No launch zone: Is cosmonautics possible on super-Earths?

Mankind is exploring space thanks to chemical rockets. Yes, their efficiency leaves much to be desired: to put a conditional ton of cargo into Earth orbit, it is necessary to burn many tons of fuel. Nevertheless, they work. Rockets allow us to build satellite constellations and orbital stations, as well as to send probes to other planets. Thanks to them, humanity is laying the foundation for its future space expansion, which may already be using more advanced engines.

But what if we lived on a super-Earth? There are no analogs of such bodies in the Solar System, but they appear to be among the most (and possibly the most) common types of exoplanets in the Milky Way. Super-Earths are larger than our planet and have more gravity. This raises a logical question: if a man-made civilization arose on such a body, would it be able to explore space with rockets? Or will it be “trapped” in its home world?

In this article, we will consider how the required launch thrust of a large rocket (1300 tons in mass) will vary depending on the gravity of the planet. As an example, we will take four bodies: Earth, Mars, the exoplanet K2-18 b, in whose atmosphere traces of biosignatures have recently been found, and a hypothetical super-Earth whose gravity is 3.6 times greater than Earth’s. Let’s calculate how much thrust in meganewtons (MN) a rocket must develop to lift off from the surface at different thrust-to-weight (T/W) ratios.

Thrust-to-weight ratio (T/W): what it is and why it matters

Before we move on to specific planets, let’s define the concept of thrust-to-weight ratio, which is denoted as T/W. This is the ratio of the thrust of the engines to the weight of the rocket. Weight is the force with which gravity attracts the rocket (on Earth, it is determined by the formula weight = mass × 9.81 m/s2). If T/W = 1, it means that thrust is equal to weight – the rocket only balances gravity and can only hover above the launch pad.

The red arrow is the thrust of the engine, and the blue downward arrow is the weight of the rocket. When the thrust becomes slightly greater than the weight, the rocket starts to rise. Image: Schoolphysics

For the rocket to start rising, T/W must be slightly greater than 1 (to create a non-zero upward accelerating force). For example, with T/W = 1.1, the thrust is 10% higher than the weight, which is enough for a slow start. Larger T/W values (1.3-1.5 or more) mean more powerful engines relative to weight – the rocket takes off faster, losing less fuel to overcome gravity. In practice, most orbital rockets are launched with a T/W in the range of ~1.2-1.5. For example, the legendary Saturn 5 had a T/W of about 1.15 at launch, while the modern heavy launch vehicle SpaceX Starship (in full configuration with a Super Heavy stage) will have a relatively high T/W of ~1.5.

The first Saturn 5 rocket (AS-501) on the launch pad, before the launch of Apollo 4. Image: NASA

Starship’s powerful first stage generates about 73.5 MN of thrust to lift the entire system weighing ~5000 tons. Thus, the T/W ratio determines how much thrust the engines have to lift a particular rocket off a particular planet. Let’s look at how this works for a 1300-ton rocket on different worlds.

Gravity and the required launch thrust: Mars, Earth, and K2-18 b

The planet’s gravitational field significantly affects the requirements for a launch vehicle. The greater the acceleration g, the greater the launch thrust required to lift off from the surface. Let’s look at four cases – Mars, Earth, exoplanet K2-18 b, and a hypothetical “super-Earth” – for the same 1300-ton rocket and see how the required thrust changes:

Mars (g ≈ 3.7 m/s2). Mars has about 2.6 times less gravity than the Earth. A 1300-ton rocket there weighs only ~4.8 MN. So, to start the ascent with T/W=1.0, ~4.8 MN of thrust is enough. For a reliable launch with T/W≈1.3, ~6-7 MN of thrust will be needed – several modern engines can provide such thrust. It is not surprising that a rocket with Raptor engines will be able to take off from Mars without a first stage.

Mars. Source: CU/LASP EMM/EXI ITF/Kevin M. Gill

Earth (g ≈ 9.8 m/s2). On Earth, a 1300-ton rocket weighs ~12.8 MN. The minimum thrust for takeoff is the same ~12.8 MN (at T/W = 1.0). But in practice, a margin is needed. For example, if you set the starting T/W to ≈1.5, the required thrust increases to ~19 MN. This is more than 6 Raptor engines can provide, so a powerful first stage is needed to launch from Earth. The 33 Super Heavy engines provide ~75 MN of thrust, which corresponds to a T/W of ≈1.5 for the entire system at launch. Excess thrust allows for rapid climb, reducing gravity losses.

