Indirect methods: Principles
The orbits of the planets in space
Dynamical methods consist in detecting the movement of the star (visible) owing to the presence of the planet (invisible). The star and the planet both orbit around the centre of gravity of the system. The orbits follow Keplerâs laws, due to the reciprocal gravitational attraction of two bodies. These orbits may be slightly disturbed if there are other planets in the system.
Keplerâs laws imply that the orbit of the planet is an ellipse with one of the foci being occupied by the star. This elliptical orbit is characterised by 6 parameters including:
- a, the semi-major axis ? of the orbit
- the eccentricity e of the ellipse
- i the orbital inclination ? is the angle between the orbital plane and the reference plane of the sky.
The planetâs movement on its orbit is characterised by the period P of orbital revolution. The value of P depends only on the value of a and the mass of the star, M*. G is the universal gravitational constant:
$$ P = 2 \pi \sqrt{ \frac{a^3}{G \times M_*} } $$
These figures show the movements of the star and the planet: the observer sees the movement of the star but cannot see the planet.
At the top, the orbits are circular, the radial velocity ? of the star is periodic and sinusoidal.
At the bottom, the orbits are eccentric, and the periodic movement is more complex.