Even the closest stars are so far away as to appear as nothing but little dots in the sky. Stars dwarf their planets, so our ability to see planets of other solar systems is minimal.
We can, however, infer their existence, by looking at minor, cyclical changes in the signals from the stars themselves.
A planet orbiting a star will exert a small tug upon it’s parent, towards or away from us, at different points of it’s orbit. This wobble is just large enough to be picked up as changes in the star’s radial velocity.
Inferring the presence of a planet from these changes in the light is difficult. where several planets orbit the star, at different frequencies, the changes in signal are laid on top of one another. it is necessary to look for evidence of a repeated pattern, and subtract it from the sum of the signal, gradually working backwards, uncovering evidence of further regularities, and hopefully of further, less influential planets.
Other entirely unrelated factors may also contribute to the changes in signal, further compounding the problem.
The search for life on systems outside our own is fraught with false hope and disappointment.
The Gliese 581 star is a close neighbour, only 20 light years away. In 2007, strong evidence of a third exoplanet, within the goldilocks zone, was discovered. A year later, a radio signal sending greetings from Earth was sent there.
More recently, better data has allowed us to factor in the presence of sunspot activity from the signal, peeling back another layer of noise. Subtracting that strengthened the regularity of the signal detected for the planets dubbed B, C and E, but D, previously considered to be a strong candidate for life, has faded from the picture entirely. (The others are well outside the Goldilocks zone.)
By the time our signal of hope reaches Gliese, it is likely that we will know that it’s intended target was nothing but a mirage, an artefact of our inability to see more clearly when we were younger.