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Table 2.1 summarizes the main factors for different planetary objects, assuming that they are in orbit around a star like the Sun, lying at a distance of 10 parsecs from Earth.

2.2 The Indirect Detection of Exoplanets

We have seen that the direct detection of an exoplanet orbiting a star, even one close to the Solar System, is extremely difficult. It is not, however, absolutely essential to be able to obtain an image of the planet to reveal its presence. In certain cases it is possible to detect the planet by observing the effect it has on its parent star, thus by observing the star itself. The techniques that are based on this principle are known as 'indirect' methods, in contrast to direct imaging. In this section we discuss the principal indirect methods of detection. Here, we should explain that these methods are by no means theoretical, but that, with a few exceptions, all the exoplanets currently detected have been found by indirect methods.

2.2.1 The Effect of a Planet on the Motion of Its Star

It is commonly said that a planet orbits a star. This assertion is true if one neglects the mass of the planet relative to that of the star, or if the motion of the planet is considered in very rough terms. In reality, the star and its planet (or planets) are bound by gravitation, and each of the bodies in the system (star and planet or planets) has a motion about the centre of mass (the centre of gravity) of the system. The position of the centre of mass G, in a system with N bodies, each of mass mi; the centre of which is at Oi, is defined by the following vector relationship:

In particular, for a two-body system (the star being denoted by '*' and the single planet by 'p'), the centre of mass lies between the star and the planet, and the vectorial expression just given becomes an algebraic one:

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