Mobius Bridge is a mega-construction structure for the 31st century, built above the Earth's equator Mobius Bridge would be ring structure serving as a habitat platform. Unlike many space rings proposed in science fiction works like Larry Niven's Ringworld the Mobius Bridge would not use centripetal force to provide the source of gravity, instead the Earth's gravity well would provide the attraction force. For the Earth to provide the pull of gravity more naturally to the body of the Mobius Bridge, the structure of the Bridge would need to orbit around the Earth with the same angular velocity as the Earth's natural rotation.
Traditional approaches to placing objects in Earth Orbit would make it impossible for a space based structure to provide a gravity force not provided by some kind of additional acceleration put on a selected object. The design of the Mobius Bridge would require some unique solutions to keep the ring structure both in orbit and having objects placed on the Bridge still feeling the downward tug of gravity. Several potential solutions could be considered for keeping the Bridge suspended. The first potential solution considered would involve using a collection of tethers linking up with counterweights, similar to the solutions suggested for building a space elevator.
For a sufficiently low mass bridge designs a massive collection of thrusters would provide the necessary counter forces to keep the Bridge in orbit. Unfortunately by the time the station got big enough to allow for a proper habitat the energy requirements to keep it suspended in space would only make sense for a species with near god like levels of energy production and control. The most likely solution for keeping the Mobius Bridge in orbit would be to have the structure be made from two primary components. The habitat segments of the Bridge would lazily drift over the Earth's equator maintaining the same day night cycle as the ground below. Within the frame of the habitat would be one or more massive magnetic orbiting rings. Each of these orbiting rings would serve as a track-way for the habitat structure to ride on, similar to magnetic levitation trains here on Earth. The dynamic interaction of the forces between the inner rings and the habitat ring create a situation where the net balance leaves residents of the habitat ring experiencing the slightly reduced pull of the Earth's gravity, several hundred kilometers above the ground.
Roughly speaking the force of gravity on the Bridge would be a result of the tangential velocity of the ring and its distance from the center of the Earth. (for those who aren't power nerds, this means you are accounting for the tendency of objects being spun to pull outwards and that the force of gravity gets weaker at a distance) To make the calculations easier, the primary sources of accelerations can be separated into two primary equations. The biggest impact on the gravity felt by objects in the habitat ring of the Bridge would be the distance between the bridge and the Earth. The force of gravity between two objects can be calculated using Newton's Law of Universal Gravitation, (see Fig 1)
In this equation the variables are defined as follows
F is the force of gravitational attraction.
G sub c is the gravitational constant (Fig 1A).
M1 and M2 are the respective masses of the objects being analyzed.
r is the distance between the center of mass of the objects
While the above form is the most universal form of the Law of Gravitation for cases where M1 is much larger than M2 a slightly different version is used, where only the mass of the major body really needs to be considered.
Where g represents the rate of acceleration between the two objects, Gsubc is still the same and MEarth is the mass of the Earth, which is roughly 5.9736E+24kg and r represents the distance from the center of mass of the Earth to the center of mass to the object. On the surface of the Earth r averages roughly 6370 km, for the Mobius Bridge that value will most likely fall between 6500 km and 6900+ kilometers from the Earth's center.
For the station being built at 130 km above the Earth's surface, or just 30 km above the line that defines what is legally space, the force of gravity would work out to be roughly 9.44 m/s^2. At 530 km above the average surface of the Earth, gravity would still be an acceptable 8.37 m/s^2. (note that these values don't yet factor in the centripetal force)
Another consideration for making the Mobius Bridge would the trade off of habitable surface area vs how much of the sky would be blocked out by the station. Making the Bridge too large would cause tremendous environmental impacts, affecting the amount of sunlight reaching plants, migratory patterns of regional fauna, and more. To limit the impact of building a Mobius Bridge around the Earth, engineers would need to determine how much of the sun and moon could conceivably be blocked by the structure before being problematic. According to these sources NASA and Wikipedia the Sun and Moon are both roughly 0.5 degrees or 1800 arc seconds across from the perspective of an Earth bound observer (the decision to use angles allows for consideration of the perceived size of objects with respect to a terrestrial observer as opposed to the absolute size which will be constrained the most by this). As this document deals with estimated values, we will roughly constrain the relative width of the station to between 1/100th and 1/10th the angular diameter of the Sun and Moon (between 0.005 and 0.05 degrees across).
