Question

Suppose our Sun is about to explode. In an effort to escape, we depart in a spacecraft at v=0.800 c and head toward the star Tau Ceti, 12.0 ly away. When we reach the midpoint of our journey from the Earth, we see our Sun explode, and, unfortunately, at the same instant, we see Tau Ceti explode as well.(a) In the spacecraft's frame of reference, should we conclude that the two explosions occurred simultaneously? If not, which occurred first?

Answer 1

Sun exploded 16 years after Tau Ceti.

Considering a scenario in which the Sun is going to explode.

In order to escape the explosion, we depart in a spacecraft with a speed of v = 0.8c.

The star Tau Ceti is 12 life years away.

At the midpoint of the journey, the Sun as well as Tau Cetik explode. at the same instant.

Now, the distance between the Sun and the spacecraft:

L = L(p) √( 1 - (v/c)²)

L = (6 ly) √[1 - (0.8)²] = 3.6 ly

Now, we observe Sun to be flying away from us at a speed of 0.8c whereas the light from the Sun approaches at a speed 1c.  Therefore, the gap between the Sun and the blast of the Sun wave is opened at a speed of 1.8c.

Therefore, the time passed ever since the Sun exploded is:

t = 3.60 ly / 1.80c = 2 years.

Now, we observe Tau Ceti moving toward us at a speed of 0.8c, whereas the light from the blast approaches at a speed of 1c which is only 0.2c faster. Then the gap between the Tau Ceti and its blast wave is 3.60 ly and growing at a speed of 0.2c.

Therefore, the time for which it has been opening for is:

t = 3.60 ly/ 0.20c

t = 18 years.

Therefore, Tau Ceti exploded 16 years before the Sun.

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