Space Elevator - Your take on an exam question

[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

 

[OlderDan]

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.

 

[kyle8921]

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.