Exoplanet K2-18 b (g ≈ 12.4 m/s2). This is a so-called super-Earth, a planet near the star K2-18, which has recently been discussed a lot in connection with possible biosignatures. According to the JWST telescope, methane and carbon dioxide were detected in the atmosphere of K2-18 b, as well as possible traces of dimethyl sulfide (DMS), a gas produced by living organisms on Earth. This has revived interest in this exoplanet as potentially habitable. The parameters of K2-18 b are known quite well: a radius of about 2.6 R⊕ (2.6 Earth radii) and a mass of ~8.6 M⊕. It is denser than water, but lighter than rocky Earth – possibly having a thick atmosphere with hydrogen and an ocean beneath it (the so-called Hypocene world). Astronomers assume that this world has no solid surface at all. In this case, even if intelligent life were to emerge there, it is quite difficult to imagine that it would be able to create a technogenic civilization. But for the sake of our thought experiment, let’s assume that K2-18 b does have a solid surface from which to launch rockets.

The surface gravity acceleration of K2-18 b is estimated to be ≈12.4 m/s2, i.e., ~1.27g. This is somewhat greater than Earth’s gravity, so a 1300-ton K2-18 b would weigh ~16 MN. The minimum thrust for launching there is at least 16 MN (T/W=1.0), and for a steady takeoff, all ~20 MN are needed (at T/W≈1.25). If we were to transfer a rocket to this exoplanet, it would need about 25-30% more thrust than on Earth to lift the same cargo.

K2-18b in the artist’s imagination. Source: University of Cambridge

However, the main problem with heavy planets is not only the higher weight of the rocket, but also the much higher orbital velocity. For K2-18 b, due to its larger radius and mass, the first space velocity (horizontal velocity in low orbit) is estimated to be about 14.2 km/s. Taking into account gravitational and aerodynamic losses, the rocket must reach ~17-18 km/s to reach orbit. This is almost twice as much as is required on Earth (~9.3 km/s orbital + losses of ~1 km/s). Such a huge Δv puts a chemical rocket at an extreme disadvantage. With the growth of the required Δv, the share of payloads rapidly decreases. While on Earth, modern multi-stage rockets launch an average of ~3-5% of their launch mass into orbit (about 4% is typical), on K2-18 b, the theoretical specific return would be less than half a percent. Calculations show that a rocket weighing 250-500 tons is needed to deliver 1 ton of cargo to K2-18 b orbit! In other words, the mass ratio (the ratio of the launch mass to the mass after fuel burnout) must be huge. For comparison, on Earth, ~25 tons of rocket is enough for 1 ton of cargo (for example, a Falcon 9 weighing ~550 tons launches ~22 tons), and K2-18 b would need ten times as much. Even the giant 5000-ton Starship would be able to lift only about 5-10 tons from this planet to low orbit.

Starship launch. Source: SpaceX

So even a seemingly not-so-great 27% increase in gravity would present designers with a very serious challenge. In a world like K2-18 b, Earth-based launch vehicles would be extremely inefficient. Yes, they would be able to put some small payloads into orbit. But building something like the ISS, or a GPS, or launching interplanetary probes would require the use of far more resources than on Earth. And while on our planet, designers were able to start with relatively small rockets and increase their size later, the potential inhabitants of K2-18 b will not have that luxury. They will have to start immediately with heavy and super-heavy carriers.

All of this raises some very interesting questions about what direction engineering would have taken in such worlds. Perhaps the designers of space technology would not have considered chemical rockets in principle, but would have focused on alternative systems like nuclear pulse engines. Or they would simply abandon the idea of space exploration as too complex and not worth the resources invested.

Graph of thrust versus T/W for different planets

The graph shows how much launch thrust (Y-axis, in meganewtons) a 1300-ton rocket requires depending on the thrust-to-weight ratio T/W (X-axis). Four cases with different gravity accelerations are shown: Mars (3.7 m/s2), Earth (9.8 m/s2), K2-18 b (≈12.4 m/s2), and a hypothetical super-Earth (35.3 m/s2). The gray dashed line marks the conditional threshold of g = 40 (m/s2), the so-called “no launch zone” beyond which chemical rockets are no longer able to reach orbit.

