How fast did the Finger brake?
The Unexpected Finger fired her engines for 210 days (t = 1.8×107s) to shed her velocity of v = 0.2c = 6×107m/s.
So the Finger decelerated at a rate of a=v/t = (6×107m/s) / (1.8×107s) = 3.3m/s2, which is a gentle one third of an Earth gravity.
That was her average deceleration.
To power her deceleration, the Finger burned fuel equal to twenty percent of her average mass. So she began braking at ten percent above her average mass, lightening as she burned her fuel. By the time she stopped, she had dropped ten percent below her average mass.
Her thrust was constant, so lighter mass meant faster deceleration. Her mass started at ten percent above average, so her deceleration started at ten percent below average, or 0.9 × 3.3m/s2 = 3m/s2. As she burned fuel, her acceleration rose steadily to a maximum of ten percent above average, or 1.1 × 3.3m/s2 = 3.6m/s2.
This is a bit disappointing. A ship the mass of a coast-guard cutter, pushed by lasers that fire a megaton per second, decelerates at only a third of gravity? Obviously her engines aren't very efficient.
Oh, did I not mention the engines were lasers?
