Table of data

 

speed fraction of c

time earth frame yr

time on ship yr.

length m

mass kg

fuel kg or L

gamma

0.001

10,000

10,000

10 m

1,000

0.001

1.0000005

0.1

100

99.5

9.95

1,005

10

1.005

0.5

20

17.4

8.7

1,150

300

1.15

0.866

11.5

5.75

5

2,000

2000

2.00

0.707

14.1

10

7.09

1,410

820

1.41

0.99

10.1

1.42

1.4

7,100

12,200

7.1

0.999

10.01

0.455

0.45

22,000

42,000

22

0.9999

10.001

0.14

0.14

71,000

140,000

71

0.99999

10.0001

0.045

0.045

220,000

438,000

220

0.999999

10.00001

0.014

0.014

707,000

1,400,000

707

gamma = 1/(1-v^2/c^2)^0.5

Time earth frame Te= distance/speed = 10 lightyears/v

Time on ship Ts = Te/gamma

length = L/gamma

mass = mass x gamma

fuel energy = mc^2 (gamma-1) = measured in necessary anti-water (plus water) times 2 to start and stop

= 2 x (gamma-1)

for a speed of 0.866c this amount of energy costs $2 * 10^13 or 20 trillion dollars.