Astronomers look for exoplanets by looking at the effects those planets have on the stars that they orbit. Astronomers are able to detect exoplanets because the planets have some kind of measurable impact on their stars. Astronomers have used other methods to discover and study exoplanets.
Exoplanets are very hard to directly see with telescopes. This is because they are hidden by the bright glare of the stars they orbit. When a planet is very distant from the host star, the planet only spends a very small fraction of its orbit in a condition that is detectable by this technique, and thus, it is impossible to determine a planets orbital period with much ease.
This technique is performed by blocking out the light of its host star, which exposes the thermal signatures of exoplanets. As implied by the name of this technique, this technique is carried out by measuring a drop in brightness of a parent star when the Exoplanet passes in front of the host star, and is best used to discover larger planets with smaller orbits. As with the transit method, large planets that orbit nearer to the host star are easier to detect than others that orbit near their host stars, because those planets capture a larger amount of light from the host star.
In other words, it is very hard to detect the light being reflected off the atmosphere of the planet when its parent star is much brighter. It is extremely difficult to image an exoplanet directly, because the starlight is overwhelming the planet -- more than a million times. This technique for exoplanet discovery works by having the stars gravity field act like a lens, eventually amplifying light from the background star far away, but this is only possible if two stars are nearly perfectly lined up, explaining why such few exoplanets have been discovered using this technique.
Although only a few planets have been discovered using only this method to date, this could eventually prove the more fruitful technique, as it does not require that the exoplanet transit directly between us and a star that is much farther away to allow us to detect it, opening up a far wider array of possible discoveries. The precision required to discover a planet orbiting a star using Astrometry is extremely hard to obtain, and because of that, only one planet has been discovered using this method, though Astrometry has been used to perform follow-up observations of planets discovered using other methods. This technique can also be used to identify planets orbiting a star, measuring minute changes in the stars position as it swings about the center of mass of a planetary system.
The transit technique has also the advantage of detecting planets around stars located several thousand light-years away. Earth-like planets cannot be detected by the transit method, as wobbles caused by Earth-like objects are too small for present instruments to measure. Finding signals caused by small planets in data may be difficult, if not impossible, using conventional techniques, in cases in which interactions between planets change the periodicity of transit phenomena.
A complementary technique is transit photometry, which measures dips in starlight caused by those planets whose orbits are oriented in space so as to periodically transit between their star and a telescope; observations of transits reveal the sizes of planets, as well as their orbital periods. Unlike most other techniques, which have detection biases toward planets with smaller (or, for resolution imaging, larger) orbits, microlensing techniques are more sensitive to detect planets about 1-10 astronomical units from sun-like stars. The primary advantages of the gravitational microlensing technique are that it can detect planets of small masses (in principle, as small as Mars masses, using future space projects like WFIRST); it can detect planets with large orbits, comparable to Saturn and Uranus, that have orbital periods too long for the radial velocity or transit methods; and it can detect planets around very distant stars. Modern spectrographs can also readily detect Jupiter-mass planets orbiting at distances as short as 10 astronomical units from their host stars, but the detection of these planets requires years of observations.
Direct imaging has also been used to discover some especially massive "rogue" planets--those floating free in space rather than orbiting the star. Planets orbiting brown dwarfs -- objects that are technically not classified as stars, since they are neither hot nor massive enough to produce fusion reactions, and therefore emit little light -- may be easier to spot, too. More massive stars are more likely to harbor planets that are larger than Saturn, but that correlation might not hold true for smaller planets. Most stars hosting planets are main-sequence stars that are similar to our suns spectral class.
Some characteristics are shared by the majority of known exoplanets, as well as by the stars that they orbit. Stars containing large fractions of heavier elements (i.e., all elements except hydrogen and helium) are likely to host detectable gas giant planets. If we know a stars size and a planets distance from it (the latter determined through a different method of detection, radial velocity, lower in this list), and observe a planet blocking out some percent of a stars light, we can compute a planets radius solely based on those values.
The transit technique does not just allow us to estimate planets radius, but it provides information about their masses, which then gives insight into their density and composition. Astronomer Kate Follette, who works with this technique, told EarthSky the number of exoplanets found by the transit method is variable, depending on ones definition of planet. Direct observations are a better tool than indirect ones, but since the planets are so far away, and are essentially hidden from view by the way they are small and dim relative to their host stars, direct observations are generally not possible.
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