I will attempt to answer what I perceive to be the core of your question. I will not burden the audience with details of how such a premise stretches the boundaries of science.

I would even go as far as eliminating the term rich from the equation, as rich merely refers to those possessing material wealth, and be it 100,000 years ago when the one with the most animal hides was the richest, or 5,000 years ago when the one with the most crops was the richest, or today when the person with the most money is the richest, the people with the greatest material wealth have always been and will continue to be the patrons required for the true exploitation of any technology or quest. So, I will take the involvement of the wealthy as a given.

What we have left gives us a clearer answer:

If and when such a scenario were to play out, human kind will follow the path it has always followed. Mankind has never abandoned an area that they have colonized. No matter how hard the circumstances of life were when they left an area, some ventured to the vastness of undiscovered lands seeking betterment while others remained behind to deal with and endure life in the areas that were left behind.

This will surely be the case under the premise you describe. Some will venture out, place all of their efforts on making a new beginning in a new world, but also others, even if in the minority, will remain behind and continue to toil with existence in our old planet, making the best to salvage that which was left behind.

Such is the nature of humankind, and such would be the scenario.

We have discovered an exoplanet that could/possibly support life - Gliese 581d. It's more than 20 light years away in the constellation of Libra. On Friday the 28th August we sent 25,878 messages, file size 2,845,345 bytes.

We said Hello From Earth. I said hello.

Its worth the time going to the site and seeing what people hope and wish for if we do ever contact life on another planet. It's a pleasant surprise :)

It also goes a little way into answering this question - if we discover a planet will it already be occupied? We might not have as much choice as we wish for

Anyway, NASA does good things for our society, even if we never get to another planet, all the spin offs like semi-conductors, better baby food, water purification technology...the list is huge!

The answer is no.
Rich people like 3 things to be rich, powerful, and important. Not to mention they wouldn't have the creature comforts that they are used to on the new world.
I think that the pollution will be much less in the future because they will move a lot of the manufacturing off world to Mars or the like when it gets cheaper. the poor will live there. Why would the rich, important and powerful people have to move?

This just me thinking hope it was useful

The answer lies in your question - the rich are already working on new ways to get to that Earth, but first they must find it, so they are attempting to do so, either publicly or privately. No matter how I cut it, both are funded by big money that think they can do anything.

Do you have any idea what the distances involved would be?

There's a reason why huge numbers are referred to as "astronomical".

As Douglas Adams said:

"You may think it's a long way down the road to the chemists, but that's just peanuts compared to space." :)

No sane person would think it's possible, barring a revolution in which we discover that physics as we know it is all wrong. And what we mean by all wrong here is something like discovering that by walking through the back of a magic wardrobe we can travel from London to Los Angeles faster than an email can. The magic wardrobe can be given a fancy scientific name, but it'll be about as magical and unrelated to how we currently know the universe to work as if it was a magic wardrobe.

If rich people want to fund research in fundamental physics for that reason, I won't argue with them. :)

I can see that happening. Although, as rough as our problems are, it might be easier to fix the problems with the current Earth than it would be to figure out how to actually get to Earth2.

http://www.blogcdn.com/www.tvsquad.com/media/2005/04/earth2.jpg

When a "new earth" is found, if ever,
it would take years of exploration to ensure that it's habitable.
In other words, this ain't as simple Christopher Columbus' exploration,
where travel between continents took "mere" weeks or months!

So, the rich would have to wait for the governments to research
and squabble amongst themselves,
and, by then, everyone who would have liked to go to the new world,
would be long since dead and gone,
and any subsequent 'nouveau riche'
would probably think of it as a mere passing fancy of their ancestors.

Even if the rich (or anyone else, for that matter) could go "right now",
it would be decades, if not centuries, to reach "new earth",
so, again, they would be long since dead and gone
before the ship ever landed (cryogenics hasn't been perfected, yet).

Furthermore, even if "Star Trek" warp speeds were possible,
what would they do upon arrival?
There are no farms, manicured lawns, built estates, shopping centers,
golf and tennis clubs, et al.
You don't think the rich are going to build those on their own, do you?

