Asteroseismic detection of exoplanets relies on the fact that the presence of an orbiting planet can influence the star's pulsation frequencies. The planet's gravitational pull exerts a periodic force on the star, causing slight variations in its pulsation patterns.

The Kepler Mission, launched in 2009, was specifically designed to search for exoplanets using the transit method. However, its high-precision photometric data also enabled the study of stellar oscillations, leading to the discovery of several exoplanets through asteroseismology.

Asteroseismic exoplanet detection primarily utilizes non-radial pulsations, which are oscillations that involve the star's interior and surface layers. These pulsations are sensitive to the presence of an orbiting planet, as they can be perturbed by the planet's gravitational influence.

The presence of an exoplanet can induce irregular variations in the pulsation frequencies of its host star. These variations are caused by the gravitational tug of the planet, which alters the star's internal structure and pulsation patterns.

Asteroseismic exoplanet detection typically involves the analysis of pulsation frequencies in the microhertz (µHz) range. These low-frequency oscillations are particularly sensitive to the presence of exoplanets, as they can be influenced by the planet's gravitational effects.

Radial velocity variations, a technique commonly used for exoplanet detection, is not directly employed in asteroseismic exoplanet detection. Asteroseismology relies on the analysis of stellar pulsations, while radial velocity variations measure the star's motion induced by the orbiting planet.

Asteroseismic exoplanet detection has the advantage of being sensitive to exoplanets with longer orbital periods, which are often missed by other methods. This is because the gravitational influence of long-period exoplanets can still induce detectable perturbations in the star's pulsation frequencies.

Asteroseismic exoplanet detection is limited by the fact that it is sensitive to stellar activity. Stellar activity, such as flares and sunspots, can generate variations in the star's pulsation frequencies that can mimic the effects of an orbiting planet.

Rotational modulation is not a significant source of noise in asteroseismic exoplanet detection. It refers to the variation in a star's pulsation frequencies due to its rotation, which can be accounted for in the analysis.

Asteroseismic exoplanet detection is most sensitive to exoplanets in the size range of super-Earths to Neptune-sized planets. These planets have a significant gravitational influence on their host stars, leading to detectable perturbations in the pulsation frequencies.

The PLATO Mission (PLAnetary Transits and Oscillations of stars) is specifically designed for asteroseismic exoplanet detection. It aims to study the interiors and oscillations of stars, including the detection and characterization of exoplanets through asteroseismology.

The primary goal of the TESS Mission is to search for exoplanets around bright stars, including those that are suitable for asteroseismic follow-up studies. By observing these stars, TESS can identify exoplanet candidates that can be further characterized using asteroseismology.

Asteroseismic exoplanet detection primarily provides information about the exoplanet's mass and radius. By analyzing the perturbations in the star's pulsation frequencies, astronomers can estimate the gravitational influence of the exoplanet and infer its mass and size.

Asteroseismic exoplanet detection provides valuable insights into the formation and evolution of exoplanetary systems. By studying the pulsation frequencies of stars with exoplanets, astronomers can gain information about the exoplanet's mass, radius, and orbital parameters. This information helps constrain models of planet formation and evolution, shedding light on the processes that shape exoplanetary systems.

The future prospects for asteroseismic exoplanet detection are promising. Continued improvements in the sensitivity and precision of space missions, the development of new asteroseismic techniques, and increased collaboration among astronomers and astrophysicists will contribute to the discovery and characterization of a wider range of exoplanets using asteroseismology.