Question

5. The Helios spacecraft traveling at a speed of 0.60 c relative to the Earth-Sun system, detects the explosion of a very powerful solar flare at it passes by the Sun on its way to Earth. Sometime later on Earth, the constellation of satellites used to track GPS positions fails. Using the data from the Helios spacecraft as it passes by Earth, scientists calculate that the solar flare happened 7.0 min before the failure of the satellites, according to clocks on board Helios.

   For reference purposes, the distance between Earth and the Sun is 8.0 lmin relative to Earth-Sun system.

   1. (a) What is the value of (∆s)2 between the explosion of the solar flare and the failure of the GPS satellites

      as measured in the frame of the Helios spacecraft?

   2. (b) What is the value of (∆s)2 between the explosion of the solar flare and the failure of the GPS satellites as measured in the frame of the Earth-Sun system?

   3. (c) Solar flares emit large amounts of energy in the form of electromagnetic radiation and fast-moving charged particles. Is it possible that the GPS system failed on Earth as a consequence of the explosion of the solar flare? Explain.

Answer 1