Final answer:
The astronaut would see the explosion of a satellite but would not hear any sound because there is no medium for sound waves to travel through in space. GPS satellites account for relativistic effects to maintain accuracy. Also, satellites obey Kepler's second law, moving faster when closer to the parent body and slower when farther away.
Step-by-step explanation:
The question deals with satellite connections and observations made by an astronaut during a satellite explosion. A scenario is given where a satellite explodes after exiting the Earth's atmosphere. The statement that accurately reflects the observations made by an astronaut on a spacewalk is that the astronaut would see the explosion, but would not hear a boom. This is because sound cannot travel through the vacuum of space, and thus, no sound from the explosion would reach the astronaut's ears.
In reference to the additional information provided about satellite operations for GPS navigation, it is vital to understand that satellites must account for the theories of both special relativity and general relativity to maintain precise timings. Without accounting for these relativistic effects, the accuracy of a GPS would deteriorate rapidly.
Regarding Kepler's laws of planetary motion, the correct statement is that a satellite does indeed increase its speed as it gets closer to the parent body and decreases its speed as it moves away. This movement follows Kepler's second law, which explains that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time, implying variable orbital speeds.