Relativistic Constant Acceleration

x = c2/g (cosh gτ/c − 1)         t = c/g sinh gτ/c

gτ/c = log[1 + gd/c2 + √(2gd/c2 + (gd/c2)2) ]

c/g = (2.998 × 108 m/s) / (9.806 m/s2) = 3.057 × 107 s = 0.969 year

 

    D = 2 d Tc = 2 d/c     TN = 2 √(2d/g)     Tproper = 2 τd     Tclock = 2 t(τd)     vmax = c tanh(d/c)
500 km (Atlanta) 0.00166 s 452 s = 7.53 min 452 s = 7.53 min 452 s = 7.53 min 2.2 km/s = 8000 km/h
400,000 km (Moon) 1.33 s 12,800 s = 3.55 h 12,800 s = 3.55 h 12,800 s = 3.55 h 63 km/s
270 M km (Mars) 900 s 3.32×105 s = 3.84 d 3.32×105 s = 3.84 d 3.32×105 s = 3.84 d 1600 km/s = 0.0055 c
4.4 LY (α Centauri) 4.4 Y 1.30×108 s = 4.13 Y 1.13×108 s = 3.59 Y 1.90×108 s = 6.03 Y 280,000 km/s = 0.95 c
25,000 LY (galactic center) 25,000 Y 9.8×109 s = 311 Y 6.1×108 s = 20 Y 7.9×1011 s = 25,002 Y 0.9999999968 c = c − 0.96 m/s
2 M LY (Andromeda) 2 M Y 2800 Y 28 Y 2 M Y (1 − 5 × 10−13)  c
13.8 G LY (visible universe) 13.8 G Y 230,000 Y 45 Y 13.8 G Y (1 − 10−20)  c