How long to reach 0.9 c, accelerating at 1 gravity?

Assume that at time t=0, I am in a space ship starting at rest relative to the earth, and then I accelerate so that I continuously experience an acceleration equivalent to 1 earth gravity (about 9.81 Newtons). At what time would I observe that I am travelling at 90 percent of the speed of light, relative to the... show more Assume that at time t=0, I am in a space ship starting at rest relative to the earth, and then I accelerate so that I continuously experience an acceleration equivalent to 1 earth gravity (about 9.81 Newtons).

At what time would I observe that I am travelling at 90 percent of the speed of light, relative to the earth? That is, how long after I started accelerating would I reach the speed of 0.9 c ?
Update: Please note: A few people have been answering 45 weeks. This is wrong. I don't know the right answer, but I know 45 weeks is wrong. The reason is, those who calculated 45 weeks did not use relativity, they only used Newtonian equation (velocity=acceleration x time). The answer 45 weeks is absurd, because if... show more Please note:

A few people have been answering 45 weeks. This is wrong. I don't know the right answer, but I know 45 weeks is wrong. The reason is, those who calculated 45 weeks did not use relativity, they only used Newtonian equation (velocity=acceleration x time). The answer 45 weeks is absurd, because if the Newtonian method worked, then I would be able to accelerate 90 weeks and go twice as fast, 1.8 times the speed of light. The theory of relativity is based on the fact that it is impossible to accelerate to faster than light.

Please notice that I specified the acceleration as 1 gravity. That is, at any time, I could swing a pendulum on my spaceship and check that my acceleration is 9.81 Newtons. But this does not tell me how fast my speed is changing. When I look out my space ship window with my telescope, and watch the earth, as I get close to the speed of light, time begins to dilate and space begins to contract.

I have no idea how to do the math for this.
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