The dots represent the calculated values for T/W = 1.0, 1.2, 1.4, 1.6, and 2. It is noticeable that for each planet, the dependence is linear (thrust is directly proportional to T/W). The line for the super-Earth is the highest – even at T/W=1, it requires ~45 MN of thrust, while the Earth is ~12.8 MN, and Mars is only ~4.8 MN. Higher T/W simultaneously raises the requirements for all three cases, but the gap between the curves is huge: at T/W=1.5, the Earth rocket needs ~19 MN, the Martian rocket ~7 MN.

The limit of chemical missile capabilities: A “no launch zone” on super-Earths

As can be seen from the graph, a hypothetical superheavy planet with a gravitational acceleration of about 3.6g (≈35 m/s2) requires enormous thrust – tens of meganewtons even with a moderate T/W. But providing a large initial T/W is only half the problem. The other half is to achieve orbital velocity, which on massive planets can exceed the capabilities of chemical engines. The fact is that a chemical rocket is limited by the specific impulse of the propellant, I_sp, and the proportion of mass that is propellant. The Tsiolkovsky equation (rocket equation) relates the maximum change in velocity Δv to the rocket parameters:

where g_0 = 9.81 m/s^2 is the standard earth acceleration, m_0 and m_f are the masses of the rocket before and after fuel exhaustion. This equation shows that even an ideal chemical-fueled multi-stage rocket has a practical ceiling on its capabilities. According to optimistic estimates, the Δv limit for chemical systems is somewhere around 13-15 km/s. The maximum achieved by mankind – ~17 km/s (New Horizons mission to the third space station) – was realized through multiple accelerations in space and gravity maneuvers, but not a direct vertical launch. If, for example, >20 km/s is required to enter the planet’s orbit, conventional chemical rockets are no longer able to achieve this. According to engineers, if the orbital velocity exceeds ~30 km/s, then using chemical propellants will not work.

Accordingly, it is possible to introduce the concept of a conditional limit beyond which a launch with a traditional rocket becomes impossible – a kind of “no launch zone”. The most convenient way to characterize this limit is with a gravitational parameter. For rocky planets like the Earth, the surface gravity is critical at about ≈4g (about 40 m/s2). Conventionally, if a planet has g > 40 m/s^2, no modern chemical rocket will be able to launch a payload into the orbit of such a planet, even with an ideal multi-stage configuration.

The artist’s idea of a super-Earth. Source: NASA

Our scenario with a 3.6g super-Earth (pink curve in the graph) almost reaches this limit. At g=3.6g, the orbital velocity is estimated to be ~21-22 km/s, which exceeds the threshold of ~13-15 km/s for chemical fuels. On such a planet, Tsiolkovsky’s law prohibits astronautics – to reach space, we would have to look for alternative approaches (e.g., nuclear or other high-energy engines, space elevators, etc.). In other words, too much gravity can condemn a civilization on the planet to gravitational isolation: without access to orbit and beyond, despite any level of technology development, but using only chemical jet engines.

The solution to the Fermi paradox?

To summarize, we note that the Earth, with its moderate gravity of ~1g, is a rather “lucky” planet for the development of astronautics – our chemical rockets were able to successfully overcome its gravitational barrier and allow us to explore space. Mars, with its much lower gravity, is even easier to fly into space, which will make it much easier for mankind when it gets there.

The Earth’s gravity allows us to build large structures like the ISS in orbit. Source: NASA

But the inhabitants of a notional super-Earth with a gravity several times stronger than Earth’s will not be so envious in this respect. They will have to look for engineering solutions beyond the usual rockets, be it giant multi-stage carriers or revolutionary technologies like a space elevator or nuclear pulse engines. Thus, the planet’s gravity sets the bar clear for space dreams: the higher the bar, the more powerful (and sometimes fantastic) the means must be to overcome it.

Some researchers even admit that this is one of the possible explanations for the so-called Fermi paradox. We live on a planet whose gravity allows space travel, and therefore we actively fantasize about meeting with alien intelligence and look for traces of its activity, from radio transmissions to traces of astronomical structures like the Dyson sphere.

A hypothetical Dyson sphere. Screenshot from the game Dyson Sphere Program

But what about the inhabitants of a planet “locked in” by its gravity and knowing that they could not leave its confines? In such a world, there would be no “one small step”, no satellite TV, no GPS, no space telescopes – let alone any astro facilities. Would its inhabitants send signals into space, knowing that they would never even get beyond the atmosphere? Will they try to look for traces of their brothers in intelligence? Will they be interested in studying the sky, or will it be considered a pointless endeavor?

So far we have no answers to these questions. But who knows, maybe they really hide one of the reasons for the great silence of the Universe?

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