Thursday, May 2, 2013

How Long to Alpha Centauri?

Martin Lewicki

Astronomy Educator, Adelaide Planetarium, University of South Australia
 First published in the Astronomical society of South Australia Bulletin May 2013

The famous Alpha Centauri binary star system is our nearest stellar neighbour at a distance of 4.4 light years. This binary sun-like star system features in many science fiction stories and has been the subject of imagined futuristic colonizing journeys. In spite of Alpha Centauri's relative nearness to us, its distance of 45 trillion kilometers poses a formidable challenge in terms of travel time with current space craft propulsion technology. Articles written about travel time to the Alpha Centauri system attempt to illustrate how long would it take a conventional current day space craft to get there traveling at its typical escape velocities out of the solar system.

Most state that a space craft traveling at the current record breaking speed of Voyager 1 at 65,000 km/h or 17 km/sec aimed at Alpha Centauri would take about 80,000 years to arrive. (Voyager 1 itself is not actually aimed at Alpha Centauri). I have heard this figure repeated many times in web articles, in lectures and in planetariums. While the calculation is correct in theory, in practice it is the wrong strategy because it incorrectly assumes that Alpha Centauri remains permanently the same 4.4 light years from us. Alpha Centauri like all stars has a relative space motion to us. It is the reason why after several thousand years the space motions of stars in our sky will begin to deform the familiar shapes of many constellations. This motion as it appears on the sky is easily looked up in any star catalog and is known as proper motion and radial velocity.

Proper motion is the transverse (apparent sideways) motion of the star on the sky and is expressed as arc-seconds per year in right ascension and declination. Radial velocity is the star's apparent velocity toward or away from us in the line of sight. With this information and some trigonometry it is possible to calculate the true space motion and velocity of the star relative to us and work out where it will be in the future or past. This is a crucial factor to be accounted for when aiming a space craft for a long journey to a star.

In the case of Alpha Centauri its proper motion is -3.678 arc seconds in right ascension and +0.482 arc seconds in declination and a radial velocity of 21.7 km/sec in approach. Combining these figures we get a space velocity of Alpha Centauri approximately toward our direction at 32 km/sec at an approach angle of 47 degrees.

At this velocity and approach angle, Alpha Centauri will pass at its closest to us in 27,700 years at a distance of 3.2 light years and in a direction 43 degrees away in the sky from where it is now in Centaurus. At it closest approach it will be among the stars at the border of Antlia and Hydra shining at a brighter magnitude of -1.0 At this time Alpha Centauri's radial velocity will be zero (neither moving toward or away) and its transverse proper motion (sideways) will greatest. From this point on it will begin to recede from us and head out in the direction of Hydra.

A direct shot at Alpha Centauri will ensure a complete miss as shown by the 80,000-year gray trajectory. Alpha Centauri will  by then have moved to lower left (dashed line). The most efficient trajectory is the 27,700 year trip along the blue line, but at  twice the speed of the fastest escaping space craft – Voyager 1.  Illustration by Martin Lewicki


In 80,000 years from now Alpha Centauri will be 7.4 light years away in southern Cancer dimmed to magnitude 0.8 and 100 degrees away across the sky from where it is now in Centaurus. This means if you aim a Voyager 1 class space craft at where Alpha Centauri is NOW the space craft will find nothing there when it gets there in 80,000 years. If instead we aim the Voyager 1 space craft in the direction of Alpha Centauri's nearest approach in Antlia/Hydra in the anticipation of intercepting it in 27,700 years, we would fail yet again. Alpha Centauri's space velocity of 32 km/secs would out-run the slower 17 km/sec rate of the space craft, leaving it behind, never catching up! So none of the current escaping interplanetary space craft such as the Pioneers, Voyagers or New Horizons can ever get to Alpha Centauri - even if they were pointed right at it. Alpha Centauri would simply out-run them all!


Alpha Centauri's trajectory during an 80,000-year trek across the sky. Many familiar constellations also become distorted due to the space motions of their stars in the intervening time.  Adapted from Stellarium by Martin Lewicki

And The Answer Is?
Clearly the minimum space velocity of a Voyager 1 class space craft will need to be greater to intercept Alpha Centauri when it is nearest to us in 27,700 years. If we launched now it will need to attain a velocity of 34 km/sec - about twice the current velocity of Voyager 1 to make the rendezvous in time. This is the minimum speed required to ever catch Alpha Centauri! Any slower just would not make it. Only one other space craft out-speeds Voyager 1. Helios-2 launched in 1976 to study the space environment within 0.3 and 1AU of the Sun can attain a speed of 67 km/sec when at perihelion. While it is not actually escaping the solar system if this motion was translated to a gravitational slingshot toward Alpha Centauri's it would intercept the star before its closest approach to us and would get there in about 15,600 years(1). ***


References:

(1) Calculation by Mark Taylor.

Universe Today

Calculations:


Heavens Above

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