The first exoplanet, 51 Peg, was discovered in 1995 using the Doppler method. In this method, the star is observed with very high resolution spectroscopy such that spectral shifts of a few parts per 10 million can be detected. This is sufficient to see the small and subtle motion induced in the star by the orbiting giant planet. This only works if the inclination of the system is a relatively large number. If the planet is orbiting the star in the plane of the sky, there's no motion to and from the observer, the inclination is zero and the effect is zero. An animation shows this reflex motion, not to scale. As the reflex motion is in the plane of the sky, it's easy to see but impossible to tag by spectroscopy. As the inclination becomes 90 degrees, the maximum effect is seen. When it's 90 degrees, transits or eclipses are also possible because the planet passes in front of the star. We can imagine that exoplanet systems are randomly distributed in three-dimensions in the Milky Way, so we will randomly observe inclinations of these systems. In the case of an inclination of 90 degrees, an equatorial inclination, the full Doppler shift will be detected. If it's in the plane of the sky, no Doppler shift and planets are not detectable this way. Since we don't know the inclination of any particular system, we deduce that on average the Doppler method underestimates the mass by a factor of two, that's the average over sine inclination. But the statistical properties of the systems are well understood. We can get a sense of this reflex motion in this Doppler effect by taking our solar system as an example. The Sun does not spin about its center, the reflex motion caused by Jupiter causes the sun to pirouettes about a region very close to its edge. There's also a reflex motion of about 12 meters per second induced on the sun by Jupiter, and that's the Doppler effect we would measure from a far to show that Jupiter existed. The reflex motion itself induces a wobble in the star, and in principle this is detectable. But using the solar system as an example, the Sun wobbles by an amount that's only about five millihertz seconds every 12 years, and this is presently too small to detect. You can think of Doppler detection in simple terms like a balance beam, where the mass of the star is balanced with the mass of an exoplanet and a pivot point. As the mass of the planet goes down, it needs to be further away from the Sun or the star to reach the balance point. That means that the reflex motion becomes smaller, and the velocity of that reflex motion becomes smaller. The first planet discovered was 51 Peg. It had an enormously fast and completely unprecedented speed of 4.4 days, and it's a Jupiter mass planet. This was a surprise led to the discovery of other hot Jupiters, and it took a while before we started to find giant planets in normal giant planet orbits. The Doppler method is an indirect way of detecting an exoplanet by the reflex motion that it induces on its parent star. Reflex motion can be manifested in two ways, one by the wobble of the star as seen on the plane of the sky. That's an effect of a few millioseconds for a massive planet too small to be currently detectable. But it can also be detected by the Doppler shift, by taking high resolution spectrum of the star, and that's the technique that first succeeded in detecting exoplanets in 1995. That massive was used for the first few 100 discoveries which were exclusively done with the Doppler technique, that method was used to exclusively discover the first few 100 exoplanets. The Doppler method on average returns a mass that's a factor of two underestimate because of the unknown inclination of the system. But the statistical properties of exoplanets are recovered, if we assume their orbits are randomly oriented in three-dimensional space.
