Space exploration is an extraordinary pursuit  that is  fundamental for furthering  human progress and knowledge. However it is  incredibly resource-intensive  and  its sustainability is hindered due high cost and energy demands  of escaping to Earth's gravitational sphere. Launching satellites or spacecraft to other celestial bodies demands overcoming Earth's gravity, which accelerates objects downward at 9.81 m/s². Achieving escape velocity of approximately 11,186 m/s is essential to break free from this pull, but doing so requires vast amounts of fuel and financial resources.For instance the Saturn V rocket, used during the Apollo missions, burned nearly 950,000 gallons of fuel, which would cost about $3.4 million today. Even after escaping Earth's gravity, additional fuel is needed to reach a spacecraft's destination, making long-term and deep-space missions unsustainable. This heavy reliance on fuel limits the frequency and scope of space exploration.To address these challenges, we must explore more sustainable solutions that reduce fuel consumption and costs. One promising innovation is the development of space tethers. These systems use mechanical forces to help spacecraft gain altitude and velocity. By leveraging inertia and centrifugal force, a tether can attach to an orbiting spacecraft, using its motion to generate energy. Harnessing centripetal force, the tether acts like a slingshot, efficiently flinging the spacecraft beyond Earth's gravitational pull.

Space tethers do  come with some  technical challenges:

• Momentum Loss:The tether loses circular momentum after releasing the spacecraft, requiring a mechanism to restore it.
• Attachment difficulties:Docking with small, fast-moving spacecraft demands high precision.
• Material Durability:Tethers must endure the harsh environment of space, including extreme temperatures and micrometeoroid impacts.
• Massive counterweight:A tether system in Earth orbit would require a counterweight 1,000–2,000 times the payload's mass.
• Synchronization:After flinging a payload, the tether must be reeled in and reset to maintain alignment with its orbit.

Despite these challenges, space tethers hold immense potential to revolutionize space travel, offering a path to more frequent, cost-effective, and sustainable exploration of the universe.

 

 

To address the problems mentioned, we have come up with some solutions, starting with one of the largest challenges which is the mass of the counterweight. As mentioned earlier, the counterweight needs to be 1,000 times the mass of the payload. For example, the Saturn V rocket had a payload of 26,700 kg for the Apollo missions. If we apply this to the tether system, the counterweight would need to be 26,700,000 kg.

One possible solution is to reduce the weight of the spacecraft/payload itself by constructing it from lighter materials, such as carbon composites, metallic foams, and lightweight alloys. These materials are incredibly strong and lightweight and are planning to be used in further space missions. This makes them ideal for reducing the overall mass of the spacecraft, which will reduce the mass of the counterweight. Another example of using lightweight materials can be seen in the Mangalyaan spacecraft, launched by the Indian Space Research Organisation (ISRO) for mission Mungal. For this mission, they used a combination of aluminum and composite fiber-reinforced plastic sandwich materials for the main body. The spacecraft had a total mass of 1,340 kg, of which 852 kg was fuel. By applying similar methods to the tether system, we could reduce the mass. Another potential solution involves using multiple smaller counterweights in a distributed configuration, which would allow for more manageable components rather than relying on a single massive counterweight meaning we can add and reduce the mass we want according to missions. This approach could make the system more flexible and easier to control, while also distributing the mass in a way that reduces the risk of failure or inefficiency. 

Another issue we mentioned was the potential disruption of the tether's momentum caused by the momentum of the payload being plugged into space. To address this, we have a relatively simple solution: we will launch an equal amount of mass both into space and back to Earth. By balancing the mass being launched in both directions, we can maintain the tether’s momentum. This approach could lead to even greater benefits if we expand the use of space tethers by building additional space hooks on other planets or moons. With more space hooks in different locations, we could establish a system where spacecraft travel more frequently between Earth and other celestial bodies. This means that with multiple space hooks in operation, we would need less fuel for each mission, meaning less mass, leading to the counterweight’s mass being reduced. 

To ensure the durability and functionality of the tether, especially the string part or fishing line of the hook, we need a material that can withstand these harsh conditions. One potential solution is to use Zylon. Zylon is incredibly strong, light, and durable, making it an ideal candidate for use in the space tether system. It has been shown to withstand high radiation levels and extreme temperatures. Its strength to weight ratio can handle the strains that come with tethering a spacecraft in orbit, including the pull of Earth's gravity preventing the hook part and counterweight from being snapped in half. Additionally, Zylon's resistance to degradation from ultraviolet radiation and its stability in the vacuum of space would make it a reliable material for maintaining the integrity of the tether over long periods.

