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If a spacecraft heading to Alpha Centauri at 10% light speed, given a close approach to the main star, would deploying large solar sails, just before entering the solar system, slow the spacecraft enough to remain in orbit of that star ?

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    $\begingroup$ Sure. If you crash into the star. $\endgroup$ – Mark Adler Mar 18 '16 at 4:13
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No

1-10% of the speed of light is really, really fast. A solar sail would not receive a noticeable amount of light before it is about 5 AU away from the star (even then much less light than at 1 AU from the Sun), and from there, it is just 6-60 hours before the probe hits the star or flies past it, with your given velocity. That is a too short time, as solar sails use weeks or months to do even much smaller changes in velocity.

More generally, here are a few things you can check:

  1. Determine if the sail can even slow you down:
    Pick a place at any distance from the star, and calculate the force of the gravitational pull. $\frac{G(M_{star}M_{sail})}{r^2}$. Compare that with the force of the light pushing the sail. $\frac{2E}{c}$, where $E$ is the energy hitting the sail per second, and c is the speed of light. If the gravitational pull is stronger, it is so everywhere, as both forces scale the same way. Then it would not be able to slow down at all.
  2. Determine how much it is going to slow down in the case it is strong enough:
    As the force from the sail acts essentially the same as if the star had a lower mass, we can pretend so to keep the calculations simple. Use the previously calculated forces, and give the star a "new" mass: $M_{new}=M_{star} \cdot \frac{F_{gavity}-F_{sail}}{F_{gavity}}$. (Do not panic if you get a negative value, that is perfectly normal). Now, you can calculate how much energy the probe can get rid of from infinity, to a target radius $r$: $E = M_{sail} \cdot -\frac{M_{new}}{r}$. Subtract that from the initial kinetic energy of the probe, $E_{initial}=M_{sail} \cdot \frac{v^2}{2}$ and you can calculate the new velocity, $v_{final}=\sqrt{2 \cdot E_{final}}$.
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  • $\begingroup$ Maybe we can slow down with a gravity assist. The acceleration would destroy anything on-board, though. $\endgroup$ – gerrit Mar 18 '16 at 11:23
  • $\begingroup$ @gerrit For gravity assists, Vinf in equals Vinf out. You would then need a planet moving at a few percent of the speed of light. (about 100x faster than Mercury). It has to be very massive too. $\endgroup$ – Hohmannfan Mar 18 '16 at 11:30
  • $\begingroup$ I was thinking of a gravity assist around the star, not a planet. Not sure how fast stars move through interstellar space relative to each other and our interplanetary spacecraft, though. $\endgroup$ – gerrit Mar 18 '16 at 11:31
  • $\begingroup$ It's possible for a sail to attain capture even if it can't slow you down against the pull of gravity. That energy you gained while falling in you'll give back on the way out--and the Oberath effect still applies so you don't just get to add up the deceleration, either. $\endgroup$ – Loren Pechtel Mar 18 '16 at 22:04

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