High School Feasibility of Yuri Milner's Breakthrough Starshot

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SUMMARY

Yuri Milner's 'Breakthrough Starshot' aims to send a tiny craft, weighing less than 1 gram, to Alpha Centauri using a lightsail propelled by lasers from Earth. The craft is designed to reach speeds of 30% of light speed, approximately 100 million kph, allowing it to arrive at its destination in about 20 years. After the brief acceleration phase lasting around 10 minutes, the spacecraft will continue on its trajectory without further control from Earth. The project has potential military applications, and any advancements may remain classified.

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How far can laser control of a small spacecraft extend?
I've been reading about Yuri Milner's 'Breakthrough Starshot'. It posits sending a very small craft, less than 1 gram, to Alpha Centauri, by way of a lightsail propelled by an array of lasers fired from Earth. It is proposed that this craft will be able to reach 30% of light speed, i.e. around 100 million kph, and would reach its destination in about 20 years at that speed. Once there, it would send back data on the planets orbiting that star, by signals that would take four years to reach Earth (that system being four light-years distant.)

I'm very interested in this idea and have spent some time perusing their website, but there's one obvious question that strikes me, which is, how far could control be extended by way of a laser beam fired from earth? Surely not the hundreds of billions, or trillions, of kilometers that would seem to be required by this proposal? It seems an obvious defeater for the idea but maybe there's something I don't understand about it.
 
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The lasers are only used during the brief acceleration phase. Of the order of 10 minutes, up to a distance of maybe 2 light minutes or ~30 million km. Afterwards the spacecraft continue on whatever trajectory they got from this acceleration phase. Many will miss, but some can get close enough to be useful.
 
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Right! Well, that's something I missed from watching the intro video and the other materials. Thanks. (I notice that all the news items on the site are from 2016-17 so I wonder if there's been much progress on it.)
 
Quotidian said:
Right! Well, that's something I missed from watching the intro video and the other materials. Thanks. (I notice that all the news items on the site are from 2016-17 so I wonder if there's been much progress on it.)

Large parts of the project have potential military applications. Any progress will be classified.
 
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I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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