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When we find an exoplanet by observing the dimming of its parent star, this means that the planet passes in front of the star from our view.

What if our view of a star system is from its "top" or "bottom"? Then from our view, none of its planets would pass in front of the star so we could observe a dimming. How would we know, then, whether such a star has or doesn't have planets?

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First of all, it is not that you can always find the planet (if it is there).

Anyway, if this is the case, when we observe the system not totally face-on, we resort to radial velocity measurements. The principle is simple, the actual much less. The orbiting of the planet around the star causes the star to "oscillate" around the center of mass. Here you can see a good example:

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However, when the system is exactly face-on, the Doppler shift is useless, but still the gravitational effect of the planet onto the star is useful and used. Here is what happens in the latter case:

enter image description here

It is clear that the star undergoes a change in position. Then usually, the radial measurements go along with astrometrical measurements, to identify the position of the star along the planet's orbit.

Of course, you need some conditions are verified to allow this measurement. First of all, you planet must be massive enough to bring a sensible change in the position of the star. Then your instrument must be sensible enough to resolve the tiny effect originated by this change. Possibly, also other conditions play a role, but I am not an expert (you can take a look at here).

For a general comprehension, also a wiki for Methods of detecting exoplanets.

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There are (at least) two ways that you can do it, both of which work best for massive planets that are located far away from their parent star (which may be quite rare).

The first is direct imaging. Several planets have been found using this technique (e.g. http://adsabs.harvard.edu/abs/2013EPJWC..4713004N ). It obviously works best if you have very good spatial resolution, which these days is accomplished using adaptive optics. It also works best in the infrared, because in that part of the spectrum, the contrast between the brightness of a star and the brightness of a companion giant planet is big, but not insurmountable.

The second is using the astrometric wobble (change in position) seen in a star's position as it orbits its common centre of gravity with a massive planet. The amplitude of this wobble will be bigger for planets that are more massive and further away from the star. However, if they are too far away, then the wobble period will be too long to sensibly detect it on timescales of years. At least a couple of previously known planetary systems have had this wobble measured (e.g. http://adsabs.harvard.edu/abs/2014ApJ...795...41M , http://adsabs.harvard.edu/abs/2010ApJ...715.1203M), but it thought that the Gaia astrometry satellite will discover lots of planetary systems in this way (see http://adsabs.harvard.edu/abs/2013EPJWC..4715005S for details and estimates of numbers).

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