Calculate the factor by which the light gathering power of the ground based Subaru 8.3 metre telescope exceeds

Question

that of the Hubble Space Telescope (HST), which has a 2.4 metre objective mirror. What advantage does the HST have over the Subaru telescope?

Answer 1

Light gathering power scales as the square of the aperture, so Subaru has (8.3/2.4)^2 or almost 12 times the light gathering power of the Hubble.
Resolution scales linearly with aperture, so the 8.3 Subaru has 8.3/2.4 = 3.46 times the resolution of the Hubble. This means that , it theory, Subaru can see detail 3.46 times smaller than Hubble could, but the turbulent atmosphere refracts light arriving at the telescope in such a way as to blur the image. So the Hubble, with the advantage of being above the atmosphere can see smaller detail because it reaches its theoretical resolution limit, whereas the atmosphere prevents Subaru from getting anywhere near its theoretical resolution. Also, air glow limits how dim an object can be seen from the ground. Hubble does not have to deal with that and so can see fainter light, even though it actually gathers 12 times less light than Subaru.

Answer 2

Theoretical difference LGPs is (8.3/2.4)^2.

The Hubble has the advantage of being in space and does not have the earth's atmosphere to interfere with the light.