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The first discovery of a planet using this method Keplerb was announced in Massive planets can cause slight tidal distortions to their host stars.

In addition, the planet distorts the shape of the star more if it has a low semi-major axis to stellar radius ratio and the density of the star is low.

This makes this method suitable for finding planets around stars that have left the main sequence. A pulsar is a neutron star: Pulsars emit radio waves extremely regularly as they rotate.

Like an ordinary star, a pulsar will move in its own small orbit if it has a planet. Calculations based on pulse-timing observations can then reveal the parameters of that orbit.

This method was not originally designed for the detection of planets, but is so sensitive that it is capable of detecting planets far smaller than any other method can, down to less than a tenth the mass of Earth.

It is also capable of detecting mutual gravitational perturbations between the various members of a planetary system, thereby revealing further information about those planets and their orbital parameters.

In addition, it can easily detect planets which are relatively far away from the pulsar. There are two main drawbacks to the pulsar timing method: Therefore, it is unlikely that a large number of planets will be found this way.

Like pulsars, some other types of pulsating variable stars are regular enough that radial velocity could be determined purely photometrically from the Doppler shift of the pulsation frequency, without needing spectroscopy.

The ease of detecting planets around a variable star depends on the pulsation period of the star, the regularity of pulsations, the mass of the planet, and its distance from the host star.

The first success with this method came in , when V Pegasi b was discovered around a pulsating subdwarf star.

The transit timing variation method considers whether transits occur with strict periodicity, or if there is a variation. When multiple transiting planets are detected, they can often be confirmed with the transit timing variation method.

This is useful in planetary systems far from the Sun, where radial velocity methods cannot detect them due to the low signal-to-noise ratio.

It is easier to detect transit-timing variations if planets have relatively close orbits, and when at least one of the planets is more massive, causing the orbital period of a less massive planet to be more perturbed.

The main drawback of the transit timing method is that usually not much can be learned about the planet itself.

Transit timing variation can help to determine the maximum mass of a planet. In most cases, it can confirm if an object has a planetary mass, but it does not put narrow constraints on its mass.

There are exceptions though, as planets in the Kepler and Kepler systems orbit close enough to accurately determine their masses. The transiting planet Keplerb shows TTV with an amplitude of five minutes and a period of about days, indicating the presence of a second planet, Keplerc , which has a period which is a near-rational multiple of the period of the transiting planet.

In circumbinary planets , variations of transit timing are mainly caused by the orbital motion of the stars, instead of gravitational perturbations by other planets.

These variations make it harder to detect these planets through automated methods. However, it makes these planets easy to confirm once they are detected.

Duration variations may be caused by an exomoon , apsidal precession for eccentric planets due to another planet in the same system, or general relativity.

When a circumbinary planet is found through the transit method, it can be easily confirmed with the transit duration variation method.

The first such confirmation came from Keplerb. The time of minimum light, when the star with the brighter surface is at least partially obscured by the disc of the other star, is called the primary eclipse , and approximately half an orbit later, the secondary eclipse occurs when the brighter surface area star obscures some portion of the other star.

These times of minimum light, or central eclipses, constitute a time stamp on the system, much like the pulses from a pulsar except that rather than a flash, they are a dip in brightness.

If there is a planet in circumbinary orbit around the binary stars, the stars will be offset around a binary-planet center of mass.

As the stars in the binary are displaced back and forth by the planet, the times of the eclipse minima will vary.

The periodicity of this offset may be the most reliable way to detect extrasolar planets around close binary systems. The eclipsing timing method allows the detection of planets further away from the host star than the transit method.

However, signals around cataclysmic variable stars hinting for planets tend to match with unstable orbits. Gravitational microlensing occurs when the gravitational field of a star acts like a lens, magnifying the light of a distant background star.

This effect occurs only when the two stars are almost exactly aligned. Lensing events are brief, lasting for weeks or days, as the two stars and Earth are all moving relative to each other.

More than a thousand such events have been observed over the past ten years. Since that requires a highly improbable alignment, a very large number of distant stars must be continuously monitored in order to detect planetary microlensing contributions at a reasonable rate.

This method is most fruitful for planets between Earth and the center of the galaxy, as the galactic center provides a large number of background stars.

During one month, they found several possible planets, though limitations in the observations prevented clear confirmation. Since then, several confirmed extrasolar planets have been detected using microlensing.

This was the first method capable of detecting planets of Earth-like mass around ordinary main-sequence stars. Unlike most other methods, which have detection bias towards planets with small or for resolved imaging, large orbits, the microlensing method is most sensitive to detecting planets around astronomical units away from Sun-like stars.

A notable disadvantage of the method is that the lensing cannot be repeated, because the chance alignment never occurs again. Also, the detected planets will tend to be several kiloparsecs away, so follow-up observations with other methods are usually impossible.

