Analemma Tower, a skyscraper offering a view over the cosmos. Orbital mechanics

Designed by the US-based Clouds Architecture Office, this futuristic project is bound to blow your mind.

It proposes a new way of living without ever setting foot on the ground, a concept so revolutionary that even birds might find it unsettling (Fig. 1). The plan involves hanging a skyscraper from an asteroid orbiting Earth. The asteroid will provide a permanent mobile base, supporting the building from space, rather than from the ground, as traditionally done.  The skyscraper will stretch from above the Earth's surface to well beyond the atmosphere (Fig. 2), effectively 'scraping' the air with its base and the vacuum with its top.

Fig. 1. Analemma Tower hangs over New York. Source: Clouds Architecture Office (modified)  

Although not feasible with today's technology, the project is grounded in real physics and highlights an important subject of future space constructions. Whether we will ever want to live above the Earth, we are already working there, keeping the International Space Station (ISS) continuously occupied. The design relies on the principles of orbital mechanics, a highly counterintuitive branch of physics. Our life experiences shape our intuition, and for now, only a small number of people have had the opportunity to experience orbital motion. The Analemma Tower design presents an excellent opportunity to explore the workings of orbital mechanics while providing a realistic depiction of what the future may hold.

Fig. 2. Analemma Tower projects well above the Earth's atmosphere. Source: Clouds Architecture Office

What's in the name? The name Analemma Tower was selected to reflect the asteroid's orbit, which is the key factor influencing the skyscraper's design. To keep the skyscraper permanently above a localised area on the ground, the asteroid must be in a geosynchronous orbit, which has an orbital period of 24 hours matching Earth's rotation. If the orbit were equatorial, the skyscraper would stay above a fixed point on the equator. However, the project designers wanted it to hover over New York, where they reside. Consequently, the asteroid's orbit had to be tilted to align with New York's latitude, causing the tower to trace the Analemma pattern (Fig. 3), which inspired its name.

Fig. 3. An Analemma pattern, drawn by the Sun, occurs due to the 23.5-degree tilt of Earth's axis as it rotates around the Sun. By Jfishburn at English Wikipedia, CC BY-SA 3.0.

Significance of the geosynchronous orbit. The geosynchronous orbit is located at an altitude of about 22,236 miles (35,786 km). Although this altitude poses extraordinary design challenges, requiring the length of cable and tower to match this height (Fig. 4), the choice of a geosynchronous orbit is a necessity. In this orbit, the entire structure, including the asteroid, cable, and tower, would move in sync with Earth's rotation. This alignment ensures that the lower part of the tower moves in tandem with the Earth's atmosphere, significantly reducing atmospheric drag and structural oscillations. A non-synchronous orbit would result in the tower being continuously dragged through the atmosphere at high speed, eventually causing it to be torn apart.

Fig. 4. Analemma Tower is an enormous, self-sustaining complex designed to accommodate all aspects of daily life, including living spaces, offices, farming areas, leisure activities, shops, religious services, and funeral arrangements. Source: Clouds Architecture Office (modified)

Why was the asteroid chosen as an anchor? The altitude of a geosynchronous orbit must align with the center of mass of the entire orbiting structure, which includes the anchor, the cable, and the tower. For the orbit to remain stable, the center of mass must be within the anchor's body, which requires the anchor's mass to be significantly greater than the combined mass of the cable and tower. Given the tower's size, a massive rocky asteroid seems to be the most suitable choice. A sufficiently large asteroid will absorb the cable stresses caused by activities within the tower and winds affecting its lower part.

The orbital mechanics underlying the project. In orbital motion, there is an ongoing battle between orbital velocity and gravity. When velocity wins, an object moves higher. When gravity takes over, it pulls an object down. Gravity varies with altitude, being strongest at the Earth's surface and diminishing with distance from Earth. In a stable orbit, velocity perfectly counterbalances Earth's gravitational pull at that specific altitude, allowing a satellite to maintain a permanent distance from Earth. This explains why all satellites, including our natural satellite, the Moon, stay in their orbits without falling to Earth.

Fig. 5. The International Space Station (ISS) maintains a stable altitude of 250 miles (400 km) because its orbital velocity of 7.67 km/s (4.75 miles per second) precisely offsets the gravitational field strength of 0.9 g.

As altitude increases, gravity decreases, necessitating a slower orbital speed. On the other hand, a lower orbit demands a faster speed to counterbalance stronger gravity. Therefore, whether an object rises, falls, or remains at the same distance from Earth depends on how its orbital velocity compares to the velocity required at that altitude. For example, the International Space Station (ISS) orbits Earth at an altitude of about 250 miles (400 km), where gravity is 90% of its strength at Earth's surface (Fig.5). The station maintains a stable orbit because its speed of 17,100 mph (27,600 km/h) precisely balances the gravitational force at that altitude.

