Space elevator

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An artists impression of a "climber" ascending a space elevator from Earth. A similar model can be used on Mars.

The transport from Mars' surface to Mars' orbit and vice versa can be achieved by a Space Elevator. The idea is to install a high-tensile rope from the surface to the synchronous orbit and a certain length beyond, connected to a counter weight.

Since the gravity of Mars is lower than the gravity of Earth the requirements to the tensile strength of the rope is less, making this construction easier.

History

The original concept for a "Space Tower" can be traced back to Konstantin Tsiolkovsky,[1] a Russian rocket and space pioneer. He is quoted as saying in 1895:[2]

"...on the tower, as one climbed higher and higher up it, gravity would decrease gradually; and if it were constructed on the Earth's equator and, therefore, rapidly rotated together with the earth, the gravitation would disappear not only because of the distance from the centre of the planet, but also from the centrifugal force that is increasing proportionately to that distance. The gravitational force drops... but the centrifugal force operating in the reverse direction increases. On the earth the gravity is finally eliminated at the top of the tower, at an elevation of 5.5 radii of the earth (22,300 miles)..."

Naturally, the Space Tower would be crushed under it's own weight, so the idea of a Space Elevator was born. In 1960, Yuri N. Artsutanov,[3] a Russian engineer, conceived the possibility of using a "skyhook" where a satellite is inserted into geosynchronous orbit and a cable lowered to the Earth's surface. As the cable is lowered, a counterweight is attached to the satellite and pushed into higher and higher orbit, thus keeping the cable's center-of-mass in a constant position. Once attached, the cable would be under tension, allowing payloads to be transported into the satellite's orbit.

Space elevator and radius of Martian moons.

Standard concept

The standard concept is for a system with a cabin, otherwise known as a climber, moving up or down a cable, often called a tether. The cable extends beyond the geostationary orbit to act as a counterweight to the cable.

There are already competitions to build climbing technologies, aiming to construct a machine that is able to climb a cable with a velocity of at least 1 meter per second.

The space elevator uses less energy than a chemical rocket for the same service. On Mars, propellant is produced from electricity so the costs are directly comparable. Due to the rocket equation, a rocket necessary requires more energy than a space elevator. However, the mass ratio to reach orbit on Mars is 3, while the mass ratio for Earth is 19. So the advantage on Mars is less important than for the Earth.

An interesting complement to the elevator concept is that the end can serve as an economical launch platform, as it is moving faster than Mars escape velocity.

The moon problem

The moons Phobos and Deimos are in low orbit and intersect the cable in intervals. To cope with this situation an active adjustment of the cable's position might be required to avoid a collision. Bringing down Phobos would abolish part of the problem. The Deimos problem might be solved by replacing the extension of the elevator by a counterweight located below Deimos' orbit. A non equatorial space tether[4] might allow for sufficient distance from the orbit of Phobos, if such an infrastructure can be build and put in place. There should be few additional costs for a non equatorial cable. The tether anchoring force required to move the attachment point away from the equator does not seem to be excessive and the change in length is minimal. However, since the cable does not pass by the equator, there are no orbits that intercept the cable at non zero velocity. This introduces added complications to docking with the cable.

Providing the Deimos problem can be solved, a space elevator is much easier on Mars than on the Earth. Due to the lower gravity and smaller length, a Mars elevator could be made from existing materials.

Technical analysis

This section is derived from a paper by P. K. Aravind Department of Physics, Worcester Polytechnic Institute[5]

Calculation of taper ratio

A tapered cable offers better performance than a constant section cable. The taper ratio equation is the following:

Taper ratio=e(Rpg/2T*((R/Rg)3-3(R/RG)+2))

Where:

T: Material yield strength (GPa)

p: density of material (kg/m3)

Taper ratios
Mars Earth
Mass of planet M kg 6.42E+23 5.98E+24
Radius of planet R m 3.40E+06 6.37E+06
Radius of geostationnary orbit Rg m 2.04E+07 4.22E+07
Gravity g m/s2 3.8 9.81
T (GPa) p (kg/m3) Taper ratio
Steel 5 7900 4662520 1.74E+33
Zylon 5.8 1540 13 3.85E+05
Kevlar 3.6 1440 49 2.60E+08
Carbon nanotube 130 1300 1.1 1.6

Calculation of cable length

The calculation for the cable length, with the external cable acting as a counterweight for the internal cable, is the following:

H=R/2*(sqrt(1+8(Rg/R)3)-1)

This gives a length of 69 000 km for Mars and 159000 km for Earth.

Based on these numbers, the author finds that a counterweighted carbon nanotubes cable capable of supporting a 1000 kg lifter would mass 150 tonnes.

Based on these proportions, a similar cable on Mars would mass about 75 tonnes. A cable made from Zylon, for the same capabilities, might mass 1000 tonnes, since the tapper ratio is 13 times higher.

The throughput of such a cable would be quite low. Supposing a velocity of 1000 km per hour travel on the cable would require 20 hours. With a cargo of 500 kg on the climber, the yearly transfer rate would be about 360 trips per year, or about 200 tonnes. This is clearly inadequate for a space settlement and such a structure would need to support a number of vehicles moving simultaneously, carrying higher masses and probably at higher velocities. For 2000 tonnes per year the cable might mass 10 000 tonnes, and for 20 000 tonnes per year 100 000 tonnes.

The cost of the cable, if fabricated on Earth, would be mostly transportation. At 500$ per kg, for example, the 600 tonnes per year capacity cable would cost a minimum of 5 billion dollars. Plus fabrication costs. This does not seem cost effective compared to chemical rocketry. In particular if the vehicles uses aerobraking for landing, and therefore very little propellant.

In the short term, the Mars space elevator seems costly and less effective than chemical rocketry. Once an important in-situ production capacity is in place, the transportation costs go away and the structure might be more interesting economically. The development of carbon nanotubes in practical wires would also favor the space elevator.

Orbit-to-surface concept

For the purpose of building an autonomous colony the transportation from orbit down to the Martian surface is the main focus. For this use case a climbing technology is not necessary, and the elevator is much simpler. Only a brake needs to be installed in the cabin, preventing free falling. In this case every transport down the rope consumes a new cabin

Advantages

  • No fuel is required to be burnt. This concept might be cheaper than traditional rocketry, and potentially reduces the mass to launch off Earth.
  • Smooth landing, suitable for fragile machinery.
  • Could have a high traffic volume as the movement is only one way.

Disadvantages

  • Remains heavy.
  • Fuel is required to match velocity with the cable. This may use more fuel than direct entry and aerodynamic braking.

Phobos elevator concept

A variation on the space elevator idea is the Phobos elevator[6]. This would significantly reduce the cost of lifting material from the Surface of Mars by using a suspended tether down into the martian atmosphere and an extended tether up towards space. Phobos itself would serve as source of the construction material for the elevator.

In Science-Fiction

  • Red Mars, Green Mars, and Blue Mars by Kim Stanley Robinson (1992, 1993, 1996). Space elevators on Earth and on Mars where the cables are made of carbon nanotube which are manufactured on an asteroid. The resulting cable is then lowered into the atmosphere to be attached to the surface. An asteroid is used as a counterweight. During the Mars revolution, the Red Mars novel graphically depicts the effects of a catastrophic space elevator failure, when the cable is severed in orbit.[7]
  • In Star Trek: Voyager episode Rise the idea of a space elevator is part the story.[8]

See also

External links

References

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