Introduction

A space elevator is a proposed method of space launch utilizing a structure extending from a planetary surface up into space. Typical designs involve a cable anchored to the surface which terminates in a counterweight beyond synchronous orbit. This counterweight ensures that the elevator's center of mass is located exactly at synchronous orbit, making the system move as a whole with the planet's rotation and remain properly extended directly above the anchor point on the surface.

Forces and Design

Space elevators are an example of a megaproject, and must be carefully optimized to be feasible. Each portion of the elevator must be no stronger or weaker than is absolutely necessary. The segment of the elevator at synchronous orbit naturally moves with the planet's rotation and has no net force on it. However, segments below synchronous orbit feel an excess of gravitational force pulling in, while segments above synchronous orbit feel an excess of centrifugal force pulling out. To hold the system together these forces must be countered with the elevator's tensile (stretching) strength. This means that every segment of the elevator inside synchronous orbit must be strong enough to "hold up" everything below it, while outside synchronous orbit it must be strong enough to "hold in" every segment beyond it. Making a segment thicker makes it stronger, but also makes it heavier. These physics result in an optimal elevator having a tapered shape, which is thickest at synchronous orbit and thins going inward and outward until the surface and counterweight are reached, respectively.

The taper ratio of the elevator's cross-sectional area at synchronous orbit and the surface can be written as (Pearson 1975):

where α is a dimensionless factor,

and h is a "characteristic height",

Here rp is the planet's radius, rs is the radius of synchronous orbit, σ is the tensile strength of the elevator material, ρ is its density, and g0 is the planet's surface gravity.

Space elevator materials must be very strong and light, that is, they must have a large tensile strength and low density. Otherwise, the elevator will have to be impossibly thick at synchronous orbit to hold up even the thinnest thread at the surface. The characteristics of some strong, light materials are contained in the table below.

Tensile
Strength
Density
Specific
Strength

[GPa]
[g/cm³]
[GPa·cm³/g]
High Tensile Steel
1.3
7.87
0.17
Basalt Fiber
4.8
2.7
1.8
Carbon Fiber
3.5
1.75
2.0
Kevlar
3.6
1.44
2.5
Colossal Carbon Tube
7.0
0.116
60

Not all of these materials are adequate for planets the size of Earth and Mars. Steel is too weak and heavy for both planets, and while basalt fiber, carbon fiber, and Kevlar have potential on Mars, they are impractical for Earth. By comparison, dwarf planets and large asteroids like Ceres are undemanding in their material requirements.
Planetary
Object
Surface
Gravity
Planetary
Radius
Synchronous
Orbit
Dimensionless
Factor
Taper Ratio

[m/s²]
[km]
[km]
α
High Tensile
Steel
Basalt
Fiber
Carbon
Fiber
Kevlar
Colossal
Carbon Tube
Earth
9.81
6,378
42,166
0.775
3.1×10127
7.0×1011
3.4×1010
2.7×108
2.23
Mars
3.71
3,396
20,429
0.753
8.9×1024
208
115
45
1.17
Ceres
0.265
487
1,190
0.420
1.39
1.031
1.027
1.022
1.009