Using the engines today how long will take humanity to reach earth like planets?
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HD 219134b is apparently closest "super earth"; 21 light years away. New Horizons, our speediest yet, is currently running at about 15 km/sec relative to the sun. At 9.46e12 km/lightyear HD 219134b is 2e14 km away At 3.16e7 seconds per year, New Horizons will travel about 4.74e8 km/year. 2e14/4.74e8 = 422000 years.
HD 219134b isn't even a very good earth; gravity is too high.

Wayfaring Stranger
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Apparently new horizons will eventually start to loose momentum to about 13 km/s? – cstruter Aug 26 '15 at 07:53
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1@cstruter Yes, of course. New Horizons is still well under the gravitational influence of the sun, and will continue slow for some time. I picked its current velocity as an estimate of a speed near the best we can currently do, not an immutable constant. I doubt New Horizons is even headed towards HD 219134b. – Wayfaring Stranger Aug 26 '15 at 09:45
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