With the technologies that we have got, is it possible to completely migrate 1/3rd of the world's population to another planet which has characteristics similar to those of earth ? Possibly it will happen.
That would be no. While in 100 years we just might have the ability to travel to another planet (and if you count in solar system then it will be much less) it would still take a HUGE amount of resources to move 2,300,000,000 people off this rock. That is about 1/3 of the current population.
Lets just take China, it's is 1/8th of the worlds population currently. Let's say we want to move them all, every single person, to the US. Just getting them on planes and boats and crossing.
The 747 average about 500 people per flight (18 hrs), super tankers might be able to squeeze in 20,000 (WAG (Wild A$$ Guess) for a 2 week trip across the Pacific). So say half and half for this little number exercise. 500,000,000 people by plane and the same by ship. that would take 1,000,000 plane trips and 100,000 ship trips. Lets say there are about 1,000 of these tankers, it would take each 25 trips, at a month turnaround time for a total of 25 months. Say 1000 airplanes, are also working, that would be 1000 trips each, at a minimum of 1.5 days turnaround, that's 60 months of constant flying (no time for repairs and maintenance). So moving 1/3 of the the human population OFF THE PLANET is virtually nil.
Remember this is just transporting them from one side of the ocean to the other, with a couple suitcases and enough food for a very short trip. The cost of putting people into orbit is significantly more, and having a living environment out there the cost goes up. Another WAG if we have 100,000 humans living off Earth in 100 years I think we're going to be doing pretty good.
EDT Notes: Some Math errors were pointed out and (I found some more!) A couple by a factor of 10. I also bumped up the tankers passenger list from 5000 to 20,000 (might still be low) but don't want diseases to spread among those traveling and it isn't like those still waiting are going to die if they don't leave in time.
Any other mistakes I missed (or added?)
As asked, the answer is no. To reach the nearest star in 100 years it would take at absolute minimum 100,000 times more energy than the Earth currently consumes to simply accelerate and decelerate 2 billion people. You can read all the gory details below. So I'm going to answer an expanded question, "could a third of humanity be living off Earth in 100 years?"
I'm going to draw from existing estimates and near-future technology that's already been shown to work. No zero-point energy, no warp or hyper drives, no wormholes, and we're not going to solve gravity. What I will allow is more efficient and reusable rocket design, space elevators, efficient recycling, fusion power, and deep sleep chambers.
How many people are we talking? The UN estimates the population in 2115 will be 6, 10 or 16 billion depending on how optimistic you are making it 2, 3.3 or 5.3 billion people we're getting off the Earth. I'd like to believe if we can organize an effort to move billions of people off the planet, we can get our population growth under control, but I don't think whether its 2 or 5 billion will have a big impact.
Where are they all going? An orbital habitat? An uninhabitable planet in this Solar System? A habitable planet in another Solar System? Each of these affects two variables: the change in velocity required and the mass per person. How much stuff do we need to ship for the population to survive?
If we send humans to a habitable planet in another solar system, that's a lot of velocity to escape the Solar System and get there in less than 100 years. You need to send enough food, water and air for that whole time (even sleeping) plus fuel to slow you down once you get there. However, once you're there, with a few tools you'll be self-sufficient like pioneers of old.
An orbital habitat requires the least amount of velocity, just enough to get to low Earth orbit, but since we need to build the whole thing it requires moving a lot of mass per person. It has no resources to draw on but sunlight, and so all the food, water, soil and air will need to be shipped up. Recycling and growing food could be self sustaining, but there will always be leaks and inefficiencies, so periodic shipments are required.
Going to an uninhabitable planet, probably Mars or maybe hollowing out some dwarf planets, requires more velocity than Earth orbit, extra fuel for landing a significant amount of mass, extra mass for machinery, shelter, food, water and air to sustain the population until they create a bubble. Farming is a dicey proposition as there is far less sunlight that far out (moving an asteroid sufficient to house billions of people to Earth orbit is out of the question).
How are they traveling? Depends on where they're going. If it's Earth orbit we can allow multiple Space Elevators and Fusion Power. Since the power is coming directly from the Earth, and fusion gives us a huge power source, it effectively negates the energy cost of putting stuff into orbit.
If it's to another object in our Solar System we can use conventional rockets, but it's going to take a lot of fuel to get there, and we're not coming back. 90% of the mass of a rocket is fuel. We could probably get it down to about 5 tons of fuel for each ton of cargo (the difference from the 7 tons in the article is because our Space Elevator allows us to assemble our spacecraft in High Earth Orbit for free).
If we're going to another Solar System, we have new problems. We need to escape the Sun's gravity, but that's peanuts compared to the velocity required to get to another Solar System in 100 years. Let's say we find a new Earth in the closest star Alpha Centauri a mere 4.3 light years away. To get there in 100 years we need to travel at 5% the speed of light or 15,000 km/s. That's 600 times the velocity to get to Mars. It gets worse: our hypothetical colony ship has to slow down once it gets there.
