http://en.wikipedia.org/wiki/Earth

The world is expected to continue supporting life for another 1.5 billion years, after which the rising luminosity of the Sun will eliminate the biosphere.^[17]

The future of the planet is closely tied to that of the Sun. As a result of the steady accumulation of helium ash at the Sun’s core, the star’s total luminosity will slowly increase. The luminosity of the Sun will grow by 10 percent over the next 1.1 Gyr (1.1 billion years) and by 40% over the next 3.5 Gyr.^[41] Climate models indicate that the rise in radiation reaching the Earth is likely to have dire consequences, including the possible loss of the planet’s oceans.^[42]

The Earth’s increasing surface temperature will accelerate the inorganic CO₂ cycle, reducing its concentration to the lethal levels for plants (10 ppm for C4 photosynthesis) in 900 million years. The lack of vegetation will result in the loss of oxygen in the atmosphere, so animal life will become extinct within several million more years.^[43] But even if the Sun were eternal and stable, the continued internal cooling of the Earth would have resulted in a loss of much of its atmosphere and oceans due to reduced volcanism.^[44] After another billion years all surface water will have disappeared^[17] and the mean global temperature will reach 70°C.^[43] The Earth is expected to be effectively habitable for about another 500 million years.^[45]

Now, there is indeed something interesting about this. We humans as individuals have always known that we are destined to die, and there has also been published speculation about the extinction of mankind as a species. We have even understood that the Sun will evolve into a red giant in about 5 billion years or so and then life on Earth will become impossible, for the Earth itself might be destroyed completely. But the realization that life on Earth will be wiped out much sooner is disturbing, much like a man, at age 30, being told that will be dead at about age 40 when he already knows that his life expectancy is about 70 years.

http://en.wikipedia.org/wiki/Andromeda-Milky_Way_collision

The Andromeda-Milky Way collision is a predicted galaxy collision that is due to take place in approximately 3 billion years’ time between the two largest galaxies in the Local Group – the Milky Way and the Andromeda Galaxy.^[1][2]

Shocking! So even before the Sun dies, our own galaxy will be ripped to shreds.

We greatly fear change even though we ourselves are a product of change. For example, the mass extinction that wiped out the dinosaurs made it possible for mammals to take over the world and thus for us to evolve eventually. It is only logical and mature to live our lives in the here and now and not worry so much about what will happen a billion years from now. This is not to say that we should ignore the threat of global warming that we humans may indeed be causing. But that is a relatively minor issue within a much shorter time frame. We can handle that, and must. Just like a man who knows he will live only ten more years would be foolish to commit suicide the next day and thus deprive his loved ones of his presence.