these considerations it is possible to verify that higher frequency radio waves originate closer to the photosphere, the ones with lower frequency in the corona, which then gives the Sun a greater dimension in the sky.
In the case of a ‘disturbed Sun’, it is possible to delineate a low variability component, ranging from days to months, which is evident at wavelengths from 3 to 60 cm and a high variability component characterized by strong emissions of radiation in time intervals from seconds to hours. The first component is closely associated with the presence of sunspots even when not directly visible because they are beyond the edge of the Sun. Then this radio emission originates in regions above the photosphere.
The second component (with high variability) instead is linked to strong emissions that follow the occurrence of flares, violent matter explosions initially visible in the visible band of H-alpha (for example with specialized solar telescopes). Flares can be divided into impulsive or eruptive. The former have a short duration, from seconds to minutes, and develop only in the lower layer of the solar atmosphere. The latter have longer life, from minutes to hours, and can generate huge amounts of energy and matter ejected into space. Flares are caused when charged particles are suddenly accelerated. The energy required for this acceleration is derived from the magnetic field around the most active areas of the solar surface. During the impulsive phase of the flare, there is a fast increase in the intensity of radio waves with centimeter or decimetre wavelengths. The most powerful eruptive flares emit radiation for several hours.
The radio activity bound to these phenomena is classified (Wild, Smerd, Weiss , 1963) in function of the characteristics of this emission:
Type I: short events that occur in large numbers associated with a continuous emission (duration: from hours to days)
Type II: strong events with frequency shift from high to low values (duration: minutes)
Type III: strong events with short duration with frequency shift from high to low values (duration: seconds)
Type IV: continuous emission (duration: from hours to days)
Type V: continuous emission associated to type III, recorded in frequencies lower than 100 MHz (duration: 1-2 minutes)
The characteristics of these types are well illustrated when considering the events that follow a solar flare.
The radio Sun: Representations of the two phases following a solar flare (from: Wild, Smerd, Weiss – Solar Bursts, Ann. Rev. Astron. Astrophys., vol. 1, 1963)
In phase 1, there is a strong type III emission immediately after the onset of a flare visible in the H-alpha line. There is a very strong radio emission that ends quickly and that, it is believed, is derived from the oscillations of the plasma associated with the expulsion of electron beams in response to flare. Sometimes, especially at frequencies below 100 MHz , the flare is associated with a more continuous and long lasting emission, the type V. The electromagnetic waves of this type are generated by the acceleration of electrons along the magnetic field lines in the corona.
In events strongest , ie in the eruptive ones, there is also the phase 2 which begins with short and net signals peaks which often also include a second repeat (harmonic). This emission comes by the shock wave front to the gas cloud above the flare. At times, immediately after you can record a weaker but continuous signal that can last from hours to days and that is called type IV . The latter is related to the synchrotron emission coming from the gases above the flare and it can have short and strong signal peaks classified as type I.
Among the radio burst type IV there is one type , called “mu-burst type IV” , in which the signal is emitted, with wavelengths from 30 cm to 1 cm, so even above 10 GHz. This allows us to understand that the Spider230 radio telescope can also be used for studies of thesesolar atmosphere phenomena, possibly associated with a H-alpha solar telescope to study simultaneously the different components of the electromagnetic spectrum coming from the same phenomenon, namely a flare.
The radio Sun: radio spectrum of an intense event linked to flares (from: Wild, Smerd, Weiss – Solar Bursts, Ann. Rev. Astron. Astrophys., vol. 1, 1963)
Sometimes, during the most intense phenomena, high energy cosmic particles are emitted from the Sun and, when they encounter the Earth’s magnetic field, they generate magnetic storms and auroras.
Largest radio telescopes in the world are used by professional radio astronomers, and often you can also visit them. Radio telescopes are extraordinary instruments, equipped with giant parabolic antennas or other, designed to work as single instruments or as interferometers. They are used to study objects in the Universe in radio waves frequencies but often are also used for satellite communication or studies of Earth’s atmosphere. Here you have a list with some of the largest radio telescopes in the world and a brief description for each instrument.
Very Large Array – VLA (USA) Probably one of the most famous radio telescopes in the world thanks to films like “Contact”, it uses 27 Cassegrain antennas each 25 meters diameter that can be moved along a Y shaped rail system.
Largest radio telescopes: VLA (Credit: Alex Savello)
Arecibo (Puerto Rico) Up to 2016, it was the largest parabolic antenna in the world, thanks to its 305 meters diameter. The antenna was placed on a natural depression in the ground and it has no mount: the radio telescope can point different sky regions moving the central feedhorn.
Largest radio telescopes: Arecibo (Credit: Arecibo Observatory)
GBT (USA) The Robert C. Byrd Green Bank radio telescope has a parabolic antenna with asymmetric surface and an off-axis illumination. In Green Bank there are also other large radio telescopes such as the 43-meter diameter one with equatorial mount.
Largest radio telescopes: GBT (Credit: NRAO/AUI/NSF)
Atacama Large Millimeter/submillimeter Array – ALMA (Chile) The ALMA radio telescope includes many 7 and 12 meters diameter parabolic antennas that have been installed in Atacama desert in Chile, about 5000 meters above sea level. Thus, it will study also the high radio frequencies usually blocked by the atmosphere.
