Breaking the Rocket Equation
Interstellar Travel by means of Accelerated Fuel
The Plight of the Rocket Equation
The prospect of crossing the empty seas of interstellar space is one that is fraught with a flood of technical challenges. Arguably, the most prominent challenge is overcoming the famed Tsiolkovsky rocket equation, which dictates how much fuel a spacecraft requires to attain a certain velocity change. Take a simple mission to Mars, for example. A spacecraft which begins its journey on an Earth-based launch pad and ends on the rusty regolith of the Red Planet will require a total velocity budget of about 20 km/s. A simple crunch of the Tsiolkovsky equation reveals that such a spacecraft demands a mass of fuel 146 times greater than the combined mass of the spacecraft and payload itself. The mass of the ship can be mitigated by separating the rocket into stages where, after each stage of fuel is burned, the empty portion of the ship is severed. That way, the mass of the payload can be larger, as the empty fuel stages aren’t carried along as deadweight to the target destination. Despite this, however, the Tsiolkovsky fuel-to-mass ratio remains a facet of physics, and cannot be changed.
The rocket equation basically kills any form of fuel-based propulsion system looking to venture beyond our Solar System within human timescales. For an interstellar starship vying to undertake a crewed mission to our closest stellar neighbor, Proxima Centauri, an average velocity of at least 8% of the speed of light is necessary. Even a modest 150 tonne interstellar spacecraft with a propulsive exhaust velocity of 440 km/s would require more fuel than the estimated mass of the entire observable universe to meet this threshold, and even this exhaust velocity is >100 times greater than the capability of current rockets. Optimistic fusion rockets of the future may be able to attain effective exhaust velocities of close to 700 km/s, reducing the amount of fuel required to about 82,000 Suns. Only the highly speculative antimatter rocket would yield fuel-to-mass ratios low enough to be practical for interstellar missions, but antimatter has proven to be expensive, time consuming, and energy intensive to manufacture.
The limitations of the rocket equation have forced us to look elsewhere for a solution to interstellar travel. In one solution, interstellar hydrogen is collected directly from space by a powerful magnetic field and fed to a propulsion system like a ramjet, effectively carrying no fuel. In another, a powerful array of Earth or Moon-based lasers homes in on a reflective radiation sail, sending the associated payload careening towards the stars. Both the interstellar ramjet and the laser propelled sail suffer from critical design hurdles which make crewed missions using them arduous:
- The interstellar ramjet would require a massive on-board power source to increase the exhaust velocity of its propulsion system to close to the speed of light, lest it succumb to the effects of drag from its own magnetic field.
- Lasers diverge across space, making them ineffective on even interplanetary distances. This means that, in order to propel a spacecraft anywhere close to the speed of light using Earth-based lasers, the payload must be accelerated at >1000 G’s before the laser is out of range, restricting this method to uncrewed probes.
Accelerated Fuel Concept
There may, however, be a sneaky way to break the rocket equation by making use of aspects of both these methods, while also utilizing a traditional rocket. The concept involves launching fuel pods from the Earth at high velocities towards a constantly accelerating interstellar spacecraft, the velocity and position of these pods perfectly matching that of the ship upon rendezvous. Because the spacecraft is not responsible for accelerating its own fuel, the overall fuel-to-mass ratio remains exceptionally low, only dependent upon how often new fuel pods arrive at the spacecraft for pickup. The more frequently these pods are launched, the less fuel the spacecraft must ferry, and the lower the fuel ratio. Ideally, the spacecraft always runs out of fuel just as a new shipment arrives, and since this new fuel is already travelling at their velocity, they just have to collect it and burn it to reap the velocity benefits.
Accelerating fuel pods to an already accelerating spacecraft sounds taxing, but this may not be the case. Since the distances between stars are so vast, a vessel can attain a great fraction of the speed of light while exhibiting a very low acceleration. A vessel which averages just 0.56 m/s² (~0.06 G’s) will attain half the speed of light (0.5c) at half the distance to Proxima Centauri. Alternatively, the fuel pods are only restricted in acceleration by their own material properties and on-board electronics. Fuel pods made from near-future technology could be safely accelerated at upwards of 10,000 G’s. The first several fuel pods would only need to be modestly accelerated to catch the slowly moving spacecraft, but once the ship’s velocity starts to pick up, greater fuel accelerations would be necessary. These fuel pods could be launched with traditional rockets, but that would defeat the whole purpose of accelerating fuel pods to mitigate fuel usage. Instead, the pods can be equipped with radiation sails and accelerated rapidly by a powerful array of 100, 1-giggawatt lasers on the Moon (to avoid atmospheric effects). The use of lasers would allow the final fuel pod to achieve 0.5c within a few hours or so before going out of range, enduring a maximum acceleration of ~5000 G’s. To maximize the range of the lasers, the radiation sails would require diameters in the range of 5–10 kilometers. Despite this immense size, the sails could be manufactured from one of several low density materials which are known to reflect visible laser light. This would keep the overall mass of the sail negligible compared to the mass of the fuel pod.
