You have a spacecraft that is capable of reaching a speed of0.99c and desire to travel to Vega, a nearby star about 25 lightyears away. In order to keep track of your position, yourspacecraft sends out a flash of light every second (by your ship’sclock) during the journey that can be picked up on Earth. Inaddition, the Earth sends out a flash every second (by the Earthclock) that you can see with a telescope on your ship.

Thus equipped, you depart to your destination, where afterarrival you send a radio signal to Earth saying that you havearrived. After spending 0.5 years there, you send a second radiosignal that says you are departing to return to Earth.

In answering the following questions, Ignore the negligible timeit takes to accelerate and decelerate your spacecraft, and assumeEarth and Alpha Centauri have negligible relative motion (comparedto the speed of light!):

(a) On the outward journey, what is the frequency of flashesseen coming from your spacecraft back on Earth? Similarly, what isthe frequency of flashes you see coming from Earth?

(b) After getting up to 0.99c, how far away does Vega appear toyou at the start of the journey? How many years does it take to getthere according to your spacecraft clock?

(c) How many years (on the Earth’s clock) after you left Earthwill they receive the radio signal that you have arrived?

(d) While you are at Vega, what is the frequency of the flashesthe Earth sees from your spacecraft? What is the frequency you seefrom the Earth’s flasher?

(e) What is the frequency of the Earth’s flasher you see on theway back? What is the frequency of your flasher as seen by theEarth?

(f) How many years after you left (by the Earth’s clock) willthe Earth receive the signal that you have started back?

(g) How many years after you left (by the Earth’s clock) willhave elapsed when you get back? How much older will you be?