Originally posted by lausey
Excuse the notation. Not sure accuracy, as I did this at work quickly when I am supposed to be working.
x = final position relative to starting point
x0 = position at starting point
t = time to reach x
v0 = initial velocity
a = accelaration
x - x0 = v0t + (1/2) at^2
x0 = 0
x = 80 million km = 8 x 10^10 m
t = 20 days = 1.728 x 10^6 s
v0 = 0 ...[text shortened]... 10^10) / (1.728 x 10^6)^2) = 0.0536 ms^-2
A little over 5 centimeters per second per second.
Perfectly correct, about 5 milli G's. A lot of distance covered for such a tiny thrust, eh! I wonder if you would feel it if you were inside that spacecraft.
If you kept that up for 200 days accel and 200 days decel with the same acceleration, you would be 16 billion Km from earth and stopped or 10 billion miles, 2.7 times the distance of Pluto.
To get to Pluto with that acceleration, it would take 121 days to get halfway where you turn your engines around and decel for the rest of the trip, so it takes 242 days or about 8 months and you attain a maximum velocity at the halfway point of about 550 Km/sec or 350 Miles/sec. That is pretty fast indeed.
My favorite dream trip would be to the solar foci, which starts at about 55 billion miles or about 80 billion Km from the sun (where gravitational lensing of the sun starts to focus light from distant suns) and I think about a bit further out, the 1000 AU point, 1.4E11 Km, or 1.4 E14 meters, also at that 0.053 M/S^2 accel, takes about 846 days to the halfway point or about 1700 days for the whole trip (a bit over 4.5 years one way) and a maximum velocity of 3,920 Km/sec or 2450 Mi/sec. Pretty impressive velocity if you ask me!
My most favorite dream trip would be to Alpha Centauri, at .053 M/S^2, would take 26 years and at the halfway point you would be doing 22,000 Km/sec or about 14,000 miles/second, about 0.07C. Sounds almost doable for humans. Of course if you spend say, 5 years studying AC, and come back it would take 57 years round trip but still possible. I would think a journey like that would be one way however. Then you send back data at light speed so about 30 years after you leave, assuming you make it ok, Earth would start receiving close up and personal data from Alpha Centauri! What a trip that would be, and with more or less existing technology.
One thing to note: At 0.07C there would not be much in the way of relativistic time dilation so the trip times are pretty much what you see is what you get, as opposed to getting about ten times faster where the trip time for you on the craft seems to take only about half the time it looks like it took from Earth's perspective.
Anyone want to check my figures? I use S=(AT^2)/2 as starting point for distance and reworking it to T=(2S/A)^0.5 which is the halfway point so to get the total trip time, multiply time 2. And using that time, plugging it into V=AT gives maximum velocity (at the halfway point) then the engines turn around and slowly decel the rest of the way. Using meters/sec^2 and meters for distance.