‘Oumuamua is the fastest known interstellar visitor to our Solar System, with a heliocentric hyperbolic excess of 26.33 km/s. What that means, if we want to chase it, is that we have to go faster – at infinity – to catch it. From Earth’s orbit that’s an initial speed of 49.675 km/s, but of course, as the relative velocity is thus zero, we’d never catch it. So we have to go faster.
But to really study ‘Oumuamua up close we need to stop. Just for the sake of the exercise let’s imagine we want to launch in 5 years. Just for fun we’ll assume we can get a Kilopower mini-reactor with a specific power of 25 W/kWe supplied. How fast can we brake from to match ‘Oumuamua’s eventual asymptotic speed of 26.33 km/s using just off-the-shelf technology?
Plasma drives are commercially available for station-keeping of Geosynchronous Satellites. The Russian company Fakel has sold Stationary Plasma Thrusters (SPTs) for a couple of decades. The SPT-140D masses 8.5 kg, 4,500 W power, a specific impulse of 1770 seconds, a thrust of 0.29 newtons, and a lifetime of 4500 hours. The jet-efficiency is ~56 %. The propellant is Xenon, which stores reasonably easily in liquid form, even if there’s not a huge amount produced each year.
Presently they’re developing a higher powered version, the SPT-230, which has been tested up to 3,200 seconds Isp and 15 kW jet-power, with an efficiency of about ~75%. According to a recent catalogue, they’re aiming for a 9,000 hour life-span, an Isp of 2,700 seconds, a mass of 25 kg. With a power of 15 kW and efficiency of 0.75 that’s a thrust of ~0.85 N.
A useful figure of merit is the total propellant ejected over the lifetime of the engine. Let’s assume the high performance version of the SPT-230 is available. Assume the “9,000 hours” to mean in continuous thrust mode, that means 0.85 N/9.80665/2,700 seconds x (9,000 hours x 3,600 seconds) = 1,040 kg propellant is ejected per engine.
So we have a 600 kg Kilopower system, 350 kg of probe (New Horizons less hydrazine and RTG), and a couple of engines for redundancy and maneuvering. Total mass ~ 1,040 kg. We load up with an equal usable mass of Xenon propellant. That’s a mass-ratio of 2, so a delta-vee of 18,353 m/s total. If we allot 353 m/s to maneuvering, then the braking budget is 18 km/s.
Therefore the hyperbolic excess we can start with is ~44.33 km/s. Of course ‘Oumuamua won’t actually be at ‘infinity’ when we reach it so it’ll be moving a bit quicker. As of 01/01/2019 it’ll be 9.5 AU from the solar barycenter and moving outwards at 29.636 km/s. A useful speed to remember is 4.74 km/s – that’s 1 AU per year. So Jan 1, 2019, ‘Oumuamua is moving outwards at 6.25 AU/yr. That will quickly decline as it moves much further away. By 2023 it’ll be further away than Pluto. By then it’ll be doing 27.3 km/s, very slowly decreasing from that point on. I’ll assume 27 km/s – about 5.7 AU/year. So 45 km/s is the chase speed of our interceptor.
Braking while under constant thrust means the acceleration increases as the mass-ratio declines. We’re using a mass-ratio of 2 and the average speed over the 9,000 hour ‘burn’ is about 36.5 km/s (7.7 AU/year) over a distance of 7.91 AU. That’s a rather leisurely intercept. To get up to that hyperbolic speed, the Project Lyra proposal is to dive close to the Sun and perform a very high acceleration burn. If the perihelion burn takes place in 2027, it takes about 12 years to intercept ‘Oumuamua in 2039 at about 125 AU from the Sun.
While the Voyagers are presently about that far from the Sun they’re not actively navigating to a small target. The final approach will be incredibly challenging, since the light levels will be 15 times lower than New Horizons encountered at Pluto. Thanks to our ~300 m/s reserve, the task will be somewhat easier but complicated by the almost 35 hour round-trip time for radio waves.