Rocket equation 101: The Moon as a launch platform
Earth alone cannot power our future in space, and other realizations from the rocket equation.
When dabbling with the laws of motion in the 17th century, Isaac Newton first realized that it’s indeed possible to send an object out of Earth, into space. As long as an object is shot away from Earth with a high enough velocity, it will reach space and orbit our planet.
With the launch of the Sputnik satellite in 1957 onboard a powerful rocket, the Soviet Union achieved exactly that. For the first time in four billion years of life on Earth, something was intentionally sent to space.
Give a satellite another speed boost, by either launching it on a more powerful rocket or using thrusters onboard, and it can escape from Earth’s gravitational hold completely. That’s how you can send missions to Venus, Mars, Saturn and beyond. But one of these two things is not like the other.
Enter the Tsiolkovsky rocket equation.
The rocket equation is what allows scientists and engineers to quantify and compare the energy required to reach various destinations in space. Its implications are far-reaching but not intuitive so I shall attempt to explain them without use of any math.
Getting to space
The rocket equation tells us that the amount of energy a rocket must expend to go from the Earth’s surface to an orbit 250 kilometers above, called low Earth orbit, is almost thrice as much as going from that low Earth orbit to the Moon! Likewise, getting to low Earth orbit costs twice as much energy than what is required to reach Mars from that same orbit.1
Even if we include the energy expenditure to land on the Moon instead of just reaching it from low Earth orbit, getting to Earth orbit itself turns out to be about 50% more expensive. In other words, attaining Earth orbit is the first and the most significant barrier to space exploration.
The giant leap for humanity was not stepping on the Moon but getting to Earth orbit.
The rocket equation doesn’t just dictate how much energy you must spend to reach various destinations in space but also if you can reach space at all.
The satellite is but a small fraction of the total mass of the rocket that lifts it and yet has an effect on the rocket itself. Therein lies the core problem of rocket science.
Increasing the satellite’s mass, to make it more useful perhaps, also means more rocket fuel is required to put the satellite in the desired orbit. But more fuel makes the system weigh more. This means some more fuel is required to launch the now-heavier system into space. As a rule of thumb, fuel requirements increase exponentially with every step increase in mass added to the satellite.
This is how we end up with rockets being mostly fuel and then some metal. Even the mighty Saturn V that sent astronauts to the Moon was 85% fuel, 13% rocket—including the rocket body, its plumbing and parts—and the rest 2% being the Moonbound spacecraft with astronauts sitting inside!
At this point, if we were to make Earth more massive, a rocket would have to expend an enormous amount of energy against a more gruesome gravity well. More fuel would be required to get to space, and your rocket might be something akin to 9 times more fuel than metal. Increase Earth’s mass further and the fuel-to-mass ratio would start skyrocketing to a point where it’s simply not possible to engineer such a near-all-fuel rocket!
Crunching the numbers in this manner, it turns out that if the Earth was 50% more massive, you simply wouldn’t be able to get to space even with the most energetic fuel combination—liquid hydrogen and liquid oxygen—available in chemical rockets.
Such a massive rocky planet is not imaginary, several of its kind exist. Of the over 4,000 planets around other stars we’ve discovered to date in our galaxy, about a thousand are something scientists call ‘Super Earths’. These are planets which are up to 10 times more massive than Earth and up to twice as large. Beyond that limit, planets don’t remain rocky and start turning into Uranus- or Neptune-like gas giants.
Many of these Super Earths lie in the respective habitable zones around their stars i.e. conditions there could support life as we know it. Given that we’ve only searched a small fraction of our galaxy for planets, it’s fair to say there could be millions of Super Earths, many of which could host life.
If intelligent life were to develop on these Super Earths, they’d have a hard time building rockets that get things off-planet. Since even the most energetic chemical rockets won’t get them to space, they’d be incentivized to build something with more thrust that can, like nuclear propulsion based rockets. These will likely be far more expensive than chemical rockets but sometimes nature doesn’t give you a choice.
Just like the rocket equation makes it exponentially harder to get off a planet with added mass to the planet, it also makes it exponentially easier to get off objects with lesser gravity. Now if only we had an object less massive than Earth that is accessible and resourceful.
In order for humanity to survive and thrive long term, it makes sense to have a permanent human settlement on Mars as it offers us a relatively benign environment. Doing so would require sending hundreds to thousands of tons of material from Earth to the martian surface via dozens to hundreds of huge rocket launches. That’s pretty much exactly what SpaceX’s Starship hopes to do. Here’s where our celestial neighbor, the Moon, can make things better.
The Moon has a much weaker gravity than Earth, allowing rockets to take off with ease. This was most notable during the Apollo missions, when even a spacecraft hosting two astronauts could make its way to lunar orbit. Moreover, the Moon lies at the outer edge of Earth’s gravity well, meaning it’s easy to escape our planet’s pull completely if launched from the Moon. Almost five times easier in fact.
If we establish a vast, permanent settlement on the Moon first, we can eventually tap into its resources to launch rockets from the Moon itself. NASA and ISRO missions have discovered plenty of water ice on the Moon’s poles. It’s possible that future human habitats built from mining the metal-rich lunar soil tap into this water ice for consumption needs. This water can also be split into hydrogen and oxygen for use as rocket fuel. Rockets taking off from an industrially enabled Moonbase can ride the lunar interplanetary highway to reach Mars more efficiently than from Earth.
Sure, it would be expensive to build an industrial Moonbase but if the goal is to expand sustainably into the solar system, we’re playing the game on the scale of hundreds to thousands of years. In this large scheme of things, the Moon can be the rocket platform to build and expand a sustainable Mars presence for much cheaper than an equivalent one done from Earth.
The Moon’s accessibility, low gravity barrier, and resource potential are the reason why its proponents vouch for a sustainable return to the Moon first rather than targeting Mars. As the saying within the lunar circles goes:
You can’t be a martian without being a lunatic.
Being a Moon-first guy myself, I even made a meme to that effect.
The belt and beyond
The Moon’s advantages may extend to making homes for ourselves in the outer solar system as well. The rocket equation tells us that even if objects in the outer reaches of the solar system may be closer to Mars than the Moon, the more massive red planet’s deeper gravity well means more energy is required to get out of it than to reach those destinations from there.
Getting to the asteroid belt from the Moon’s surface is at least 40% less energy demanding for a rocket than from Mars’ surface—even though Mars is about 75 million kilometers closer to the belt! This is the difference gravity makes, and which the rocket equation allows us to see. The Moon can accelerate expanding our settlements to these resource-rich asteroids. Some of these objects, like Ceres and Vesta, can in turn play the same role as the Moon can for Mars and the asteroid belt, and expand human settlements to moons of Jupiter and Saturn, and beyond.
This finally brings us to the single most important takeaway from the rocket equation. The ability to extract and harness raw materials from low-gravity, resourceful space objects would free us from the tyranny of dragging everything out of Earth’s gravitational pull.
We cannot hope to be traveling among the stars if we don’t even expand into the solar system in an Earth-independent way and avail for ourselves a much larger resource pool. In-space manufacturing and industrialization is not just a good-to-have but a fundamental requirement for expansion into the solar system. Only then humanity will be in an adequate position to venture to the nearest star and hopefully do it before the Sun doesn’t shine.
Thanks to Adithya K Pani for reviewing the article.
Republished by The Wire Science.
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Technically, energy expenditure is not the same as delta-v, which is the actual measure of work required by rockets to reach different destinations. But since energy expenditure is proportional to delta-v, they have been approximated to be the same to make the article tangible for the masses.