where d is the actual width of a selected object and D is the distance between the observer and the body and δ is the resultant angle. (see Fig 5)
Ex: If engineers decide that they want to make a station that keeps its inhabitants at roughly 0.9 g's they would need to build it at an altitude of about 330km. (See Fig 4) at that altitude and with the given constraints of keeping the station from not blocking the Sun excessively we get the equation shown in Fig 6
Solving for d @ D=330km we get the range 28.77m < d < 287.7 m
The final design would need to be a careful balance between the width constraints required for ecologically sustainable properties, maximizing internal working space, and a host of other variables. One fortunate trait of the Mobius Bridge is that you are not limited to making a single structure around a planet, given enough time and patience by an advanced civilization a planet might be found with a collection of archologies that would rival the ring's of Saturn in beauty.
Follow Up Materials
One additional means of maintaining the operational altitude of the Mobius Bridge would be the use of electromagnetic tethers as a means of using the Earth's magnetic field to gently counter the pull of gravity and compensate for uneven mass distribution, both within the archology and the outside universe. These tethers work by utilizing the Lorentz Force within the Earth's magnetic field. (I will try to add a less physics cut and paste explanation, once I understand this enough to do so)
Disclaimer Bit
It turns out the idea for building a Mobius Bridge was suggested at least as early as the 1870's by many geek's favorite inventors Nikola Tesla. Wikipedia has a cool entry on Orbital Rings that provides a host of additional details. A group called the Alna Space Program seems to have done an incredible amount of research into the design requirements of building an Orbital Ring, but I think I'm still going to call it a Mobius Bridge (seems sexier) The author/engineer Paul Birch published a paper in the 80's into creating an orbital ring and other dependent structures, including a lightsail wind mill, and an orbital sphere built around a planet.
Other outlandish engineering proposals can be found on the Wikipedia entry for Megastructures, although something as large as the Mobius Bridge, you might as well go grandiose and call it a giga-structure. Developing an orbital ring platform for planets like Venus could be integral in long term attempts to terraform the planet.
Other Stuff
Using the Lorentz Force for crazy orbits
Further Reading on Tether Propulsion
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| What the the Orbital Rings might look like Source: http://io9.com/if-earth-had-a-ring-like-saturn-508750253 |
For a sufficiently low mass bridge designs a massive collection of thrusters would provide the necessary counter forces to keep the Bridge in orbit. Unfortunately by the time the station got big enough to allow for a proper habitat the energy requirements to keep it suspended in space would only make sense for a species with near god like levels of energy production and control. The most likely solution for keeping the Mobius Bridge in orbit would be to have the structure be made from two primary components. The habitat segments of the Bridge would lazily drift over the Earth's equator maintaining the same day night cycle as the ground below. Within the frame of the habitat would be one or more massive magnetic orbiting rings. Each of these orbiting rings would serve as a track-way for the habitat structure to ride on, similar to magnetic levitation trains here on Earth. The dynamic interaction of the forces between the inner rings and the habitat ring create a situation where the net balance leaves residents of the habitat ring experiencing the slightly reduced pull of the Earth's gravity, several hundred kilometers above the ground.
Roughly speaking the force of gravity on the Bridge would be a result of the tangential velocity of the ring and its distance from the center of the Earth. (for those who aren't power nerds, this means you are accounting for the tendency of objects being spun to pull outwards and that the force of gravity gets weaker at a distance) To make the calculations easier, the primary sources of accelerations can be separated into two primary equations. The biggest impact on the gravity felt by objects in the habitat ring of the Bridge would be the distance between the bridge and the Earth. The force of gravity between two objects can be calculated using Newton's Law of Universal Gravitation, (see Fig 1)
 |
| Figure 1: Newton's Law of Universal Gravitation |
 |
| Figure 1A |
G sub c is the gravitational constant (Fig 1A).
M1 and M2 are the respective masses of the objects being analyzed.
r is the distance between the center of mass of the objects
While the above form is the most universal form of the Law of Gravitation for cases where M1 is much larger than M2 a slightly different version is used, where only the mass of the major body really needs to be considered.
 |
| Figure 2: Acceleration of Gravity Near the Surface of a large body |
For the station being built at 130 km above the Earth's surface, or just 30 km above the line that defines what is legally space, the force of gravity would work out to be roughly 9.44 m/s^2. At 530 km above the average surface of the Earth, gravity would still be an acceptable 8.37 m/s^2. (note that these values don't yet factor in the centripetal force)
The second major influencing variable for determining the acceleration of gravity on objects on the Mobius bridge is the centripetal force caused by station rotating with the same angular velocity as the ground below.
