I'd be interested in seeing this math. I can't believe it could possibly take 3000 years to achieve interstellar travel,
...I can 100% promise you that in less than 3000 to 4000 years from now,...
...a lot of theories on it exist already, some of the technologies even already exist. It's not going to take 3000 years, it's not going to take 1000 years.
While I wish 500 years was the target goal, that's simply not enough time to develop the technology necessary planetary exploration. The problems are several and do have rather complicated and yet undiscovered solution sets:
Energy & Propulsion Problems:
One of the most critical components will be the R&D necessary to derive a viable source of convertable energy. Within the energy sub-problem to solve, will be those of both On-Board Storage Requirements and Joules of Output. 1 Watt = 1 Joule per Second, or 3.41 BTUs per Hour. The total Joules per Second used in just the acceleration phase alone (getting a ship of sufficient scale to any echelon of sub-light speeds) is right now, astronomical in number. While conventional propulsion systems might seem powerful for the aerospace applications of today, the energy output necessary to propel a ship of sufficient size, scale and mass to beyond even the edge of our own solar system, would take more energy than is current in use right now through out our entire planet at this very minute. Clearly, we have no liquid fuel chemistry solution that comes anywhere near close to solving this problem. Therefore, something revolutionary in the discipline of Inorganic Chemistry will have to take place, that rivals that discoveries of Galileo, Newton and Einstein, combined. That's the intellectual challenge we face in just the energy problem alone.
Now, regarding Propulsion Systems. You have to understand that any mission that includes Interstellar travel, will by definition be a Mission Critical endeavor. Mission Critical in technical terms simply means: Zero Critical Failure. Nothing that is critical to the success of the mission can go unresolved. That does not mean that in-flight, or in-voyage systems failures will not occur. They will and they will occur with some regularity. What mission critical means, is that no failure can reach a level that would terminate the mission. This concept is very important to understand and it plays a huge role in the overall design and engineering processes that will yield such a propulsion system. Failure, simply won't be an option. So, we will need to optimize the entirety of our Materials Science ethos, to a level that we have never considered before, including that used in all previous manned missions to space with the Mercury, Gemini, Apollo, Saturn and Shuttle programs combined. Of course, will use everything we learned in those programs and missions, but all of that combined will pale in comparison to what will be needed to achieve the level of power availability necessary for this kind of space travel. And, that's just the new materials science component of the new Propulsion System designs!
The core propulsion system design itself, in my opinion, will need to be a nuclear solution. One of the exciting things about this solution is the potential that Thorium might offer. Unlike Uranium, Thorium is a far more exploitable source for instantiating controlled nuclear reactions that yield usable Joules of energy. Thorium, is also much more abundant, easier to reach within the earth's crust and less volatile than Uranium, in its excavated form of Thorite, or Thorianite, and it has a deeper ionization path than does Uranium. Thorium, does not produce dangerous waste and does not requires vast quantities to achieve nominal levels of comparable energy output. While Thorium R&D, has been held hostage by politicians who have been lead astray by fossil fuel barons who see their profits going down the tubes as a direct result of its advancement, and by a private sector that cannot turn billions/trillions in profits from a nearly endless supply of cheap energy, its potential for getting humanity involved in Interstellar travel cannot and should not be underestimated.
The potential [known] benefits of using a Thorium powered Propulsion System on-board an Interstellar vehicle carrying human beings, goes right to the heart of helping to reduce some of the R&D burden in the Materials Science that will be necessary to engineer a mission critical powerplant. The requirements for radiation shielding of the crew and passengers (for example) on long Interstellar voyages, would be greatly reduced, as a Thorium based reactor won't require high-pressure to stabilize it and because Thorium, has no problem dissolving in a fluoride-salt mixture. So, that means a reactor based Propulsion System that can operate at high temperatures without the typical problems associated radiation local distribution and/or leakage. This is far superior to the high-water pressure Uranium core reactors of today, that have significant waste and radiation leakage problems, when/if there is a containment failure and/or core meltdown.
Because of the politicization of Thorium, over the years - the world has yet to benefit from its advantages over Uranium. Insufficient R&D funding from both the public and private sectors have stalled its development, but I think it is only a matter of time before Thorium, takes its rightful place as the world's dominant source of "clean-er" energy and someday, one of the high potential candidates for powering the first Interstellar ship from earth's orbit.
