# What's Wrong with Vacuum-Filled Vertical Tube Escape Velocity?

• a1call
In summary, the input yielded a velocity of 11.2 km/s (Earth's Escape Velocity) at freefall from a height of 6.4 km.
a1call
Ignoring drag, terminal velocity and friction, input 1143 seconds here:
http://keisan.casio.com/exec/system/1224835316
It yields a velocity of 11.2 km/s (Earth's Escape Velocity) at freefall from a height of 6.4 km (a fraction of the height/depth of Everest, Antarctic ice cap and deepest oceanic depth).
Consider a 6.5 km Vaccum filled vertical tube with a half circle at the bottom which a ball could roll at the bottom and redirect upwards after freefall through it.
Such a ball will have a velocity greater than the escape velocity at the bottom of the tube.
This can't be right since considering the tube be a complete U shape then at top/end of the path the speed would be the same as the start of the path namely 0 and no escape would be achieved.
Where did I go wrong?

Last edited by a moderator:
a1call said:
Where did I go wrong?
Here:
a1call said:
6.4 km
Count the digits. You're off by a factor of 1000.

Also, keep in mind that the equation used there is an approximation for a uniform gravitational field (near the surface only). That g is not actually a constant, so the higher you go the more wrong your numbers will be.

Yes thank you I saw my error and was also pointed out on the other board that gravity decreases by altitude.
But I am still confused.
The question now is that changing the height of the tube to whatever value where we could achieve escape velocity at the bottom would still be a conflict from 0 velocity at the end of the U path. Unless the required height happens to be infinity. Is it?

a1call said:
Is it?
It is.
Check the definition of escape velocity. Usually it's done in terms of kinetic energy equalling potential energy. At infinity the body has got the maximum potential energy (least negative, so 0) and minimum kinetic energy (0). It follows that the velocity is 0 there.

In other words, escape velocity is the velocity a body needs to be able to fully climb out of the gravity well of some other massive body with no leftover velocity. And since gravity extends to infinity, the potential is 0 only there.

a1call said:
Unless the required height happens to be infinity. Is it?

Yes, that's the definition of escape velocity - the lowest speed at which the object will never return to earth. If the speed were to reach zero at any finite height the object would eventually fall back to Earth (this is the exact same situation as if we held the object at rest at that height than released it - it would fall).

Thank you both for resolving my issue.

Seems like 4g enough.

## 1. What is "vacuum-filled vertical tube escape velocity"?

"Vacuum-filled vertical tube escape velocity" refers to the theoretical concept of using a vacuum-sealed vertical tube to launch objects into space. It is based on the idea that the lack of air resistance in a vacuum would allow objects to achieve higher velocities than traditional rocket launches.

## 2. Why is there interest in this concept?

There is interest in this concept because it has the potential to significantly reduce the cost and complexity of space launches. It also has the potential to open up new possibilities for space travel and exploration.

## 3. What are the main challenges with this concept?

There are several challenges with this concept, including the technical feasibility of creating a vacuum-sealed tube that is tall enough to achieve the necessary escape velocity, the structural integrity of the tube under extreme pressure differentials, and the potential safety hazards for any objects or people inside the tube.

## 4. Has this concept been tested or implemented?

While there have been some small-scale experiments and simulations, this concept has not been fully tested or implemented on a large scale. There are still many unanswered questions and challenges that need to be addressed before it can be considered a viable option for space launches.

## 5. What are the potential benefits and drawbacks of this concept?

The potential benefits of this concept include lower cost, increased efficiency, and the potential for faster and more frequent space launches. However, the drawbacks include the high cost of building and maintaining a vacuum-sealed tube, potential safety concerns, and the need for extensive testing and research before it can be considered a reliable method of space travel.