In our daily lives, we usually don’t realize how strong gravity is unless we’re doing something that works against it, such as climbing a hill on a bicycle, going up stairs, or lifting a heavy object. But think about this: even the most powerful athlete can only jump about 70-80 cm at most. Falling from a height of just 1.5-2 meters can be fatal, or at the very least, we can break something. For elderly people, the situation is much worse. Back and joint pain, and fatigue – all are effects of gravity.

ESA (European Space Agency) astronaut Paolo Nespoli says: *“Gravity is a very, very strong force. We do not understand here on Earth how gravity has such a hold on our bodies and what is around us. You do feel it when you come back from space because you have been in a non-gravity environment for a long time and then you see all these forces grabbing you. You look at stuff and you feel your hands are heavy, you feel your watch weighs a ton, your books, the materials around you, your head is extremely heavy. It is really a very strong feeling.”*

In *The Expanse*, one of my favorite science fiction series, Earth and Mars are referred to as *“gravity wells,”* despite Mars having an average gravitational acceleration of 3.72076 m/s² (about 38% of Earth’s gravity).

Because of this extremely strong gravity, we need very powerful, massive rockets to send astronauts into space. The Saturn V rocket we used to go to the Moon during the Apollo program was unimaginably large.

I’ve often thought that Earth’s gravitational force is almost at the limit. If gravity were a bit stronger, the force required to break its chains would be so great that we might never have been able to reach space. The rockets we would need to build would require much more fuel, which would make them much larger and therefore much heavier, leading to an even greater need for fuel, and resulting in an unbreakable cycle.

## Aliens on Super-Earth Planets Could Be Trapped by Gravity

A super-Earth is an exoplanet with a mass larger than Earth’s but smaller than that of gas giants like Uranus and Neptune, typically ranging from 1.25 to 10 times Earth’s mass. These planets can vary in composition, potentially being rocky, having thick atmospheres, or even being covered in vast oceans. Super-Earths are of particular interest in the search for extraterrestrial life due to their potential to support atmospheres and liquid water. However, their stronger gravity could influence the development of life and planetary conditions. Many super-Earths have been found in the habitable zones of their stars, making them key targets for studying the potential for life beyond our solar system.

Super-Earths are believed by astronomers and astrophysicists to be capable of supporting alien life. So, the question arises: if humans can create spacecraft and go to space, then why can’t extraterrestrial beings do the same?

If intelligent life developed on a super-Earth planet, even if this life form were technologically advanced (at least as much as our own civilization, for example), they might never have been able to reach space due to the stronger gravity, which could create an unbreakable cycle as mentioned above.

Let’s assume that an intelligent civilization on Kepler-62e has reached the level of technology we achieved in the 1960s. And let’s also assume they have a moon that is at the same distance and size as ours. They want to build a rocket to go to this moon. How large would this rocket need to be? How much fuel would it need to carry?

Let’s go through the full calculation step by step to determine the escape velocity on Kepler-62e and how much more fuel a rocket would need to escape its gravity using the Tsiolkovsky rocket equation.

### Step 1: Escape Velocity Calculation

The escape velocity (v_{e}) from a planet’s surface is given by the formula:

Escape velocity from a planet’s surface

v)_{e}= √(2GM/R

Where:

- G is the universal gravitational constant: 6.674×10
^{−11}Nm^{2}/kg^{2} - M is the mass of the planet
- R is the radius of the planet

For Earth:

- M
_{Earth}= 5.972 x 10^{24}kg - R
_{Earth}= 6.371 x 10^{6}m - Earth’s escape velocity: v
_{e[Earth]}= √(2 x 6.674×10^{−11}x 5.972 x 10^{24}/ 6.371 x 10^{6}) ≈**11.2 km/s**

For Kepler-62e:

- Assuming Kepler-62e’s mass is about 4.5 times that of Earth: M
_{Kepler-62e}= 4.5 x 5.972 x 10^{24}kg = 2.6874 x 10^{25}kg - Kepler-62e’s radius is about 1.6 times that of Earth. R
_{Kepler-62e}= 1.6 x 6.371 x 10^{6}m = 1.194 x 10^{7}m - Kepler-62e’s escape velocity: v
_{e[Kepler-62e]}= √(2 x 6.674×10^{−11}x 2.6874 x 10^{25}/ 1.194 x 10^{7}) ≈**18.73 km/s**

### Step 2: Tsiolkovsky Rocket Equation

The Tsiolkovsky rocket equation is:

Tsiolkovsky Rocket Equation

Δv = v_{e}x ln(m_{0}/m_{f})

Where:

- Δv is the required change in velocity (in this case, escape velocity)
- v
_{e}is the effective exhaust velocity of the rocket - m
_{0}is the initial mass of the rocket (including fuel) - m
_{f}is the final mass of the rocket (after fuel is expended)

The Δv required for launch to orbit or escape can be approximated by the escape velocity for a simplified analysis. Thus, higher surface gravity (which relates to both M and R) means a higher Δv is required.