Given the history of the world, both past and present,
it is the poor and "wretched refuse" who move and build new worlds,
not the wealthy who have no real reason to leave their plush lives.

So, welcome the first immigrants to build the new world!

If we were to find another earth like planet then it'd either have no life, and therefore be a barren rock with no soil or other organic sediments, and therefore practically uninhabitable. Or there would be evolved life, so there'd be all the organic sediments needed to sustain the things we would need to sustain ourselves, but it would have taken millions of years to reasonably get to that point, and it is then likely that there would be other intelligent life we would have to compete with.

The latter is more likely; experiments in the '50s showed that through the process of chemical evolution, non-living organic molecules such as lipids, proteins and nucleic acids can be formed from simple precursors such as ammonia, methane and hydrogen when an electric current is passed through them. More recent experiments have backed this up and have also shown that it wouldn't even require a dense atmosphere of these gases as previously thought, because under certain circumstances ammonia, methane and hydrogen can be produced with sufficient densities within rocks. This would explain how life would begin on earth like planets whose atmospheres would be predominately made up of nitrogen and carbon dioxide.

Anyway, before I go into too much detail, my point is that life isn't the rarity it's made out to be, and will form anywhere with the right conditions, so even if we found a way to travel the great distances required we might not like the things we find when we get there - who says humans are the biggest polluters?

Oh, absolutely! I’m not picking on the rich, because I’m glad some folks are fortunate enough to have a lot of cash. However, they classically like to do things as easily as possible (i.e. maids, taking the car to a mechanic instead of doing the work themselves, and awesome, padded vacations), so logically it would be easier to start anew on another planet. Fixing Earth is a major undertaking, and not one many folks are actually willing to take part in.

We have utterly no technology to travel to another star system at this time. Even the closest star would take centuries to reach. The rich are not rich enough to try and reach a planet around another star.

I think everyone will try, not just the rich. It's always simpler to just ditch what's messed up instead of putting in the work to fix it.

Since the question does not ask "will the rich go there?" as many seem to have assumed, the issue of how difficult and/or expensive developing the requisite transport method is besides the point.

Historically speaking, developing methods of going beyond the borders of the "old world" has been the realm of governments and rich individuals. This is very reasonable, since the no-so-rich individuals can't afford to work on ways to get beyond where most people tend to go. These individuals are too busy surviving and providing for their families to be able to invest much effort in things "over the horizon."

Implied in the question was the assumption that if the rich work on developing ways of getting to a "New Earth," they would do so instead of working on saving our Earth and its environment.

The answer to that, I believe, is an emphatic no. Let's assume a way will be invented/discovered to go to a planet orbiting another star in a reasonable length of time. Let's further assume there are no indigenous sentients who would object to our colonization, possibly in a violent way, posing both moral and practical difficulties. Even under these best-case assumptions, any colonization effort would be massive, and at the end of a very very long logistical tail.

What this implies is that life on this hypothetical New Earth would for generations be harsh, and most probably dangerous on a personal level for colonists, as they slowly discover all the ways the new planet can kill them, and develop strategies to address these.

Given the above, massive migration of billions of humans to a new planet is extremely unlikely. It is also extremely unlikely that a majority of "the rich" would migrate.

Historically, when a new land was discovered, the rich did not tend to go to the "new world" themselves. Instead, they tended to send others. These others could be those who got in the way of the rich (e.g. Australia's original colonizers, as opposed to its aboriginal peoples, were those deemed by the British crown to be criminals). Often the military was involved in such expeditions (e.g. many expeditions to Antarctica were military). Finally, traders searching for riches, or their factors, sent by already rich traders to increase their patrons' wealth, often went to the far reaches of accessible territory.

So, given the assumptions stated above, the likely scenario would be that the rich, and governments of prosperous nations, will very likely exert great efforts and invest a great deal of resources in developing a way to go to a newly-discovered Earth-like planet. However, in parallel, both the rich and these governments will continue to exert themselves and expend their resources on trying to save and, to the extent possible, reclaim (or "fix") our Earth and its environment. We cannot afford this to be an "either or," so it will be "both in parallel."