(Solved): The Vogon destructor ship is approaching the Earth from the far side of the Sun. In this sneaky ...

The Vogon destructor ship is approaching the Earth from the far side of the Sun. In this sneaky approach, no indication of the ship's presence can reach the Earth until after the ship has passed the Sun. In the Earth's reference system and in the Vogon ship's reference system, two events are indisputable: 1) the Vogon ship is at the Sun and 2) the Vogon ship is at the Earth. Of course, the position coordinates and the time coordinates of these two events in the two reference systems may differ. Treat the Earth and Sun as if they are at rest relative to each other. (This isn't strictly true because the Earth orbits the Sun. But never mind; make the approximation.) As measured in the Earth-Sun reference system, the Earth-Sun distance is $$8.0$$ lightminutes. (A light-minute is the distance that light in empty space travels in 1 minute. So, 1 light-minute $$=1c$$.minute.) Relative to the Earth-Sun system, the Vogon ship's speed is $$0.80c$$. Answer the following questions. Use the Lorentz transformation as applicable. Indicate explicitly the reference systems used to develop the answers. Show your answers in units of minutes for time and light-minutes for distance. (a) In the Earth's reference system, what is the time interval between events 1 and 2? (b) In the Earth's reference system, what is the distance between events 1 and 2? (c) In the Vogon ship's reference system, what is the time interval between events 1 and 2 ? (d) In the Vogon ship's reference system, what is the distance between events 1 and 2 ? (e) In the Vogon ship's reference system, how far apart are the Earth and Sun? (f) How much time after first detecting the Vogon ship do humans have to prepare for its arrival?