1. The Earth's resources will run out well before then. Thus the reason Space exploration is that much more important. We will have to find another planet eventually if mankind is to survive.
When those resources are gone, so go any advancements in Science.
2. I don't personally believe we will ever be able to travel space at the speed of light. EVEN IF we do eventually learn to move/travel at such a great speed, we wouldn't be able to use it in space.
If you start at Point A and set to light speed to reach Point B, you will never get there because you're going to hit something inbetween.
So to make it even that much more impossible, if we come up with light speed, we then have to better that by figuring a way to maneuver at such a speed.
Unless we find a planet reasonably close which has the resources to replace those that will eventually be sucked dry from the middle of the Earth and leave us basically an empty core, then we are doomed...
Look, I'm not trying to prop myself up as a big thinker or anything but this is surprisingly narrow and superficial thinking. I am seriously not trying to flame here. Like in my comment above, you are applying our current limitations to a society that we won't even be able to recognize. Do you seriously believe that when we reach a point where we can travel to and colonize other worlds that we will be starved for resources? Michio Kaku believes that we are a few thousand years away from being a Type II civilization. Read what a Type II civilization will be able to do under the heading "Type II civilization methods" at this link.
If you start at Point A and set to light speed to reach Point B, you will never get there because you're going to hit something inbetween.
C'mon. Are you serious with this?
Fortunately, the people that will lead us to this future are big thinkers who would never be satisfied saying "We will never be able to __________."