How big of a telescopic array is needed to spot an Earth-sized planet from four light-months away?

Let's assume that an interstellar craft from another spacefaring civilization is attempting to find a planet like Earth. Their ship is approaching Sol at a velocity of .05C and they have not surveyed our system before. They hope to find a planet inside the Continously Habitable Zone (CHZ), a spherical shell extending from 0.95 to 1.37 astronomical units from Sol.





How big of a telescopic array is needed to spot an Earth-sized planet, orbiting .95 AU from Sol, from a ship that is located four light-months from Sol?





Some helpful constants to consider (please substitute corrected figures as needed):





Diameter (Earth) = 6371 km


Diameter (Sol) = 1.392 million km


Radius Inner CHZ = .95 AU = 142.118 million km


Four light-months = 149597.871 million km





To simplify the problem, please use the following assumptions:





a. Disregard orbital eccentricity (perihelion/aphelion)


b. The ship is approaching Sol at an angle perpendicular to Earth's ecliptic plane

How big of a telescopic array is needed to spot an Earth-sized planet from four light-months away?
A 7.12309523 e -3 gigatron refractive hubblistic megascope w crosshairs (the one Marvin Martian used) will do it.
Reply:First of all...The nearest star (not the Sun) to Earth is 4.5 Light Years away...





There is no planet located at 4 Light Months distance from Earth...That is roughly 2 Trillion Miles.





The nearest possible Exoplanets are 27 Trillion Miles away (4.5 LY). And your porblem when looking for those planets is not the size of the telescope but the brightness (brilliance) of that solar system's star which will preclude you seeing any of that star's planets. Check this out...Go our at night on a really dark night, and walk down an unlit highway where it is so dark you cannot see your hand in front of your face. then look into the headlights of an oncoming vehicle...Can you see anything behind or to the sides of the vehicle? Probably not. Your eyes are blinded by the brilliance of the automobile's headlights...Same holds true for those times when you look at a distant star. you cannot see the planets areound it because of the brilliance of the star.





See http://exoplanets.org
Reply:well this is going to toss a wrench in your works -- its not the size of the telescope, its what you can image with it and what magnification you can get. - larger the telescope just lets in more light. How fast you are traveling to something has no bearing on if you can see it or not.