Resolution and Light Gathering Power of Telescopes

1. Let's say you are an astronomer living on a planet orbiting Alpha Centauri, 4.3 light years away, and you want to build a telescope with which to study Earth at optical wavelengths. You want to be able to observe the planet Earth in fine detail. How big would your telescope need to be in order to resolve an object on Earth, say the size of a goat? Name an object of comparable size to the telescope. (Feel free to make reasonable estimates of certain quantities in this problem.)
2. Now suppose you want to observe Earth with radio telescopes in the same detail. What size telescope would you need to resolve goats who emit radio waves at 1 GHz?
3. Now let's come back to observing the Universe from Earth. What are the advantages of the Hubble Space Telescope over ground-based telescopes? What are the disadvantages? Describe a scenario in which you, as an astronomer, would want to use HST over all available ground-based telescopes. Now describe a scenario in which the Keck Telescope in Hawaii would be the better choice.