1. While they are having a conversation on the Student Center Plaza, the distance between Joe Cool and Patti Party-lime is equal to one meter. At the same time the planet Mars, which has a mass of 6.0 x 1013 kg, is located at a distance of 3.0 x 1011 meters from the Earth. If the masses of Patti and Joe are 50 kg and 90 kg, respectively, calculate the ratio of the gravitational force exerted on Joe by Patti with that exerted on Joe by the planet Mars. From your result, what, if anything, can you say about the idea that the supposed astrological influences arc gravitational in nature?
2. Space scientists wish to place a satellite in orbit about the sun in such a way that the gravitational force between the satellite and the sun is 1/36 of its present value at a distance of one astronomical unit from the sun. At what distance from the sun in astronomical units must the satellite be placed?
3. A certain asteroid was observed to sweep out an orbital area of 450 billion square kilometers during the year 2015.
(a) How much orbital area will the asteroid sweep out this year?
(b) How much orbital area did the asteroid sweep out during this semester's Spring Break?
4. The satellite Phoebe of the planet Saturn orbits Saturn once every 1.5 years at a mean distance of .086 astronomical units. Find the mass of Saturn in solar mass units.
(5) 5. A certain comet is observed to make appearances in the years 2015, 1988, 1961, 1934 and 1907.
(a) In what year may we expect this object to make a return appearance?
(b) What is the mean distance between this comet and the sun in astronomical units?