In addition, the only physical characteristic that can be determined by microlensing is the mass of the planet, within loose constraints.

Orbital properties also tend to be unclear, as the only orbital characteristic that can be directly determined is its current semi-major axis from the parent star, which can be misleading if the planet follows an eccentric orbit.

When the planet is far away from its star, it spends only a tiny portion of its orbit in a state where it is detectable with this method, so the orbital period of the planet cannot be easily determined.

It is also easier to detect planets around low-mass stars, as the gravitational microlensing effect increases with the planet-to-star mass ratio.

The main advantages of the gravitational microlensing method are that it can detect low-mass planets in principle down to Mars mass with future space projects such as WFIRST ; it can detect planets in wide orbits comparable to Saturn and Uranus, which have orbital periods too long for the radial velocity or transit methods; and it can detect planets around very distant stars.

When enough background stars can be observed with enough accuracy, then the method should eventually reveal how common Earth-like planets are in the galaxy.

Observations are usually performed using networks of robotic telescopes. Planets are extremely faint light sources compared to stars, and what little light comes from them tends to be lost in the glare from their parent star.

So in general, it is very difficult to detect and resolve them directly from their host star. Planets orbiting far enough from stars to be resolved reflect very little starlight, so planets are detected through their thermal emission instead.

It is easier to obtain images when the star system is relatively near to the Sun, and when the planet is especially large considerably larger than Jupiter , widely separated from its parent star, and hot so that it emits intense infrared radiation; images have then been made in the infrared, where the planet is brighter than it is at visible wavelengths.

Coronagraphs are used to block light from the star, while leaving the planet visible. Direct imaging of an Earth-like exoplanet requires extreme optothermal stability.

Mass can vary considerably, as planets can form several million years after the star has formed. The spectra emitted from planets do not have to be separated from the star, which eases determining the chemical composition of planets.

Sometimes observations at multiple wavelengths are needed to rule out the planet being a brown dwarf. The planets detected through direct imaging currently fall into two categories.

First, planets are found around stars more massive than the Sun which are young enough to have protoplanetary disks. The second category consists of possible sub-brown dwarfs found around very dim stars, or brown dwarfs which are at least AU away from their parent stars.

Planetary-mass objects not gravitationally bound to a star are found through direct imaging as well. The first multiplanet system, announced on 13 November , was imaged in , using telescopes at both the Keck Observatory and Gemini Observatory.

Three planets were directly observed orbiting HR , whose masses are approximately ten, ten, and seven times that of Jupiter.

In , it was announced that analysis of images dating back to , revealed a planet orbiting Beta Pictoris. In , it was announced that a " Super-Jupiter " planet with a mass about The New Worlds Mission proposes a large occulter in space designed to block the light of nearby stars in order to observe their orbiting planets.

This could be used with existing, already planned or new, purpose-built, telescopes. In , a team from NASAs Jet Propulsion Laboratory demonstrated that a vortex coronagraph could enable small scopes to directly image planets.

Another promising approach is nulling interferometry. It has also been proposed that space-telescopes that focus light using zone plates instead of mirrors would provide higher-contrast imaging, and be cheaper to launch into space due to being able to fold up the lightweight foil zone plate.

Light given off by a star is un-polarized, i. However, when the light is reflected off the atmosphere of a planet, the light waves interact with the molecules in the atmosphere and become polarized.

The main disadvantage is that it will not be able to detect planets without atmospheres. Larger planets and planets with higher albedo are easier to detect through polarimetry, as they reflect more light.

Astronomical devices used for polarimetry, called polarimeters, are capable of detecting polarized light and rejecting unpolarized beams. The first successful detection of an extrasolar planet using this method came in , when HD b , a planet discovered three years earlier, was detected using polarimetry.

Originally, this was done visually, with hand-written records. By the end of the 19th century, this method used photographic plates, greatly improving the accuracy of the measurements as well as creating a data archive.

If a star has a planet, then the gravitational influence of the planet will cause the star itself to move in a tiny circular or elliptical orbit.

Effectively, star and planet each orbit around their mutual centre of mass barycenter , as explained by solutions to the two-body problem.

Since the star is much more massive, its orbit will be much smaller. Consequently, it is easier to find planets around low-mass stars, especially brown dwarfs.

Astrometry is the oldest search method for extrasolar planets , and was originally popular because of its success in characterizing astrometric binary star systems.

It dates back at least to statements made by William Herschel in the late 18th century. He claimed that an unseen companion was affecting the position of the star he cataloged as 70 Ophiuchi.

The first known formal astrometric calculation for an extrasolar planet was made by William Stephen Jacob in for this star.

