Space-Time

Problems

practice

1. Write something.
2. Gravity Probe B is an earth-orbiting relativity experiment developed by NASA and Stanford University to test Albert Einstein's general theory of relativity. The media have reported that Gravity Probe B has gone in search of "the missing inch". What the hell are they talking about? Do the following calculations for a satellite in a circular, low earth orbit (LEO) at an altitude of 642 km. (Ignore the rules of significant digits when calculating distances. Record these answers with as much precision as your calculator will allow.)
   1. Using classical euclidean geometry, determine the circumference of this orbit.
   2. Using classical Newtonian mechanics, determine the speed of a satellite in such an orbit.
   3. Using special relativity, determine the amount by which the circumference of the orbit has been shortened due to the satellite's motion. State your answer in…
      1. centimeters
      2. English inches
3. Write something.
4. Write something completely different.

numerical

1. 1. Imagine that technology has advanced to the point where humans can travel through space at speeds approaching the speed of light.
      1. At what fraction of the speed of light would a second of a space traveler's existence equal a day of existence on earth?
      2. How much would a space traveler age on a journey to the Large Magellanic Cloud (a dwarf galaxy 169,000 light years from earth) were they to travel at this speed?
      3. How much would the Earth age on this journey?