It is easily seen the space elevator improves access to Earth orbits along its length. An additional aspect of the space elevator is that it can be used as a sling to launch payloads to more distant destinations.
To find out which solar orbits are accessible by this method we use conservation of momentum and energy.
where G is the gravitational constant, Msun is the mass of the sun, ME is the mass of the Earth, m is the mass of the spacecraft, rcable is the orbital altitude at the top of the cable, v1 and vF are the velocities of the spacecraft when it leaves the cable and at the destination orbit, RE is Earth's orbital radius and RF is the final orbit's major or minor axis.
Rearranging and substituting we get
We can also express vs as the velocity of the Earth around the sun plus the velocity of the end of the cable around the Earth. ThusvI = vE ± vcable
where vE equals 30,900 m/s. We can also express vcable in terms of rcable.
From the equation above we can now find what solar orbits are accessible as a function of the cable length. Both the smallest and largest accessible solar orbits are plotted in Figure 7.1.
These calculations are for orbits in Earth's equatorial plane, a rocket will be required to bring the payload back into the plane of the solar system and to circularize the orbits. Gravity assists have not been considered here. For our initial cable we will constrain our ambitions and select a cable that will allow access to Venus, Mars and Jupiter. This cable length will be 91,000 km. Once the first elevator is established, longer elevators can be constructed so the outer planets and Mercury can be reached more easily.
One additional use of the space elevator is production and delivery of a completed Mars cable (figure 7.2). The Mars cable could be produced in Earth orbit alongside an Earth elevator then released as a single unit on a trajectory to Mars. Upon reaching Mars a braking rocket or aerobraking would be required to place the cable in the proper Marssynchronous orbit. From Mars synchronous orbit the cable would be deployed and anchored. The counterweight or a second package sent to Mars would be a spacebased power beaming station. This power beaming station could utilize large solar arrays or nuclear power and a rigid mirror.
Once the Mars elevator is established transport from Earth to Mars and Mars to Earth can be done with only a plane correction rocket, attitude adjustment thrusters and climbers. For example, a climber can ascend the Mars elevator to its upper end where it releases at the proper time to acquire a trajectory to Earth. When the Mars craft approaches Earth, it attaches to the Earth elevator (the proper positioning would give an almost zero relative velocity between the cable and the craft) and descends the Earth cable to the ground.
Due to the Mars/Earth differences (lower gravity, lower synchronous orbit) the Martian cable would be roughly 1/2 the length and 1/20th the mass for the same capacity. Considering the entire cable could be built in high-Earth orbit, a 20,000 kg capacity Earth cable could be used to build and launch a 100,000 kg capacity or larger Mars elevator. The Mars elevator would have a different taper profile and not have to concern itself with lightning or man-made space debris. However, studies would have to be done to address possible Mars specific problems such as dust storms and the avoidance of Mars' moons.
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