The relation of centripetal force to net acceleration would be a negative resultant of the equation
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| Figure 3: Acceleration of Gravity at the Equator Reference: Western Washington University |
ω^2*r. Where ω is equal to to the angular velocity of the planet Earth. The value of is ω equal to 2*π/1day or 2*π/86,400s. Putting all of these variables back into a single equation we get the equation to the right. Using this equation we can create a rather useful table (Fig 4) on how much acceleration would be felt at different target orbits. (A curve showing the estimated gravitational force at various altitudes will be found further down, useful detail the platform would experience roughly 0.5 g's around 2600 km above the Earth's surface)
 |
| Figure 4: Force of gravity at 130, 330, 530, and 1000 km above the Earth |
Another consideration for making the Mobius Bridge would the trade off of habitable surface area vs how much of the sky would be blocked out by the station. Making the Bridge too large would cause tremendous environmental impacts, affecting the amount of sunlight reaching plants, migratory patterns of regional fauna, and more. To limit the impact of building a Mobius Bridge around the Earth, engineers would need to determine how much of the sun and moon could conceivably be blocked by the structure before being problematic. According to these sources NASA and Wikipedia the Sun and Moon are both roughly 0.5 degrees or 1800 arc seconds across from the perspective of an Earth bound observer (the decision to use angles allows for consideration of the perceived size of objects with respect to a terrestrial observer as opposed to the absolute size which will be constrained the most by this). As this document deals with estimated values, we will roughly constrain the relative width of the station to between 1/100th and 1/10th the angular diameter of the Sun and Moon (between 0.005 and 0.05 degrees across).
 |
| Courtesy of Wikipedia.com: Angular Diameter |
 |
| Fig 5 A geometric representation of the angular diameter Courtesy of Wikipedia.com: Angular Diameter |
where d is the actual width of a selected object and D is the distance between the observer and the body and δ is the resultant angle. (see Fig 5)
Ex: If engineers decide that they want to make a station that keeps its inhabitants at roughly 0.9 g's they would need to build it at an altitude of about 330km. (See Fig 4) at that altitude and with the given constraints of keeping the station from not blocking the Sun excessively we get the equation shown in Fig 6
 |
| Fig 6 Angular Diameter with constraints |
The final design would need to be a careful balance between the width constraints required for ecologically sustainable properties, maximizing internal working space, and a host of other variables. One fortunate trait of the Mobius Bridge is that you are not limited to making a single structure around a planet, given enough time and patience by an advanced civilization a planet might be found with a collection of archologies that would rival the ring's of Saturn in beauty.
Follow Up Materials
One additional means of maintaining the operational altitude of the Mobius Bridge would be the use of electromagnetic tethers as a means of using the Earth's magnetic field to gently counter the pull of gravity and compensate for uneven mass distribution, both within the archology and the outside universe. These tethers work by utilizing the Lorentz Force within the Earth's magnetic field. (I will try to add a less physics cut and paste explanation, once I understand this enough to do so)
 |
| Figure X G force curve with respect to altitude (in meters) |
Disclaimer Bit
It turns out the idea for building a Mobius Bridge was suggested at least as early as the 1870's by many geek's favorite inventors Nikola Tesla. Wikipedia has a cool entry on Orbital Rings that provides a host of additional details. A group called the Alna Space Program seems to have done an incredible amount of research into the design requirements of building an Orbital Ring, but I think I'm still going to call it a Mobius Bridge (seems sexier) The author/engineer Paul Birch published a paper in the 80's into creating an orbital ring and other dependent structures, including a lightsail wind mill, and an orbital sphere built around a planet.
Other outlandish engineering proposals can be found on the Wikipedia entry for Megastructures, although something as large as the Mobius Bridge, you might as well go grandiose and call it a giga-structure. Developing an orbital ring platform for planets like Venus could be integral in long term attempts to terraform the planet.
Other Stuff
Using the Lorentz Force for crazy orbits
Further Reading on Tether Propulsion