To conclude, combining the use of lightweight materials for the payload, distribution of counterweights, and the durability of Zylon for the tether string can provide a more sustainable and efficient solution for the issues that the invention of a space tether will face. 

 

 

 

Orbit and Velocity calculations

The gravitational acceleration is: g=G⋅M/R^2

Substitute the values: g=(6.67e−11)⋅(5.972e24)/(7.378e6)2

G = 7.335m/s^2

 

To maintain a stable orbit, the gravitational force must be balanced by the centrifugal force: m⋅v^2/R=G⋅M⋅m/R^2

Substituting the values: v^2= 6.67e-11x5.972e24/7.378e6

v=7783m/s

 

For the tether to be able to launch a payload out of the influence of the earth's gravitational field (escape velocity), the tether must be able to accelerate the payload to 11,008 m/s

This velocity will be transferred by the combined motion of the earth and spin around the axis combined, V total V orbit+ V spin.

 

So if our V orbit is = 7783 m/s, then 11,008 - 7783 = the velocity at which the tether must be spinning with a tangential velocity of 3,658 m/s.

 

To get the tether spinning at the required velocity at its tip, you need to apply angular velocity. The angular velocity omega (ω) is related to the linear velocity V by: v=ωr

ω= 3,658/10000000

=0.003658rad/s

This velocity is required tether to be able to sufficiently transfer the needed energy to reach the required orbital velocity.

The orbital period can be calculated using the formula: T=2πR/v

Substituting the values: T=2π×7.378e6/7.783e3

T=5,949.77sec

To spin up a space tether to the required speed, you need to:

1. Apply Initial Force: Use a mechanism like a motor, spacecraft, or launch system to gradually accelerate the tether to the desired angular velocity.
    
2. Manage Friction and Drag: At higher altitudes, drag becomes less of a concern, but you still need to ensure the tether is designed to withstand the stress without breaking and able to have leeway for unaccounted disasters or dysfunctions over time.

Energy Considerations:

• Propulsion: Use rocket engines or similar systems to impart initial momentum.
• Continuous Force: Solar sails or electrodynamic tethers can provide ongoing force once in orbit.
• Gradual Spin-Up: Mechanical systems like winches or motors can incrementally spin the tether.

 

Practical Costs and Current Real life limitations

Our contemporary technology is concurrent with what we have shown a glimpse of however our limiting motive and reason we are not currently funding and developing such technology is because there is no short-term economic incentive. Currently, we lack the space for infrastructure to viably conserve such angular velocity, we would need multiple space missions in and out consistently to maintain this delicate, tight rope-like balance without accidentally flinging a spaceship into the void or sending the entire tether, alongside billions of invested dollars crashing towards earth. In conjunction, the money we would save from cutting on fuel will be completely overshadowed by the monstrous cost, resources, and maintenance that with the current rate of expeditions and exploration, would be unsustainable and unrealistic. If we have asteroid mining operations in the asteroid belt, then a space tether would save gargantuan costs for these companies or nations looking to use these resources in the long run. Finally constructing such a behemoth of a structure 100% in space would require immense manpower and an extreme working environment, in addition to the difficulty of building a 1000 km long structure. Let alone being able to find, diagnose, and repair/perform maintenance on something this big, rotating this fast, while having millions of kilograms attached to the end.

 

In Conclusion, Space Tethers are a clear choice for future innovation and possibly a leap in our progress as a species with very realistic prospects. As we continue to advance our technology, past carbon nanotubes, and future innovations. With time, as it becomes economically viable and profitable, this could revolutionize how look forward to the future and such technology could arise in our lifetimes. We could be the ones to develop, prototype, engineer, and successfully create this next step, and why continue to foster and help young creative minds stay curious and possibly create a breakthrough.

NASA’s Technical Reports Server (NTRS)

 ID 19970027081

https://www.isec.org/researchsummary

https://www.youtube.com/watch?v=TlpFzn_Y-F0&t=1532s

https://www.youtube.com/watch?v=dqwpQarrDwk 

https://pmc.ncbi.nlm.nih.gov/articles/PMC6146922/

https://www.researchgate.net/publication/245438045_Bare_Tethers_for_Electrodynamic_Spacecraft_Propulsion 

Mr. Corey Hornick's 20-AP Physics Class

(most formulas used we learned from here)