The first technique, called astrometry, requires many images of a star and its nearby companions. These images are examined for minute changes in the star's position. If a particularly large planet orbits a star, it is possible to measure the wobble in the position of the star. For example, if some slimy alien astronomer were looking at the Sun, he, she, or it would see the Sun wobble back and forth every 11 or 12 years. Our alien friend would be watching the Sun's response to the orbit of Jupiter. All of the other planets would cause wobbles as well, but the wobble from Jupiter would be the dominant one.
The problem with this method is that the wobbles caused by even the largest planets are very small, at the limit of even the best telescopes now in operation. (Of course, alien technology might be far more advanced than ours.)
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