Question

3) (10 pts) The Thirty Metre Telescope (TMT) is a 30m diameter telescope to be built on Mauna Kean in Hawaii. The Hubble Space Telescope is a 2.4m diameter telescope in orbit around the Earth. a) (2.5 pts) What are the angular resolutions of both telescopes when observing in "visible" light (1 = 550 nm)? How many times better or worse is the HST compared to the TMT? b) (2.5 pts) What are the angular resolutions of both telescopes when observing in the near infrared (= 2.1 um)? How many times better or worse is the HST compared to the TMT? c) (2.5 pts) Which telescope is more "sensitive" in "visible" light and by how much? What about at 2.1 um? d) (2.5 pts) If you wanted to resolve an object on the Moon (distance = 384,400 km) that is lm in size, what is the diameter of the telescope that you would need if you wanted to observe in "visible" light? How large would the telescope need to be if you wanted to make this observation at 1 = 2.1 um.

Answer 1

a.) Angular resolution is guin as - 0= 1.22 16 Dis diametu of telescope Ofss = 1.22x550xlo' 2.791 x 10 mod. 0958" (ausse) OrHT 1.22 xsso xió'. 0.0046" 2.4 30 6. do 2.1 X16 m. OHSt = 122 X 2.1 X166. 0.22" OTH D = 1.22 X 2.1% 1660.0176" - 30 In both a factor the carees TMT has smalla angular resolution by a 12.5 so HST is worse than THT by 12.5 tinies Smaller the angulen resolution = better the telescope

C.) TMT is - because more it has sensitive smaller in visible as well as 2.1 pin light angular resolution than HST. d) Anglo sublended by the object on earth is 6: | , 0 0 0 0 5 3". 384400 x 16°m to acheine this angular resolution in visible light, the diameter of telescope required is geen by to 1 - 1.22 X 550x109 384400 X 163 d d; 1.22x550x169 x 384400 x los = 257.9 m for 1-2.18 100 m de 1.22 x 2.1 X 10 X384460 X 10 - 984.8 h.