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Tutorial Exercises 2.
Question 1:
It is widely believed that US spy satellites are so powerful that they can read a newspaper over your shoulder. But is this true? Many astronomers think that the main US spy satellites have 2.4m diameter primary mirrors (because they were build by the same company that built the Hubble Space Telescope, which has a 2.4m mirror). Then cannot orbit much less than 700km above the Earth's surface, or they would burn up in the atmosphere. Calculate what are the finest details they can see.

Question 2:
SkyMapper will obtain the magnitudes of about five billion objects, in each of 7 filters. Most will be rather boring stars and galaxies. But a few may be weird and exciting new classes of objects. Invent a statistic you could apply to all these magnitudes to pick out "unusual" objects.

Question 3:
The average density of stars in our local part of the galaxy is 0.7 per cubic parsec. While doing a parallax survey, you found a 1 cubic parsec region which contains 4 stars. You are writing a paper reporting the discovery of a new star cluster, but are worried that it might just be a statistical fluke. Use your knowledge of statistics to work out whether you should publish.