Space Elevator - Your take on an exam question

• Stevecgz
In summary, the conversation discussed a question on the exam about the concept of a Space Elevator and the instructor's answer. The question involves calculating the total acceleration on the craft using conventional propulsion and the rotation of the Earth. The speaker suggests using polar coordinates to find the velocity and acceleration, but cautions about the unit vectors being functions of time.
Stevecgz
I recently had an exam in my 2nd year dynamics course that included a question concerning a Space Elevator. My view on this question (or the answer to this question) seems to be different than my instructor's. I was hoping to get some of your thoughts so I could get a better understanding.

The question on the exam was exactly as follows:

"The 'Space Elevator'. Should you decide to poke around www.howstuffworks.com, you will eventually stumble across this masterpiece. The basic idea is to build a very large nanotube steel structure several kilometers straight up from the surface of the earth, and use conventional propulsion to accelerate the craft along the rail, while utilizing the rotation of the Earth to impart a rotational acceleration on the craft as well, thus increasing the total amount of available acceleration. Assuming that convention propellant moves it along the rail according to the equation r(t) = 3t^2 + 40*10^6 m, and that the Earth completes one rotation in 24 hours, determine the total acceleration on the craft imparted by the propulsion system after 60 seconds."

Thanks,
Steven

You can write the position of the craft in cartesian coordinates (messy) or in polar coordinates (much easier) and take the derivatives to find velocity and acceleration. But you have to be careful. In polar coordinates the unit vectors in the radial direction and the tangential direction are functions of time.

As a scientist, my take on this question is that the concept of a Space Elevator is a fascinating and potentially game-changing idea in the field of space exploration. However, there are several factors that need to be carefully considered in order to determine its feasibility and effectiveness.

Firstly, the use of nanotube steel as the material for the structure raises concerns about its strength and durability in the harsh environment of outer space. Extensive research and testing would need to be done to ensure that the structure can withstand the stresses and strains of being several kilometers above the Earth's surface.

Secondly, the use of conventional propulsion raises questions about the efficiency and sustainability of this method in the long term. Alternative and more advanced propulsion systems, such as electric or nuclear propulsion, may need to be considered for a Space Elevator to be a truly viable option.

In terms of the specific question posed in the exam, I would approach it by first calculating the total distance traveled by the craft after 60 seconds using the given equation. Then, I would use the rotational speed of the Earth to determine the additional acceleration imparted on the craft by the Earth's rotation. Finally, I would combine these two values to determine the total acceleration on the craft.

Overall, while the idea of a Space Elevator is exciting and has the potential to revolutionize space travel, it is important to carefully consider all the technical and practical challenges involved before pursuing it further.

1. What is a space elevator?

A space elevator is a hypothetical structure that would allow spacecraft and other objects to travel from Earth's surface into space without the use of rockets. It would consist of a long cable or tower extending from the Earth's surface into geosynchronous orbit, where it would be anchored by a counterweight. The idea was first proposed by Russian scientist Konstantin Tsiolkovsky in 1895.

2. How would a space elevator work?

The space elevator would utilize the concept of a geosynchronous orbit, where an object orbits the Earth at the same speed and direction as the Earth's rotation, allowing it to stay in the same position above the Earth's surface. The cable or tower would be anchored at the equator and would be held taut by the counterweight in geosynchronous orbit. Elevator cars or climbers would travel up and down the cable using a combination of mechanical and electrical power.

3. What are the potential benefits of a space elevator?

A space elevator could drastically reduce the cost and energy required for space travel. Rockets are currently the primary means of reaching space, but they are expensive and have limited payload capacities. A space elevator would allow for larger and more frequent payloads, making space travel more accessible and affordable. It could also serve as a launching point for spacecraft to explore other planets and moons in our solar system.

4. What are the main challenges in building a space elevator?

One of the biggest challenges is finding a material strong enough to support the weight of the cable and withstand the extreme forces of Earth's gravity and the counterweight's rotation. Currently, carbon nanotubes are the most promising material, but they are still in the early stages of development. Another challenge is designing the elevator cars or climbers to safely and efficiently transport passengers and cargo up and down the cable.

5. What is the current status of the space elevator concept?

While the concept of a space elevator has been around for over a century, it is still in the early stages of development. Many scientists and engineers are working on various aspects of the idea, including material development, design, and safety considerations. Some private companies have also expressed interest in building a space elevator, but it will likely be several decades before a functioning space elevator becomes a reality.

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