Now, looking at the Tsiolkovsky equation, we can rearrange it to express the mass ratio:

m_{0}/m_{f} = e^{Δv/ve}

This equation shows that the mass ratio (and thus the required fuel) grows exponentially with Δv. If Δv increases, the mass ratio m_{0}/m_{f} increases exponentially, meaning that for a slight increase in Δv, you need significantly more fuel.

### Step 3: Example – Earth vs. Kepler-62e Rocket Fuel Mass Comparison

The ratio of the fuel needed between Kepler-62e and Earth can be determined by comparing the two mass ratios. Specifically, since the fuel mass m_{fuel} is the difference between the initial mass m_{0} and the final mass m_{f} (i.e.,m_{fuel} = m_{0} – m_{f})

To keep things simple, we assumed the exhaust velocity of the rocket to be the same for both planets. We’ll use the same effective exhaust velocity **v _{e}=3.6 km/s** for the Saturn V moon rocket.

Mass Ratio on Earth:

m_{0}/m_{f} = e^{11.2/3.6} ≈ **22.4**

Mass Ratio on Kepler-62e:

m_{0}/m_{f} = e^{18.73/3.6} ≈ **181.3**

We can express m_{0} in terms of m_{f}:

m_{0} = m_{0}/m_{f} x m_{f}

Therefore, the fuel mass is:

m_{fuel} = m_{0} – m_{f} = m_{0}/m_{f} x m_{f} – m_{f} = (m_{0}/m_{f} – 1) x m_{f}

When comparing the fuel masses for two planets, we need the ratio of their fuel masses:

Fuel Ratio = m_{fuel, Kepler-62e} / m_{fuel, Earth}

Fuel Ratio = ((m_{0}/m_{f} – 1)_{Kepler-62e} x m_{f, Kepler-62e}) / ((m_{0}/m_{f} – 1)_{Earth} x m_{f, Earth})

**Fuel Ratio = (m _{0}/m_{f} – 1)_{Kepler-62e} / (m_{0}/m_{f} – 1)_{Earth}**

Using the mass ratios:

**Fuel Ratio** = (181.3 – 1) / (22.4 – 1) ≈ **8.43**

The fuel required for a rocket like the Saturn V to escape Kepler-62e is approximately **8.43 times greater** than the fuel needed to escape Earth. The Saturn V rocket carried approximately 2,582,100 kg (about 2,582 metric tons) of fuel in total. So, the equivalent of Saturn V on Kepler-62e should carry at least 21,766 metric tons of fuel!

This substantial increase further demonstrates the exponential impact of increased escape velocity on fuel requirements, making launches from high-gravity planets extremely challenging.

Let’s recalculate the required mass ratio and the fuel ratio for a hypothetical planet X with an escape velocity of 30 km/s.

Mass Ratio on Earth:

m_{0}/m_{f} = e^{11.2/3.6} ≈ **22.4**

Mass Ratio on Kepler-62e:

m_{0}/m_{f} = e^{30/3.6} ≈ **4,150.5**

**Fuel Ratio** = (**4,150.5** – 1) / (22.4 – 1) ≈ **194.0**

For a planet with an escape velocity of 30 km/s, the fuel required for a rocket like the Saturn V to escape is approximately **194 times greater** than the fuel needed to escape Earth. It should carry a whopping **500,908 metric tons** of fuel!

This shows just how extreme the fuel requirements become as the escape velocity increases, which would make launching from such a planet vastly more challenging than from Earth.

**Conclusion:** The reason the fuel mass for a given payload is an exponential function of planetary surface gravity is due to the exponential nature of the Tsiolkovsky Rocket Equation, where even small increases in the required Δv (which depends on planetary surface gravity) lead to significantly larger fuel requirements. This makes launches from high-gravity planets dramatically more challenging compared to those from planets with lower gravity.

So while it is certainly possible that aliens could exist on super-Earth planets, for example, Kepler-62e, their larger size and stronger gravitational forces could make it more challenging for them to explore space beyond their own planet.

As the mass and surface gravity (and consequently the escape velocity) of a super-Earth increase, the size of the rocket and the amount of fuel it needs to carry will also increase significantly, making space travel very likely no longer an option for the intelligent beings living on this planet. Or, they would require other means to leave the planet, such as nuclear propulsion.

This means that civilizations living on such planets would not have access to technologies like satellite TV, the International Space Station, GPS, a moon landing, or the Hubble Space Telescope. At least, not as early as we did.

## Sources

- Kepler-62e on Wikipedia
- Kepler-62e on the NASA website
- “Kepler-62e: Super-Earth & Possible Water World” on Space.com
- No Way Out? Aliens on ‘Super-Earth’ Planets May Be Trapped by Gravity on Space.com
- Could space aliens on hefty super-Earths be trapped by their own gravity? on the NBC News website
- What if aliens can’t reach Earth because they’re trapped in their worlds? on the European Commission Community Research and Development Information Service (CORDIS)
- Study: Spaceflight from Super-Earths is difficult [arxiv.org]
- Tsiolkovsky rocket equation on Wikipedia

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