PROBLEM SET  #2 ASTR 1110 Think each problem through, and present your logic. 1.  Halley's comet is moving at 60 km/s near perihelion, at approximately the orbit of Venus.  At aphelion it is near Neptune.  How fast is it moving?  Use Kepler's laws. 2. It is thought that comets are chunks of ice that have spent most of the lifetime of the solar system orbiting at about 10,000 AU from the Sun.  What is the period of such an orbit? 3. Use Kepler's law, and scale from the Moon's orbit to determine the period of a low Earth orbit (i.e. just above the atmosphere).  How high is a syncom satellite?  (ie. 24 hour period.) 4. Explain how Galileo proved the Sun was a sphere, not a disk. 5. A moon rocket is accelerating at 4 gees (40 m/s/s). It has mass of 106 kg. How much force is the engine producing? 6. Two hockey players stand on a frictionless surface facing each other. One has mass of 100kg and the other has mass of 50 kg. The small one swings at the large one, his fist exerting 10 Newtons on his opponents nose for 0.1 seconds. The large fellow's nose returns the force equally (Newton #3). How fast is each moving after the encounter? 7. Calculate the escape velocity of the Moon, using data from the textbook. 8. In the far future planetary systems are designed by engineers instead of nature.  The following binary planet is proposed.  The two planets are held apart by a steel rod instead of centrifugal force as shown below. They do not revolve about each other, but do rotate on their own axes. Do the oceans on these planets have tides and, if so, how many high tides are there per day?