I recently bought a subscription to Amazon’s ‘Prime’ Services, which along with offering lucrative deals on their products, granted me unlimited access to their ‘Prime Videos’. And to my delight, one of the films it featured was Christopher Nolan’s 2014 Sci-Fi endeavour, Interstellar. So as anyone in my place would, I sat down that night to re-watch what I consider to be the greatest space adventure movie of all time. Those of you who have watched it must be familiar with the premise; the earth is no longer habitable for humanity, and alternate planets must be located in another galaxy which may prove to be future homes for it. Skipping details not relevant to this article, a significant portion of the film revolves around an equation referred to as the gravity equation, which when solved could fix the ever-persisting ‘gravity problem’.
In my previous one hundred viewings of the movie, I never really understood what this problem was and perhaps didn’t dwell much on it either. The objective of this problem was to create a way to move humans off the earth and into space, but that confused me because people have been going to space for decades now; the film itself is an epic journey through the cosmos. So I finally decided to do a little research on this and in my studies came across a very momentous equation, known as the rocket equation, credited to the Soviet rocket scientist Konstantin Tsiolkovsky.
Tsiolkovsky’s rocket equation is the governing equation for the behaviour of rockets or rocket-like machines and is fundamentally a reimagining of the classic conservation of momentum theory. In a crude sense, a rocket attains motion by expelling material out from a ‘nozzle’ at very high velocities (creating thrust), which in turn causes it to move forward. This process is controlled by the rocket equation, which has three main variables. The first is the change in velocity ∆v, and it defines the energy expenditure against gravity. This value is specified by where in space you want to go and is fixed for any particular journey. Ironically, travelling from the surface of the earth to earth orbit is one of the most energy-intensive steps in any journey. Simply getting into an orbit about 400 kilometres off the surface requires half of the total energy to reach Mars.
The second variable is the effective exhaust velocity vₑ, which specifies the available expendable energy. This parameter is decided by the type of rocket propellant (fuel) used. There are many classes of these propellants, each providing different energy payments, but they all utilize chemical combustion reactions. Though these reactions provide a limited amount of energy, certain propellants are better than others and the hydrogen-oxygen combination is currently one of the best options.
With the knowledge of these two variables, we can calculate the last variable in the equation, the rocket mass fraction mₒ/mᵣ. This is the ratio of the total mass of the rocket as it prepares to leave earth (including the propellant), to its mass after all of the propellants have been exhausted. This value dictates how much of the rocket’s mass must consist of just propellant, and this is a very large number. The mass percentage of the propellant in the rocket typically ranges from 85-90% (meaning 90% of a rocket is just fuel), making them incredibly hard to fabricate and maintain. (These numbers make rockets structurally more similar to an explosive rather than another vehicle.) More importantly, this leaves very little scope to put any significant payloads out into space. With the current technology, after accommodating engines, tanks and various other mechanical structures, a mere 1-5% of the rocket’s mass remains as payload.
(Trivia: The Saturn-V rocket that carried Neil Armstrong to the moon boasted a payload of just 4%)
The standard mathematical description of the rocket equation:
∆v = vₑ ln(mₒ.mᵣ)
Getting back to Interstellar, this lack of payload was at the heart of the problem tackled by the movie. The scientists in the film wanted to create a means to evacuate the planet, and that meant carrying every single human being out into space, at the very least. But as described earlier, the current equation sets very stringent boundaries on our capacity to escape earth’s gravity, requiring huge rockets and vast amounts of energy to fling just a few people into outer space at a time. Considering this, it would be impossible to uproot an entire species off the surface, and that’s where the ‘gravity equation’ mentioned at the beginning comes in (this may be linked to what we refer to as ‘the theory of everything’). The objective was to devise a new theory to launch rockets without being constrained by the existing equation, instead functioning in accordance with the gravity equation. Here is where the element of fiction steps in.
Interstellar offers a speculative but nonetheless intriguing solution to this problem. It claims that quantum data stored in the singularity of black holes could provide the observational statistics required to manipulate gravity in a way that could greatly assist mankind’s quest to explore the Cosmos. The data led to the development of the theory of quantum gravity in 5 spatial dimensions, and the recurrence of gravitational anomalies throughout the movie was attributed to the presence of bulk (higher dimension) fields. The equation was a mathematical description of the bulk fields and described how they might generate the anomalies. Its solution, which was the quantum gravity theory, provided a way to control these anomalies and use them to vary the value of what had thus far been considered to be a constant – the gravitational constant G.
While it is not specifically mentioned in the movie, the solution may have paved way to an anti-gravity drive, where gravity itself would act as the propellant. Use of the drive presumably destroyed the Earth, but it allowed everyone to leave and eventually create the ‘Cooper Station’ showed at the end of the movie. With such a high degree of control over gravity, it would even be possible to synthesise wormholes that bend space-time to create shortcuts through the universe.
Though the above paragraph suggests technologies that are perhaps not within reach or even theoretically feasible as of now, there may be some ways to loosen the reins of our rocket equation within the realms of realistic possibility. The chemical combustion rockets pose difficulties such as insignificant payloads, lack of reusability, enormous costs and risk hazards. As mentioned, the hydrogen-oxygen combustion provides a decent exhaust velocity, but by using something lighter, such as just hydrogen, the velocity output could be doubled which would, in turn, affect the payload by a factor of up to 10. In the past, the use of nuclear thermal energy has been suggested to heat a hydrogen propellant. A newer technology considers the use of ground-based microwave powered beams to heat the propellant to temperatures of about 1800 Celsius. This technology is already in use to power Unmanned Aerial Vehicles (UAVs) and can find its way to rocket propulsion as well.
Another proposition is to include the moon in our future space endeavours. With its weaker gravity, launching rockets with large payloads from the lunar surface to space would be exponentially easier, for the same amount of energy supplied. Extracting and producing useful products from raw materials available on the moon could relieve us from dragging everything needed in space from the bottom of Earth’s deep gravity well. For example, the ice (water) that is present on the moon could be a vital source of the hydrogen-based fuel propellant. Furthermore, mining near earth asteroids can provide more materials that can be used in manufacturing rockets.
A lunar colony could become the base camp to launch rockets to other destinations across the solar system. The starting costs of creating a sustainable platform capable of building and launching its own rockets would be quite high, but with time it would prove to be very beneficial, considering the thousands of launches it could implement in the future.
The need for new places to live and access to more resources will eventually beckon humanity off the Earth. Having the means to successfully leave the planet without being held back by the rocket equation is of paramount importance, and a hydrogen-based lunar rocket platform could drastically improve our ability as a species to travel out into interstellar space and explore the universe. And who knows, maybe one day in the not so far future we’ll find ourselves peering into black holes, or making astronomical leaps through our very own wormholes.