The presence of an unseen planet orbiting a distant star can...

The presence of an unseen planet orbiting a distant star can sometimes be inferred from the motion of the star as we see it. As the star and planet orbit the center of mass of the star-planet system, the star moves toward and away from us with what is called the line of sight velocity, a motion that can be detected. Figure $13-49$ shows a graph of the line of sight velocity versus time for the star 14 Herculis. The star's mass is believed to be 0.90 of the mass of our Sun. Assume that only one planet orbits the star and that our view is along the plane of the orbit. Then approximate (a) the planet's mass in terms of Jupiter's mass $m_{j}$ and (b) the planet's orbital radius in terms of Earth's orbital radius $r_{E}$ .

The presence of an unseen planet orbiting a distant star can sometimes be inferred from the motion of the star as we see it. As the star and planet orbit the center of mass of the
star-planet system, the star moves toward and away from us with
what is called the line of sight velocity, a motion that can be detected. Figure $13-49$ shows a graph of the line of sight velocity versus time for the star 14 Herculis. The star's mass is believed to be
0.90 of the mass of our Sun. Assume that only one planet orbits the star and that our view is along the plane of the orbit. Then approximate (a) the planet's mass in terms of Jupiter's mass $m_{j}$ and (b) the
planet's orbital radius in terms of Earth's orbital radius $r_{E}$ .

Key Concepts

Line-of-Sight Velocity

This concept refers to the component of a star's velocity that is directed towards or away from an observer. In the context of exoplanet detection, variations in the line-of-sight velocity can be measured via spectral shifts, allowing astronomers to infer the presence of orbiting planets through the periodic motion of the star.

Radial Velocity Method

The radial velocity method is an observational technique used to detect exoplanets by measuring the Doppler shifts in the star's spectrum caused by its motion as it orbits the center of mass with its planet(s). This technique enables the derivation of important planetary parameters such as mass and orbital period.

Orbital Dynamics and the Center of Mass

In any star-planet system, both bodies orbit around their common center of mass. This principle of orbital dynamics allows astronomers to relate the observed motion of the star to the gravitational influence of the planet. By understanding this relationship, one can estimate the planet’s mass and its orbital radius relative to the star.

Kepler's Laws of Planetary Motion

Kepler's laws provide the foundation for understanding the motion of bodies in orbit. These laws relate the orbital period, the size of the orbit, and the masses of the orbiting bodies. In exoplanet studies, Kepler's laws are used to connect the observed periodic changes in the star’s motion to the orbital characteristics and mass of the unseen planet.

Doppler Effect

The Doppler effect explains the change in frequency or wavelength of light from a source due to its motion relative to the observer. In astrophysics, this effect is critical for detecting the tiny shifts in a star's spectral lines as it moves towards or away from Earth, enabling the detection of gravitational influences from orbiting planets.

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