How does an asteroid support the Tower? An asteroid acts as a counterweight to support the tower, pulling the tower outwards while gravity pulls it downwards. This outward pull is due to centrifugal force, created by the asteroid's circular motion, much like how clothes in a centrifuge are drawn away from its center. But why isn't the entire structure, including the asteroid, cable, and tower, drawn away from Earth, given that all its components rotate together, completing one revolution every 24 hours? This is because, despite having the same orbital period, the structure's components experience different gravitational forces and move at varying orbital velocities. Consequently, they balance speed and gravity differently.

The structure will extend vertically for thousands of miles, encountering significant variations in the gravitational field (Fig. 6). At the top, the structure will experience only around 2% of the gravity felt at the bottom. As gravity decreases with altitude, the orbital speed increases. The structure orbits Earth while staying aligned with Earth's radial gravity vector. Consequently, the top of the asteroid must move significantly faster than the base of the tower to traverse a longer distance (tinted red) within the same time frame.

Fig. 6. The various elements of the structure, comprising an asteroid, a cable, and the Analemma Tower, orbit Earth at varying speeds (red-tint). The geosynchronous altitude aligns with the structure's center of mass.

The system's component responsible for maintaining geosynchronous altitude and speed is the system's center of mass (COM), situated within the asteroid's body. The COM must travel at a speed of approximately 7,000 mph (11,300 km/h) to accurately counteract the gravity at that altitude, which is only about 2.3% of Earth's surface gravity. Above the COM, gravity weakens, requiring a slower orbital speed, whereas below the COM, gravity intensifies, demanding a faster speed. However, due to the circular motion, the speed changes in the opposite direction, increasing towards the top and decreasing towards the bottom. Consequently, centrifugal force will dominate above the COM, pulling the asteroid upwards. The upward pull will offset the downward pull on the cable and tower, where gravity exceeds centrifugal force below the COM. This tag of war between the centrifugal and gravitational forces will generate significant tension in the cable, maintaining the entire structure taut and balanced.

How would your weight change on different floors? If the Analemma Tower's base were close to the ground, its orbital speed would align with Earth's rotational speed, while experiencing the same gravitational strength of g = 9.8 m/s². Therefore, your weight would be the same as on the ground, making you feel as if you are in a conventional, ground-based skyscraper. Even on the 50th floor, your weight would barely change because this altitude has a negligible effect on gravitational strength and tangential speed. This is because the radial lines diverge from the center of the Earth, necessitating an altitude to be compared to the Earth's radius of about 6,400 km (4,000 mi).

If the tower's top were near the asteroid, its orbital speed would nearly match that of the asteroid, while experiencing almost the same gravitational strength of 0.023 g. The asteroid's orbital speed is designed to negate the gravitational pull at its altitude, creating a microgravity environment where you feel weightless, much like astronauts on the ISS. The project doesn't specify the tower's length for precise calculations. After all, the Analemma Tower is more of a conceptual idea than a practical proposition. The considerations provided offer a basic understanding of how your weight would change throughout the tower, making you feel grounded on the lower floors and practically levitating on the upper floors.

Advantages of space support over ground foundations. The project is currently unfeasible due to the lack of superstrong materials capable of withstanding the enormous tensile and shear forces affecting a cable and a skyscraper as tall as the Earth's diameter. Still, the idea of supporting such a structure from space is theoretically more achievable than constructing it from the ground up. Structures built on Earth experience compression at their base, which materials handle less effectively than the tension from hanging. A skyscraper as tall as the Analemma Tower would be crushed by its weight because the stress at its base would exceed the strength of even hypothetical materials.

So, as surprising as it may be, the concept of suspending a super-tall skyscraper from space is technically more realistic than supporting it from the ground. As we progress in space exploration, this seemingly science fiction concept could offer an alternative for establishing settlements above the inhospitable planets.  Depending on a planet's characteristics, the settlements could be positioned at a lower altitude, reducing the length of the suspended structure and easing the material and engineering requirements. For example, if Earth rotated 16 times faster, the geosynchronous orbit would be around 190 miles (300 km) high, which is just below the ISS orbit. This would dramatically reduce the length of the Analemma Tower, cutting construction challenges by 90%. While this faster rotation would largely resolve the Analemma project's problems, it would also cause chaos on our planet! However, we'll reserve this topic for another discussion.