4015 spaceship
I guess in two thousand years you would not be making your spaceship from steel. By then carbon nanotube technology will have been mastered and it will be what you will be using. Currently the scientists are producing this material which is much stronger than steel and very much lighter.
If the density of the new material is one hundredth that of Styrofoam, then it has a density of about 0.2 kg/m3 compared to iron of 7,600 kg/m3.
Consequently the spaceship mass will decrease by a huge amount.
The two cylinders will be V = 3.0 x 109 m3 of steel.
That is 3.0 x 109 x 7,600 kg for iron construction
Or 3.0 x 109 x 20 kg for expanded polyurethane construction.
i.e. 6 x 1010 kg for expanded polyurethane construction.
Hence 6 x 108 kg for carbon nanotube construction.
If made from steel it would be about 40,000 times heavier at least as it would need heavy structural components.
Just how heavy is that?
According to Wikipedia the statistics for the heaviest train that has run are as follows.
Run on 26–27 August 1989, comprising 660 wagons, 7.302 kilometres (4.537 mi) long and a total weight of 71 765 tons. The train comprised 16 locomotives (9 Class 9E 50 kV AC electric and 7 Class 37 diesel-electric). https://en.wikipedia.org/wiki/Longest_trains
That is about 7 x 107 kg.
So the spaceship is equivalent to ten or so of the heaviest trains run on Earth. So it is lightweight when we consider it is a huge interstellar transport.
Propulsion for the spaceship
You remember that fission is the splitting of the atom as happens in a nuclear power station where uranium nuclei split in two and release a lot of energy.
Nuclear powered aircraft carriers can go for eighteen years on one fuel load. It may be that this is the method to use as we want propulsion for 30 years accelerating and then likewise slowing. But if the reaction happens all the time it may be accelerate for five hundred or a thousand years and then slow for the same time.
The fission process can be also be used to provide electricity for the spacecraft operations throughout the journey as well as propulsion.
If we assume a thrust of 180,000 N
F = ma
a = F/m = 180,000N/ 6 x 108 kg
= 3 x 10-4 m/s/s
The velocity to attain is such that the trip to Maxwell takes 2000 years. Hence the time taken is 200 times the time light takes to get between them so the speed must be 1/200 that of light.
Light speed is 3 x 108 m/s
So the speed we need to take 2,000 years to get to Maxwell is 3 x 108/200
v = 1.5 x 106 m/s = 1,500 km/s
The time taken to get to this velocity with the acceleration from one motor is, starting from rest, from
v = u + at
t = v/a = 1.5 x 106 /3 x 10-4
= 5 x 109
= 5 x 109 /3600 x 24 x 365 = 5 x 109/31536000
= 159 years with one engine
What if we have the motor going for all the trip.
Accelerating for half the distance and then decelerating until we get to Maxwell.
This calculation will give us the time it will take to get to Maxwell assuming an acceleration of = 3 x 10-4 m/s/s for half the distance and then double this time as deceleration at the same rate will take place.
s = ut + ½ at2
Starting from rest so u = 0
s = 5 light years
s = 5 x 3 x 108 x 3600 x 24 x 365 m
s = ½ at2
t2 = 2s/a
= 2 x 5 x 3 x 108 x 3600 x 24 x 365/3 x 10-4
t2 = 2s/a
= 2 x 5 x 1014 x 36 x 24 x 365
t2 = 3153600 x 1014
t = 1776 x 107 s
t = 563 years of acceleration followed by 563 years of deceleration.
Total time 1126 years with one motor.
The velocity attained after 563 years of continual acceleration with one motor will be
v = u + at
u = 0
v = at = 563 x 3600 x 24 x 365 x 3 x 10-4
v = 5.3 x 106 m/s = 5,300 km/s
An obvious question is
What if we use more than one motor?
