Re: Hypothetically, if a star was 5 million miles away from Earth, instantaneou

First, we'd be dead if a star was only 5 million miles away from us.  The
Sun is 93 million miles away, on average (our orbit is not perfectly
circular).  But hypothetically, we can tackle this problem.  We'll assume a
star too small to really be a star...one that won't kill us.  Or that our
observer posesses sunblock 9 trillion and a refridgerated suit.  :)

First off, the trip would take (5 million miles)/(the speed of light,
186,000 miles/second) = 26.88 seconds in the Earth's reference frame.  So
during that time, light would continue to reach us from the star (which had
emitted the light 26.88 light seconds away, or 5 million miles as we just
calculated).  But the light coming from the star as it travelled would be
infinitely redshifted (i.e. the photons would have no energy at all), so it
would emit no light towards us.  Time on the star would also stop relative
to our clocks, so it would emit no light at all.  Once it stopped (at
exactly when we saw the light from the star vanish), we would have to wait
for the light to travel 10 million miles to get to us, or 2x26.88 sec =
53.76 seconds.  Almost a minute of dark.  Then we would see the star,
suddenly shining again from 10 million miles away.  It would have 1/4 the
original intensity, since it's twice as far away and the number of photons
per square unit area varies as 1/r^2 where r is the distance away...which
has doubled.  

But the problem with that is, we'd never survive that long.  To accelerate
any object with mass to the speed of light takes infinite energy.  To do so
instantaneously would create an infinitely strong gravitational shock wave,
which also travels (in theory) at the speed of light.  So exactly as the
star's light went out, the observer on Earth would be infinitely pulverized
by the gravitational shock wave, which would reach us just as the last of
the light did.  But I'll assume that gravitational waves are outside the
scope of the question and you're only concerned about the light from the star.