Just by the nature of this concept, fuel pods would be launched twice as often as they are picked up at the spacecraft, and the pods would always be launched at 2X the ship’s current speed. For example, if fuel pods are launched every 5 days from Earth, they only arrive every 10 days at the spacecraft, accelerating away from Earth. This means that Earth would launch the final fuel pod when the ship’s velocity is still just 0.25c. These fuel pods will continue to “catch” the spacecraft until it reaches the halfway point. This is where an issue presents itself, however, since there is no way to launch fuel to a decelerating spacecraft without having launched them before the mission began. To conceptualize this, imagine the spacecraft has reached 0.5c and has turned around to decelerate. The next fuel pod should now match their slower speed, but for that fuel pod to have arrived that far away travelling slower than 0.5c, it would had to have been launched before the spacecraft. This isn’t a huge deal for the first few decelerating pods, which could be pre-launched in the years preceding the mission. However, future pods would require velocities so slow at such great distances that they would need to be launched millions or even billions of years in advance. The last few would have needed to be launched before the beginning of the universe!
This is obviously impractical. Instead of using fuel to slow down, perhaps the spacecraft could make use of the phenomenon which plagues the interstellar ramjet. By employing a powerful magnetic field, thousands of square kilometers of interstellar protons could be diverted into a solid “impact plate” attached to the ship to absorb their kinetic energy and slow the spacecraft like a giant parachute. Unfortunately, our Sun is currently travelling through a tenuous region of space known as the Local Bubble, which contains an order of magnitude fewer interstellar atoms than the galaxy’s average. This means a more powerful field than normal will be required to execute this magnetic parachute maneuver. For a 150 tonne spacecraft to accrue enough drag to slow down for a Proxima capture, the ship’s magnetic field would need to divert and capture a radius of ~150 km of interstellar protons. At first the drag would be large, resulting in a deceleration on the order of 0.1 G’s. This drag deceleration drops off by the square of the velocity, meaning the second half of the voyage would take longer than the first. This equates to a total trip time of around 20 years or so.
Issues
The most prominent issue with this concept is designing a precise enough fuel launch system to get the pods to match the ship’s position and velocity exactly. This one is a doozy. A misalignment of the fuel pod’s radiation sail by even a tiny fraction of a degree could send it thousands of kilometers off course. If the spacecraft misses even one fuel pod, it will run out of fuel and never be able to catch the remaining pods, which will fly past the ship at ever quickening speeds. The fuel pods would likely require advanced control systems to precisely gimbal their sails during acceleration to optimize their trajectories. On-board communications could also continuously relay the pod’s current position and velocity so that the ship could make minor corrections to accommodate its approach. A small amount of reserve fuel may be prudent for the spacecraft in this sense. Another technical hurdle is the advent of fusion technology, which would probably mitigate the other major challenges of constructing multi-gigawatt laser infrastructure on the Moon, as well as a several hundred megawatt power source for the spacecraft’s propulsion system and magnetic field generator. Other general interstellar threats, such as cosmic rays and micrometeoroids, would also need to be defended against.
Conclusion
Accelerated fuel rockets still pose some substantial obstacles, but they may yet be the most technically feasible option for interstellar travel. Like 17th century balloonists working against Newton’s gravity, or Chuck Yeager challenging the laws of supersonic fluid dynamics in the 1940s, the Tsiolkovsky rocket equation may be just that — a barrier meant to be broken by a novel application of technology. The fundamental laws of physics have laid out some strict ground rules in our quest to explore the stars. It’ll be our responsibility in the centuries to come to discover the loopholes and facets of these laws in order to best equip ourselves for the voyages ahead. Space is like an ocean, each star a single island in the vast abyss of blackness which permeates the universe. Every island is unique, each containing mysteries and treasures far beyond what we could ever hope to unveil from our own. There may come a day when our race walks the stars as simply as we walk the Earth. Until then, we continue to look upwards in hopes of a brighter future.