All claims of a planetary companion of less than 0. In , the Hubble Space Telescope did succeed in using astrometry to characterize a previously discovered planet around the star Gliese The space-based observatory Gaia , launched in , is expected to find thousands of planets via astrometry, but prior to the launch of Gaia , no planet detected by astrometry had been confirmed.

One potential advantage of the astrometric method is that it is most sensitive to planets with large orbits. This makes it complementary to other methods that are most sensitive to planets with small orbits.

Planets orbiting around one of the stars in binary systems are more easily detectable, as they cause perturbations in the orbits of stars themselves.

However, with this method, follow-up observations are needed to determine which star the planet orbits around. In , the discovery of VB 10b by astrometry was announced.

This planetary object, orbiting the low mass red dwarf star VB 10 , was reported to have a mass seven times that of Jupiter. If confirmed, this would be the first exoplanet discovered by astrometry, of the many that have been claimed through the years.

In , six binary stars were astrometrically measured. One of the star systems, called HD , was found with "high confidence" to have a planet.

Non-periodic variability events, such as flares, can produce extremely faint echoes in the light curve if they reflect off an exoplanet or other scattering medium in the star system.

This is more accurate than radius estimates based on transit photometry , which are dependent on stellar radius estimates which depend on models of star characteristics.

Imaging also provides more accurate determination of the inclination than photometry does. Radio emissions from magnetospheres could be detected with future radio telescopes.

This could enable determination of the rotation rate of a planet, which is difficult to detect otherwise. By looking at the wiggles of an interferogram using a Fourier-Transform-Spectrometer, enhanced sensitivity could be obtained in order to detect faint signals from Earth-like planets.

Disks of space dust debris disks surround many stars. The dust can be detected because it absorbs ordinary starlight and re-emits it as infrared radiation.

Even if the dust particles have a total mass well less than that of Earth, they can still have a large enough total surface area that they outshine their parent star in infrared wavelengths.

The dust is thought to be generated by collisions among comets and asteroids. Radiation pressure from the star will push the dust particles away into interstellar space over a relatively short timescale.

Therefore, the detection of dust indicates continual replenishment by new collisions, and provides strong indirect evidence of the presence of small bodies like comets and asteroids that orbit the parent star.

More speculatively, features in dust disks sometimes suggest the presence of full-sized planets. Some disks have a central cavity, meaning that they are really ring-shaped.

The central cavity may be caused by a planet "clearing out" the dust inside its orbit. Other disks contain clumps that may be caused by the gravitational influence of a planet.

Both these kinds of features are present in the dust disk around epsilon Eridani , hinting at the presence of a planet with an orbital radius of around 40 AU in addition to the inner planet detected through the radial-velocity method.

Additionally, the dust responsible for the atmospheric pollution may be detected by infrared radiation if it exists in sufficient quantity, similar to the detection of debris discs around main sequence stars.

COROT and Kepler were space missions dedicated to searching for extrasolar planets using transits. COROT discovered about 30 new exoplanets.

Kepler and K2 have discovered over verified exoplanets. The infrared Spitzer Space Telescope has been used to detect transits of extrasolar planets, as well as occultation s of the planets by their host star and phase curves.

The Gaia mission , launched in December , [] will use astrometry to determine the true masses of nearby exoplanets. From Wikipedia, the free encyclopedia.

Doppler spectroscopy and List of exoplanets detected by radial velocity. List of transiting exoplanets and Transit astronomy.

List of exoplanets detected by timing. Gravitational microlensing and List of exoplanets detected by microlensing. List of directly imaged exoplanets.

A stable weak dipolar magnetic field but no planet? Proceedings of the International Astronomical Union. Publications of the Astronomical Society of the Pacific.

How Do You Find an Exoplanet? Monthly Notices of the Royal Astronomical Society. Explicit use of et al. The Example of GSC ".

Astrophysical Journal — via arXiv. Protostars and Planets V. University of Arizona Press. Archived from the original PDF on 27 September Doyle 20 September A hot Jupiter with evidence for superrotation".

Archived from the original on 15 September Frail ; Frail 9 January A Fourier view of pulsating binary stars, a new technique for measuring radial velocities photometrically".

A possible method to measure stellar quadrupoles and to detect Earth-mass planets". The Asiago Survey for Timing transit variations of Exoplanets".

P Norris and F. Stootman eds , A. Brown Dwarfs and Extrasolar Planets, A. If we want to modify the data, e. The Swap method swaps the numbers between the a and b variables.

The original variables are not affected. At the beginning, these two variables are initiated. The variables must be declared static , because they are used from static methods.

We call the Swap method. The method takes a and b variables as arguments. Inside the Swap method, we change the values.