Largest radio telescopes: ALMA (Credit: NRAO/AUI/NSF)
FAST (China) The Five-hundred-meter Aperture Spherical radio Telescope (FAST)) is a radio telescope located in southwest China. It consists of a fixed 500 m diameter dish constructed in a natural depression in the landscape and it is the world’s largest filled-aperture radio telescope.
Largest radio telescopes: FAST (Credit LIU XU)
Effelsberg (Germany) Thanks to the huge 100 meters diameter parabolic antenna, this is one of the largest radio telescopes in the world. This radio telescope weighs 3200 tons and it takes 12 minutes to make a complete 360 degrees rotation.
Largest radio telescopes: Effelsberg (Photo by CEphoto, Uwe Aranas)
Medicina (Italy) Near Bologna there are two radio telescopes: the “Northern Cross” that consists of an array of antennas in two perpendicular arms and a 32 meters diameter parabolic antenna which is also used in interferometric observations.
Largest radio telescopes: Medicina (Credits: Filippo Bradaschia)
Sardinia Radio Telescope (Italy) This radio telescope, built 35 kilometers away from Cagliari, uses a 64 meters diameter parabolic antenna designed with high accuracy (among the best of several radio telescopes in the world) in order to allow recording at high frequencies (up to 100 GHz).
Largest radio telescopes: SRT (Credits: INAF)
Lovell Radio telescope (England) With its 76 meters diameter antenna, this instrument is one of the largest radio telescopes in the world with movable reflector. It is located in Jodrell Bank (England) and it’s part of English MERLIN interferometer system.
Largest radio telescopes: Lovell (Credits: Mike Peel; Jodrell Bank Centre for Astrophysics, University of Manchester)
Parkes (Australia) Parkes Observatory is located in the south-eastern Australia and it uses a great 64 meters diameter parabolic antenna. In addition to radio astronomy, it was also used to collect the Apollo 11 transmissions coming from the Moon.
Largest radio telescopes: Parkes (Credits: Stephen West)
Square Kilometer Array – SKA Currently under study, it uses a network of thousands of antennas installed both in Australia and in South Africa. Combining the recorded signals, it will be possible to obtain a collecting area equivalent to the one of 1 square kilometer parabolic antenna.
Largest radio telescopes: SKA (Credits: SKA Organisation)
Radio astronomy is a young science, born at the beginning of 20th century. There are two figures that have historically contributed to birth of this science: Karl Jansky and Grote Reber.
Jansky was an engineer that, at the end of 20s, worked at Bell Labs in New York society where, in particular, he were dedicated to recording of atmospheric interference at shortwave. From summer of 1931, Jansky built an instrument and he began to record an inexplicable signal whose origin was not clear. In 1932 he realized that the signal had every day a small advance over time and so Jansky concluded that it had to come from outside the Solar System. He became so famous in newspapers and on radio, but despite trying to attract attention of astronomers, his discovery was not followed. Jansky did not even have to any scientific recognition for his discovery and he died in 1950.
Karl Jansky (Credit: NRAO/AUI)
Grote Reber was only to deepen Jansky results building an instrument in order to receive waves from space. He built it in his house garden, the first radio telescope with parabolic antenna in the world. His instrument was equipped with a parabolic dish with a diameter of 9.6 meters and an altazimuth mount. From 1937 he began reception attempts at 3300 MHz but got nowhere until, in 1939, he began to record signal coming from Milky Way lowering frequency at 160 MHz. He began to realize first maps of sky radio emission and, with the construction of new and more sensitive receiver at higher frequency, he gradually improved resolution capacity.
Grote Reber (Credit: NRAO/AUI)
After these initial and fantastic discoveries, few were interested in radio astronomy until the end of Second World War during which immense development of radar techniques allowed for the first time to build sensitive instruments to record faint radio signals also from more distant objects in the Universe.
Is the world exactly as we see it? It is not so simple. For example, some animals, such as bees, can see parts of electromagnetic spectrum that we can not see (such as ultraviolet light or infrared): the world does not appear to them as to us. Our eyes are in fact sensitive to wavelengths between 400 and 700 nanometers (1 nanometer is one millionth of a millimeter). Instead electromagnetic spectrum is made up of many types of waves of which the visible is only a small area:
Components of electromagnetic spectrum
Radio waves: are characterized by higher wavelengths, greater than 1 millimeter. Higher frequency radio waves are called microwaves.
Infrared: with a wavelength between 700nm and 1mm, we humans we can not see it but we perceive it as heat on skin.
Visible light: with a wavelength between 700 and 400 nm, it is the part of electromagnetic spectrum that we can see and which is expressed through rainbow colors.
Ultraviolet: it has a wavelength between 400 to 10 nm and it is responsible for our tans.
X rays: characterized by a wavelength between 10 and 0.01 nm, they are very important for medical application because they are used for medical diagnostics.
Gamma rays: with a wavelength less than 0.01 nm, are those with greater energy.
Does this mean that if we want to study the Universe in ultraviolet it is enough to build a telescope for these wavelengths, have with a camera sensitive to ultraviolet and point it toward the heaven? No, because atmosphere of our Earth acts as a filter blocking large part of electromagnetic spectrum except the visible and radio one. That’s why you can use radio telescopes from the ground to study while for other frequencies it is necessary to construct and send special telescopes in space as satellites. In electromagnetic spectrum, radio window is extended from about 15 MHz (wavelength of about 20 meters) to 30 GHz (wavelength of about 1 cm). These limits are not clearly defined as they vary with altitude, geographic location and time.