# Space elevator and Coriolis force

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• Prophet
In summary: The Coriolis force would then be the only force acting on the payload, and it would be balanced by the weight of the Earth.

#### Prophet

It seems to me that the concept of a space elevator does not take Coriolis force into account. If the elevator were in built with a space station in geosynchronous orbit and counterweight then there is more to reaching the space station than just climbing the rope. The rope would have to be anchored to the Earth at the equator and at the start of the climb would be moving approximately 1000 mph eastward. If memory serves geosynchronous orbit is about 25,000 miles from the center of the Earth and the space station would be moving eastward at over 6000 mph. I don't see how the elevator can gain that additional 5000 mph simply by climbing the rope.

I have read one article that acknowledges the Coriolis problem but they claim the effect is slight, simply pulling the rope slightly our of line. I don't think so.

I think you need to use Hamiltonian mechanics, not Newtonian mechanics, to solve but it's been over 40 years since I studied Hamiltonian mechanics.

Is NASA actually spending taxpayer money on this idea?

Supposing the space station is located directly above the Earth station of the elevator, the elevator only goes vertically upwards without changing its coordinates. The Coriolis acceleration in this case can be calculated with

$$a_C = 2\Omega v_{Elevator} cos(LAT)$$

where ##\Omega = 2\pi/86400\,s## denotes the rotational speed and ##LAT## denotes the latitude. The elevator is located close to the equator for obvious reasons, therefore ##cos(LAT)\approx 1##. Now the Coriolis acceleration can be calculated depending on the speed of the elevator, e.g.

## v_{Elevator}=100\,m/s \rightarrow a_C = 0.015\,m/s^2##
## v_{Elevator}=1000\,m/s \rightarrow a_C = 0.15\,m/s^2##.

The accelerations obtained with this estimation seem to be manageable (if I didn't make a mistake).

russ_watters, Bandersnatch, sophiecentaur and 1 other person
Prophet said:
I don't see how the elevator can gain that additional 5000 mph
The work needed to accelerate the vehicle would, I think, largely come from the spinning Earth (horizontal displacement of the tether) and not the fuel used for hoisting it.
At 100m/s, the journey would be a bit over 100hours or four days. (check my sums for 40 thousand km orbit) Not an exceptional time.

Prophet said:
I have read one article that acknowledges the Coriolis problem but they claim the effect is slight, simply pulling the rope slightly our of line. I don't think so.

But that's exactly how it works. The coriolis force acting on the payload is not an issue. The challenge is fighting oscillations.

sophiecentaur said:
The work needed to accelerate the vehicle would, I think, largely come from the spinning Earth (horizontal displacement of the tether) and not the fuel used for hoisting it.

Above the geosynchronous orbit it actually comes from the spinning Earth only. And if the energy released by the payload above this point can be used to lift the payload below, than the elevator could theoretically work without external energy source or even be used as energy source itself.

As the payload goes up the cable, the cable will be providing the sideways force on the payload. But the reaction force on the cable will cause it to bow out. It will try to bounce back due to the tension in the cable which is provided by the Earth and the weight above geosynchronous orbit.
Without doing actual calculations, I suppose that raising an object will cause a wake in the cable that will propagate to the weight, which shifts the weight slightly west and down. But the cable will tense up and the weight will bounce back, causing the weight to oscillate. Eventually, the weight will pull the Earth along and lock up with the Earth's rotation. But since the Earth weighs much more than the weight, this could take a long, long time. Instead, some kind of active feedback will be needed on the weight, which will require considerable amounts of fuel.

Khashishi said:
Instead, some kind of active feedback will be needed on the weight, which will require considerable amounts of fuel.

There is no such feedback required if the cable is attached to the ground.

## What is a space elevator?

A space elevator is a theoretical structure that would allow for transportation of people and goods from Earth's surface to space without the need for rockets or other traditional means of space travel. It would consist of a long cable tethered to Earth's surface and extending into space, with a counterweight at the other end to keep the cable taut.

## How does a space elevator work?

A space elevator works by utilizing Earth's rotation and the balance between centrifugal and gravitational forces to keep the cable taut and allow for transportation up and down. A climber or elevator car would travel along the cable, powered by either electricity or lasers, to reach space.

## What is the Coriolis force?

The Coriolis force is a phenomenon caused by the rotation of the Earth. It causes moving objects on Earth's surface to appear to deviate from a straight path, and is responsible for the rotation of hurricanes and the direction of ocean currents. It also impacts the trajectory of objects launched into space.

## How does the Coriolis force affect a space elevator?

The Coriolis force affects a space elevator by causing the cable to shift slightly to the east as it extends into space. This shift must be accounted for in the design and construction of the space elevator to ensure that the cable remains stable and does not break.

## What are the potential benefits of a space elevator?

A space elevator could greatly reduce the cost and energy consumption of space travel, as well as provide a more sustainable and efficient means of transporting goods and people into space. It could also open up new opportunities for space exploration and research, and potentially enable the development of extraterrestrial colonies.