Velocity & Navigation Problems:
It is one thing to calculate the course from earth to the moon, or to one of the planets within our own solar system, for example. But, it is quite another thing to calculate a course from earth to a distant planet that requires Interstellar travel. The reason has to do with Collision Avoidance. Meteors, Asteroids, Comets and other early universe primordial debris, is not something that you can simply plow through on your way to your destination. Somehow, you would need to Navigate the ship around these free agents of potential mission ending destruction, to arrive at your destination without being destroyed by what is relatively speaking, a piece of space dust. Colliding with a large object at low speeds would prove to be catastrophic, in the same way that colliding with small objects at high speeds.
Given the relative distance to even the nearest star systems where we now believe there might be planets capable of supporting human life, it would require cruise speeds that are large fractions of light-speed, or sub-light speed. If we don't achieve those speeds, then the time it would take to reach even Alpha Centauri, which is a little over four (4) light years away from earth, would mean that missions to these potential destinations would take generations to accomplish.
That presents all kinds of ethical/moral problems, as those people being born in space - did not ask to be part of that kind of endeavor. Also, as a practical matter, you would not want to launch these missions, if each time you knew that the the people who are alive during the start of the mission, would not be the people who finally arrived at the destination. So, for the sake of human ethics and practicality, we would have to solve the speed problem by increasing Velocity, which at the very same time enhances an already dangerous problem having to do with Collision Avoidance Navigation.
What I call the Collision Avoidance Navigation System (CANS), is a problem that I believe we can actually solve for relatively large scale objects using a very large and fully-integrated (fore and aft) radar tracking system that is coupled to the Flight Control System (FCS). However, we would still have to derive a solution for the small scale objects. At sub-light speeds (if we are able to achieve that), smaller objects with lower density can have disastrous effects on the hull of the ship, even though we could (in theory) cruise right through them while using CANS to avoid collisions with large body objects and things like small body asteroid fields. We are talking about maneuverability capabilities in space and at very high velocities that would require very precise collision avoidance systems. It sounds easier than it would actually be in reality.
There are many other issues to solve as well, but these are four (4) of the major problems that will take a significant amount of time, energy and effort to resolve to anywhere near the level necessary to put together a launch date for such a journey. However, there is one more very large problem that looms ahead:
Funding.
This is not something that any private entity would ever want to do. The actual ROI for a private entity on something like this is practically zero and there would be no prior risk-to-reward model to look at for comparison, that would even come close to helping anyone understand what they are getting themselves into. There won't even be single country that could afford to go at this kind of project alone. Therefore, it will take Global Initiative unlike anything ever attempted by humanity in the past, where the entire planet comes together to develop the strategic outline for accomplishing such a task. This would be so resource intensive, that nearly every government in the world would have to commit and contribute to some aspect of the project. It would go beyond mere money and capital expenditures. This endeavor will also require the intellectual efforts of an entire planet and a sincere commitment to seeing that the initiative does not fail.
What math are you doing to suggest 3000?
Take every great civilization that has ever existed on earth and instead of hiding, destroying, and withholding their respective knowledge - share, distribute, integrate and extend upon all that which has previously been known into today, October, 2012. Where would we be today? Then go beyond just the sharing of information through generations, and look at the actual progress that might have been made throughout the epochs had there been only one People on planet earth working together for the common good. Where would we be today? No lines on a map dividing humanity. Everyone being classified simply as a Citizen of Planet Earth, and not some sub-divided imaginary line on a map. A society in which everybody was engaged in using their higher talents for the purpose of extending life beyond this planet. A world in which everyone was engaged in the support of the Common Good, and of the extension of human life. Where would be today?
We would be ahead of humanity by about as long as humanity has been on planet earth.
It would require this world to come together in ways that it never has before. Are we capable of pulling that kind of multi-cultural global initiative off, within the next 500 years? I sure hope so, but given our current sad state of affairs as human beings who seem hell bent on destroying our planet and everything on it, I don't see us reaching that level of maturity in such a short period of time. So, you see, the problem with getting to the "next planet" is not merely a technological problem. It is also a societal problem rooted in our ability to think beyond our differences for a greater and more common good. And, that is why I think it will take a lot more than 500 years.
We are not as smart as we like to think we are. If we were, then we'd be literally reaching for the stars right now and we'd be doing it with Human beings instead of Voyager-like probes.