Getting around Sol Space

November 3rd, 2007

Interplanetary travel is pretty arduous based on current technology – chemical rockets and solar-powered ion-drives. Back in the late 1960s NASA was seriously developing a nuclear rocket called NERVA, but it wasn’t really much of an improvement on chemical rockets for anything other than trips to the Moon. NERVA’s exhaust velocity was about 8,500 m/s to about 9,500 m/s, while advanced chemical rockets get about 4,700 m/s – sounds like a big improvement, but getting to Mars in a decent time requires a lot of delta-vee.

The minimum energy Mars mission with a transfer time of 250 days – a Hohmann transfer – meant a Mars ship with six crew and a 50 ton lander needed an initial Earth-orbit mass of 727 tons. The vehicle had several major sections – Planetary Mission Module (crew habitat, life support & power), Primary Propulsion Modules (3 modified nuclear Moon shuttles), and the Mars Excursion Module – each of which would be launched via up-graded Saturn V Heavy-Lift Vehicles. Thus we’re talking over 15,000 tons of on-Earth mass to land a single lander with 3 crew on Mars for a 30-60 day stay. Some missions required another PPM thrown in, but the total trip-time didn’t improve even with that extra power. Plus the expedition had to do a Venus fly-by to reduce the total propellant mass required and the total stay-time on Mars – pure Hohmann missions need over two years lay-over on Mars.

Mission designs since then involve trickier orbits which expend a bit more propellant to cut down the trip-times by almost half. When Mars is at perihelion, on arrival, the trip-time can be as low as 130 days, but when it is at aphelion it’s more like 180 days. That’s a long time travelling even so.

What if we want to go further out? Robert Heinlein’s “Farmer in the Sky” (1950) is set on a terraformed Ganymede which has been slowly colonised via fleets of small ships carrying 500 people at a time. These fly on Hohmann transfer orbits that take almost 1,000 days (two-and-a-half years). The Earth Government wants to speed the process up, so a high-speed torch-ship is launched carrying 6,000 people on a 60 day flight. You can imagine the chaos on Ganymede of handling so many people at once – it makes up a significant part of the story.

What’s the difference in flight-plans? Well the previous ships were all nuclear powered, but the new ship – the Mayflower, of course – uses a Total Conversion reactor to accelerator reaction mass to high speed. Kind of what an antimatter reactor would do, without the messy magnets to channel pions. With a relativistic exhaust velocity the Mayflower accelerates to 93 miles per second (150 km/s) using only a tiny bit of mass-energy. On a Hohmann transfer the ship maxes a mere 24 miles per second (38.6 km/s) – why then does such a trajectory take 1,000 days if you’re only travelling about 4 times slower than the Mayflower?

Earth itself travels around the Sun at 18.5 miles per second (29.8 km/s), so 24 mi/s isn’t much faster and the orbit the ship follows is more like a circle and less like a straight line path. Plus it is slowed down mightily by the Sun – by the time it reaches Jupiter a Hohmann orbit ship is doing just 4.6 mi/s. The Mayflower doing 93 mi/s follows an almost straight line to Jupiter and slows to 89.5 mi/s (144 km/s) – virtually no slowing by the Sun at all. Thus the Mayflower takes a mere 60 days.

To travel via Hohmann transfer to Jupiter a ship needs to increase its speed around the Sun from 18.5 mi/s to 24 mi/s, and to also escape the Earth’s gravity. Say it takes off from the ground – the speed needed is 14.2 km/s, neglecting gravity losses. Once it has escaped Earth’s Hill Sphere it’s in the Sun’s gravitational dominance and is moving 8.8 km/s faster than Earth. It arrives in Jupiter’s Hill Sphere doing about 7.42 km/s relative to the Sun and 5.64 km/s relative to Jupiter. It falls towards Ganymede’s orbit, about 1,080,000 km from Jupiter’s centre, and is doing 16.4 km/s relative to Jupiter when it arrives – needing to slow by 5.52 km/s to match speed with Ganymede. Thus to arrive in Ganymede orbit from Earth’s surface takes about 19.7 km/s. More than any rocket ever built and pretty heavy going for a nuclear rocket, but doable. Might need to refuel in Earth orbit.

To match the Mayflower we’d have to increase in speed by 120 km/s relative to Earth initially, then deccelerate at Jupiter by about 144 km/s. Total velocity change: 264 km/s… which is over 13 times the velocity change needed for a Hohmann trip. No chemical or nuclear rocket – short of actual nuclear detonations – could achieve the exhaust velocity needed to make such a trip practical. The most efficient energy use would need an exhaust velocity of 165 km/s and about 4 times the empty mass of the ship in propellant – there’s a theorem that the mass-ratio using the least amount of energy for a given velocity change is 4.92, and an exhaust velocity of 1/1.6 the total velocity change (mission velocity.) Such a jet would be like riding a nuclear detonation – say your ship masses 1,000 tons and is accelerating at 1 gee. The power output is 0.4 trillion Watts – the equivalent of 100 tons of TNT exploding every second.

And, of course, there is a rocket which could get such performance – the Orion Nuclear Pulse Rocket – which really would have been propelled by nuclear explosions. Some of its developers (between 1958-1964) were hoping to visit moons of Saturn by 1970, and it could have quite easily made the trip. Small nuclear “pulse units” equivalent to 1 kiloton of TNT energy would have exploded just behind the ship’s massive “pusher plate” – the explosion could be shaped into a jet of hot plasma that would have splashed around the plate, barely heating it at all. The bigger the plate, the more efficient the energy transfer – thus the highest performance would have been achieved by multi-million ton “Orions” using megaton pulse units. That system could land a ship the size of a city on any object with a solid surface in our Solar System in a matter of weeks.

Of course, in the process, all the Earth’s fission explosives stocks would be burnt up… so what’s the problem?