[ExI] Breakthrough Starshot - To The Stars!

[Anders Sandberg]

On 2016-04-25 08:51, Rafal Smigrodzki wrote:
>
> ### I think I was making somewhat different assumptions. I am assuming 
> that to get to really crazy speeds, or to hustle larger masses at 
> respectable speeds, you will need multiple boost phases from lasers 
> positioned along the trajectory of the spacecraft. As you noted, beam 
> dispersion prevents very long boost phases from a single laser but 
> chaining multiple lasers helps avoid this problem.
>
> But of course if you start boosting from near-Earth orbit and away 
> from the Sun, soon you have to use lasers positioned very far away 
> from the Sun, and this means not being able to use photovoltaics to 
> power them.

Hmm. If you want to achieve velocity V and accelerate during a boost at 
acceleration a, you will need time V/a. During this time it will move 
over a distance (1/2)at^2 = (1/2)V^2/a. The starshot aims at something 
like 60,000 km/s using 2 minutes of 500,000 N/kg acceleration. So it 
will move 3,600,000 km during those two minutes.

A diffraction limited beam will have an angle given by lambda/pi w, 
where w is the radius at the beam  waist. Assuming an optical beam with 
wavelength around 500 nm and a kilometre-sized "launchpad", the angle 
becomes on the order of 1.6*10^-10 radians. The Rayleigh length is l = 
pi w^2/lambda = 6.28e12 meters, and the radius scales as 
w*sqrt(1+(d/l)^2). With for the above numbers become 1000.00016 m. In 
short, there is not any serious dispersion to worry about.

A smaller 100 meter launcher has about 16% larger radius at the final 
distance. For a ten meter launcher it has expanded to 58 meters, causing 
a 33-fold reduction in power.

I guess we may have to handle thermal blooming and other atmospheric 
effects that will reduce efficiency significantly, but I don't think we 
need an advanced infrastructure in heliocentric space to do this.

-- 
Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University

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