How to get from Earth to Alpha Centauri?

Off to Alpha Centauri! and to its orbiters, Tolimán and Proxima...

RC Johnson’s “The slingshot effect” (Jan 2003) is the primer on how to speed up maybe even to such a speed as to get those Ramjets workin'. But at some point, it'll be time to slow down. Again: Delta-V yo.

Cassini took almost seven years to get into a trajectory that could orbit Saturn, 9.6 AU from our sun. New Horizons on the other hand took nine years to travel the 35 AU to where Pluto was at the time… at such a speed (16260 ms^-1, boosted to 23000) the probe had to keep going. On the other hand, all the astronomical bodies in our way to Centaur's Foot are (much) larger than Pluto and Charon.

At journey's end we should be able to harness Tolimán's orbital velocity around A. Catch Tolimán when she's coming (faster) toward us; the late 1980s would have been good, so aim for some 80-year period from back then. We are riding an O'Neill "rama", so are in this for the long term anyway. When Tolimán comes toward us, she is approaching apastron at home, so is going slower. The whole system's barycenter is going toward us at −22393 ms^-1.

[I'd like to use whatever planets are in the Centauri system, but none are confirmed as yet. So I'm not counting on them.]

If we're brave enough to skim a near-solar corona, and have some way of buttressing the tidals, Tolimán's own rotation is 11000 ms-1. Again, yay shielded O'Neill. At the very least solar-sails might be of use.

En route, we also get Proxima - hence the name. As of 2017, this dwarf - then 7800 AU closer to us, and 12950 AU from A/B - is verified to be orbiting the Centauri duo but at apastron - hence why it took so long to verify that these stars are even involved (although such was always suspected). Kervella, Thévenin, and Lovis, "Proxima's orbit around α Centauri", Astronomy & Astrophysics 598 (January 2017), L7.

Proxima is coming at us slower, -21700 ms^-1 - so relatively away from us, 693 ms^-1. I expect no direct help slowing a craft. If we wait too many millennia, it won't even be on our route. About 275,500 AD the star will only be 4300 AU from the A/B focus but on the wrong side. 400,000 AD would be best but LOL. The good news here: Proxima has a planet... which we know by the Radial Velocity method... so THAT is (every eleven days) headed this way.

[The star may have a second, 6-Earth planet 1.48 AU further out, certain to sport an atmosphere; but I'd not bank on this planet being confirmed. UPDATE 12/24/22 - I don't recall why I struck that out. As of October 2022: we have a 2σ inner d but 1.48 AU phantom c is a ghost. d which we should call c now, maybe a, is inward of b.]

That b planet is 1.3 Earth mass and orbits 0.0485 AU from its star. Said star has .1221 Solar mass which is 40653 Earths. The orbital velocity of that planet is 50000 ms-1, as calculated Luger et al., “The Pale Green Dot” (2017). The mass ratio: 1:32010.

As for the size of the target:

?Math.Pow(1/(3*32010),1/3)

The planet's L1 is 0.022 AU toward Proxima; L2, 0.022 AU away. Most astronomers are assuming that this small planet is low-atmo on account of its distance from a flare-star and, further, is suspected to be tidally-locked or at least 2:3, slowing its dynamo over its 4.85 billion years thus far. We won't be aero-braking.

So, from Earth: Proxima's planet gives that 50000 ms^-1 to spare. If we don't mind adding that 5100 AU detour to our route. There was also the idea of using the Bussard Ramscoop to decelerate and pick up extra hydrogen, before entering Proxima's likely bubble at, what, 50 AU. (The 'scoop doesn't work to accelerate; there is no ramjet for our Local Bubble.)

En route - if A/B do prove to have planets fit for braking the ship - we can consider donating spare propellant and fuel to prospective Proxima colonists. Otherwise we'll need it all for the slowdown.