We can get some lower bounds of realism by calculating the kinetic energy required just to get 2 billion people up to the required velocities. Forget fuel, food, air, spacecraft and inefficiencies (which will likely add 10 to 100 times more mass). What is the minimum amount of energy required to fling the population to their target? (It turns out we don't need to go much further in our estimates than that).
Orbital Habitat via Space Elevator: 1/2 * 1.4 x 10^11 kg * (8 km/s)^2 = 4.5 x 10^18 J which is about 5% of the energy used by the US in a year. No problem. Even adding the mass of all the material and supplies, plus inefficiencies, this is well within our energy budget.
Other planet in our Solar System: 1/2 * 1.4 x 10^11 kg * (25 km/s)^2 = 4 x 10^19 J which is half the energy used by the US in a year. Since the real energy required is likely orders of magnitude more, not to mention building a fleet of disposable space ships (the energy required gets far worse if they're coming back), that would be a serious problem.
Reach another Solar System in 100 years: 1/2 * 1.4 x 10^11 kg * (0.05c)^2 * 2 = 3 x 10^25 J which is 100,000 times more than the world's energy consumption so that's not going to happen.
Conclusion? With fusion power, space elevators, and advances in recycling, farming, closed environments, and orbital construction it is plausible that a third of the Earth's population could be living in orbital habitats in 100 years. Anywhere else is infeasible, it would simply take too much energy to accelerate that much mass plus fuel, supplies and ship.
The next question is why would you do this? Flinging people off the planet to control population or live in a better environment is a popular trope in sci-fi, but realistically you'd be better served spending all that time, effort, organization, material and energy fixing the Earth. The Earth, even a messed up Earth, is a far more pleasant environment than anywhere else. You could build a biodome or dig underground to get all the benefits and none of the drawbacks of living in an orbital habitat in space or doing the same thing on another planet without having to fling it all off the Earth.
There is a better way to get the Earth expat population up. Send a much smaller population and then do what humans do best: make more humans. Assuming the Earth's population stabilizes, and assuming they land on a bountiful planet, with technology allowing a low death rate and long period of fertility, a small population can grow to a significant fraction of the Earth's in a few centuries.
1/3rd of today's Earth population or 1/3rd of the future Earth's population? Most likely, it will be the future's. One easy way to be able to more easily move that many people would be to introduce some sort of catastrophic event that reduces the Earth's population to a more manageable solution.
another planet which has characteristics similar to those of earth?
With or without FTL travel? Without FTL travel, it would take much much longer than 100 years to get there, although that will be what it looks like from Earth, to the people on board, slow boating at high percentages the speed of light, it would only take much longer than 100 years. With FTL travel? They could be there already, humans on Earth could have come here from that planet, because causality
TL;DR: You would need to shift the goalposts by light years to be able to achieve your scenarios
Ignoring technology, there's another big problem.
Let's use today's population - Google says it's 7.125 billion (OK, as of 2013).
So, our goal is to move one third of that number to.. let's say Mars. It's close. That's 2.375 billion people that need to go from here to there in 100 years.
Over 100 years, that's an average of 23,750,000 people going from here to there, every single year. That's if you could start shipping people today.
So, let's cheat a bit - theoretically we could build one-way ships to Mars today (or soon enough), so we'll let you get your infrastructure up and start the clock with the first launch.
Speaking of today, dividing that by 365 days in a year gives you about 65,000 people, every single day, for 100 years, that you need to move from here to there to make your target - and that's if we don't start the clock until the first rocket launches.
For a bit of perspective - the average immigration to Canada and the US each year is 750,000 per year. You're talking about moving that amount of people every 11-12 days.
You don't have a technology problem - you have a volume problem. :)
(And even if we cheat and count births on Mars towards our billions, unless you can get a lot of people there very fast it's not going to significantly help you.)
Well, not the current population, but getting one person into space and killing everyone else is plausible. Of course, they might not be alive very long.
However, you don't need to get anyone in space. Killing everyone would suffice, since $\frac 1 3$ is a valid answer for $\frac 0 0$.
No. The odds are no where in the realm of in our favor.
First we'd need to find a planet similar to ours. (We're just barely beginning to find planets in other solar systems. While the number is increasing fast, we really don't know which, if any, could be similar to earth with the little data we have on them)
Then we'd have to build transport for billions of people. (Assuming you're talking about the current population, we'd need some sort of transport for 2 billion people or so. Our current space endeavors have room for a dozen at most?)
And then we'd have to get there. (This is the big kicker. Simply due the size of tne universe, the distance we'd have to travel is too vast--even at the speed of light--to reach a potential twin planet in the span of 100 years.)
100 years is just not a realistic timeline for that.
I mean, unless Matt McConaughey finds that wormhole relatively soon.