# Space Elevator

Space Elevator theory and calculations

A space elevator is a proposed type of planet-to-space transportation system. The main component would be a cable (also called a tether) anchored to the surface and extending into space. The design would permit vehicles to travel along the cable from a planetary surface, such as the Earth’s, directly into space or orbit, without the use of large rockets. An Earth-based space elevator would consist of a cable with one end attached to the surface near the equator and the other end in space beyond geostationary orbit (35,786 km altitude). The competing forces of gravity, which is stronger at the lower end, and the outward/upward centrifugal force, which is stronger at the upper end, would result in the cable being held up, under tension, and stationary over a single position on Earth. With the tether deployed, climbers could repeatedly climb the tether to space by mechanical means, releasing their cargo to orbit. Climbers could also descend the tether to return cargo to the surface from orbit.

: gravitational force
: centripetal force
: Earth mass
: Earth’s angular velocity
: gravitational constant

: cable density
: cable mass
: cable length (calculated below)
: cable stress (calculated below)

### Stress

The stress, (i.e., the tension per unit of cross sectional area) is constant along the length of the cable. Calculate the stress at the end of the cable:

## 15 thoughts on “Space Elevator”

1. verum revelans says:

Thank you for solving for x. Perhaps you could put somewhere at the top of your calculation exactly what x represents?

1. Oh you are right, I will modify as soon as possible. ‘x’ represents the cable’s length.

2. Arter44927 says:

Hell yeah ;D

3. HershelKohli35561 says:

4. Can I ask you to add to this? Could you provide an additional example? many thanks!

1. Thank you for the advice. I agree with you, I am still developing the post because it is much more deeper than I thought at first.
I will demosrtate that the space elevator could be built using carbon nanotubes ๐

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