# March 20, 2010

## Space Port - Part 2 - One big ship

Outer space is big—really big—and almost entirely empty. One thing done in a lot of sci-fi movies is having the characters fly through an asteroid field, dodging asteroids like road hazards. This is silly. You would be lucky to find one asteroid in the Asteroid Belt flying straight through it, yet alone having to worry about dodging such things. Everything in our solar system is separated by distances much larger then anything we can normally work with.

In my story, ships are regularly required to travel to the outer edge of the solar system. Pluto's outer edge of it's orbit is about 50 AU, or 7.3 billion km, or 4.5 billion miles from the sun. So how long would it take to get there?

If you could get a space craft to travel 500,000 mph (not too crazy for space travel), it would take about 1 3/4 years to travel the distance. It you would like to do that in one month, you would have to travel about 10 million miles an hour.

Rocket engines are a source of force. Force in physics is usually measured in Newtons, which is kg·m/s^{2}.

Assuming the force exerted by a rocket engine is constant, we can determine it's acceleration (m/s^{2}) on some given mass (kg). Our mass is the space ship, so knowing it's mass, we can determine acceleration.

What's nice about acceleration is that it keeps increasing velocity. The standard physics equation x = x0 + v0 t + 1/2 a t^{2} will determine a position (x) after some time (t) with an initial position (x0) and initial velocity (v0). We we start of position 0 (x0 = 0) at a complete stop (v0=0), the equation simplifies to x = 1/2 a t^{2}. And we can solve for t, so t = sqrt( 2 * x / a ). We know x—that is the distance we want to travel. So what is the optimal acceleration? Acceleration due to gravity naturally. This way, we have linear acceleration and perfect gravity. So acceleration is 9.81 m/s^{2}. Thus, if you had the ability to provide a constant force with this rocket engine, it would take about 14 days to reach the outer orbit of Pluto from the Sun. That's not bad considering the distance.

But in working this out, I was faced with one obvious problem. The ship I designed is rotating. It already has gravity. The gravity introduced by linear acceleration will be in the wrong direction. If the rotation provides 1 g in one direction, and linear acceleration provides 1 g in an other direction, people are going to be standing sideways just to stay upright. This isn't going to work.

It was in the car ride back to Wisconsin talking this over with Mikala that a solution was presented. Mikala pointed out what should have been obvious: why not just have the spheres rotate? As the ship accelerates, turn the spheres such that the center of gravity at a 90 degree angle to the floor. In fact, one wouldn't even need to turn the spheres. The bottoms are heavier then the tops, because the tops are empty. If allowed to rotate, the spheres would naturally correct for the center of gravity.

So as the ship accelerates, the rotation is slowed. Since the ship is likely to be large, we will have to gradually accelerate to avoid jarring everything. A change in acceleration is known as jerk. So some constant jerk factor would have to be obtained—likely from that rate at which the rotation could be slowed to a stop.