Note that the a and b variables are defined locally. They are valid only inside the Swap method. The next code example passes values to the method by reference.

The original variables are changed inside the Swap method. Both the method definition and the method call must use the ref keyword.

We call the method with two arguments. They are preceded by the ref keyword to indicate that we are passing arguments by reference.

Also in the method declaration, we use the ref keyword to inform the compiler that we accept references to the parameters and not the values.

The out keyword is similar to the ref keyword. The difference is that when using the ref keyword, the variable must be initialized before it is being passed.

With the out keyword, it may not be initialized. Both the method definition and the method call must use the out keyword.

The val variable is declared, but not initialized. We pass the variable to the SetValue method. Inside the SetValue method it is assigned a value which is later printed to the console.

Method overloading allows the creation of several methods with the same name which differ from each other in the type of the input. What is method overloading good for?

The Qt5 library gives a nice example for the usage. The QPainter class has three methods to draw a rectangle. Their name is drawRect and their parameters differ.

One takes a reference to a floating point rectangle object, another takes a reference to an integer rectangle object, and the last one takes four parameters: The solution with method overloading is more elegant.

Recursion, in mathematics and computer science, is a way of defining methods in which the method being defined is applied within its own definition.

In other words, a recursive method calls itself to do its job. Recursion is a widely used approach to solve many programming tasks.

Inside the body of the factorial method, we call the factorial method with a modified argument. The function calls itself. A variable declared inside a method has a method scope.

The scope of a name is the region of program text within which it is possible to refer to the entity declared by the name without the qualification of the name.

A variable which is declared inside a method has a method scope. It is also called a local scope. The variable is valid only in this particular method.

In the preceding example, we have the x variable defined outside the exec1 and exec2 methods. The variable has a class scope.

It is valid everywhere inside the definition of the Test class, e. The x variable, also called the x field, is an instance variable.

And so it is accessible through the this keyword. It is also valid inside the exec1 method and can be referred by its bare name.

Both statements refer to the same variable. The x variable can be accessed also in the exec2 method. The z variable is defined in the exec2 method.

It has a method scope. It is valid only in this method. If a local variable has the same name as an instance variable, it shadows the instance variable.

The class variable is still accessible inside the method by using the this keyword. In the preceding example, we declare the x variable outside the exec method and inside the exec method.

Both variables have the same name, but they are not in conflict because they live in different scopes. The variables are accessed differently. The x variable defined inside the method, also called the local variable, is simply accessed by its name.

The instance variable can be referred by using the this keyword. Static methods are called without an instance of the object. To call a static method, we use the name of the class and the dot operator.

Static methods can only work with static member variables. Static methods are often used to represent data or calculations that do not change in response to object state.

An example is a math library which contains static methods for various calculations. We use the static keyword to declare a static method.

When no static modifier is present, the method is said to be an instance method. We cannot use the this keyword in static methods. It can be used in instance methods only.

In C , the Main method is required to be static. Before the application starts, no object is created yet. To invoke non-static methods, we need to have an object instance.

Static methods exist before a class is instantiated so static is applied to the main entry point. To invoke a static method, we do not need an object instance.

We call the method by using the name of the class and the dot operator. When a derived class inherits from a base class, it can define methods that are already present in the base class.

We say that we hide the method of the class that we have derived from. To explicitly inform the compiler about our intention to hide a method, we use the new keyword.

Without this keyword, the compiler issues a warning. We have two classes: The Derived class inherits from the Base class. Both have a method called Info.

This is an implementation of the Info method in the Derived class. We use the new keyword to inform the compiler that we are hiding a method from the base class.

Note that we can still reach the original Info method. With the help of the base keyword, we invoke the Info method of the Base class too.

Now we will introduce two new keywords: They are both method modifiers. They are used to implement polymorphic behaviour of objects.

The virtual keyword creates a virtual method. Virtual methods can be redefined in derived classes. Later in the derived class we use the override keyword to redefine the method in question.

If the method in the derived class is preceded with the override keyword, objects of the derived class will call that method rather than the base class method.

We create an array of the Base and Derived objects. We go through the array and invoke the Info method upon all of them. This is the virtual method of the Base class.

It is expected to be overridden in the derived classes. We override the base Info method in the Derived class. We use the override keyword.

Here we create an array of Base and Derived objects. Note that we used the Base type in our array declaration. This is because a Derived class can be converted to the Base class because it inherits from it.

The opposite is not true. The only way to have both objects in one array is to use a type which is top most in the inheritance hierarchy for all possible objects.

Now change the override keyword for new keyword. Compile the example again and run it. A sealed method overrides an inherited virtual method with the same signature.

A sealed method shall also be marked with the override modifier. Use of the sealed modifier prevents a derived class from further overriding the method.

The word further is important.

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