[Spandau]

I understand that astronomers predict the existence of planets around other stars through mathematics and astro-physics. To my knowledge, there is no instrument than can resolve the image of planets around other stars. I hope they can do this in my lifetime. I live in the big city and sometimes I miss the night sky. The moon, a couple of planets, and the brightest stars are all you get.

[RightWhale]

there is no instrument than can resolve the image of planets around other stars

I think it has been done, although the 'planet' would have to be a supermassive one, and probably on the borderline between gas giant and brown dwarf. Wasn't there an image published a few months ago? Just a dot of light, certainly no surface detail. It will be another 10 years before NASA has the instrument in space able to optically resolve extrasolar planetary detail.