Vehicle Thrust Arriving at the Construction Station
Trajectory Correction and Plane Change with Laser Ablation Thrust
Cargo vehicles without crew will be inexpensive, and will not have onboard computation or rocket thrusters. Instead, they will have external panels of black plastic that can be ablated by pulsed high power lasers mounted on small solar powered satellites.
Vehicles launched from earth arrive at a HEEO (Highly Elliptical Earth Orbit) construction station 10% to 15% slower than the station itself - they lead the station in orbit by up to a few hundred kilometers. A laser on the construction station itself can only "see" the "back" of the vehicle, and apply ablative thrust there; lateral thrust (north-south-up-down) is easier to apply from lasers positioned in those directions.
Separate laser stations orbiting ahead of the construction station, in similarly synchronous orbits but with apogee offsets from the station itself, are probably the easiest way to provide laser power for the thrusts. Duty cycle will be low, perhaps 15 minutes of the one-sidereal-day orbit will be useful, similar to the "arrival handling" equipment on the construction station itself. So, the laser stations will probably have batteries that charge during most of the orbit and power the pulsed lasers at arrival times. Assuming the stations are tele-operated, the other 23+ hours can also be used for maintenance and repair.
Near perigee, as the laser stations orbit rapidly down to 2000 km altitude, they may occasionally be useful for ablative laser thrust on derelict satellites and space debris as well. However, the space junk will usually be too far away, tumbling chaotically, and not be optimum for ablative thrust, while the laser energy that misses the target could damage other satellites. It seems unlikely that these lasers will have many other practical uses than their principal mission.
Assume a 1 micrometer infrared wavelength, and a typical spacing from laser satellite to cargo vehicle of 400 km. Focusing on a 0.5 meter ablation target might require a 1 meter mirror (with VERY good aiming!) on the laser satellite.
If a 5 tonne vehicle needs 10 m/s of plane change thrust, that is 5e4 Newton-seconds of thrust. If that is generated by 20 kilograms of ablated material, the average directed velocity of the material might be 2500 m/s . If that directed material is heated and directed with 13% efficiency, the total energy deposited by the laser will be around 500MJ, an average thermal velocity of 7000 m/s. If the laser is 20% energy efficient, the batteries must store 2500 MJ, or about 700 kilowatt hours. A lithium battery might store 140 Wh/kg, so this is 5,000 kg of batteries on the station. It may be easier to do the work with perhaps 3 smaller stations massing perhaps 4000 kg each, 350 kWhr each, with 2500 kg of batteries each; 2 active plus 1 spare station, with redundant lasers on each station.
Average power per day is ( 250 MJ)/86164 seconds, a bit less than 3 kW. Assuming 200 W/kg solar panels, that's less than 15 kg of solar panels. Lasers and mirrors and orbit maintenance thrusters and fuel will consume the rest of the 1500 kg of mass left over after the battery mass allowance.
Directly powering the laser from solar arrays only probably won't work. The window for using the laser might be only 200 seconds; to make 2.5 GJ in 200 seconds requires 12.5 MW, or 63 tonnes of solar panel. Not practical.
The ablated propellant from the plane change will be ejected with an average velocity of 7000 m/s, but the velocity distribution will be thermal Maxwellian, no collimation of velocity and cooling of the propellant like a rocket nozzle does. At 75000 km altitude, escape velocity is 3300 m/s. Perhaps 10% of the propellant atoms will end up in long-period elliptical earth orbits; 2 kg per 5000 kg cargo vehicle. That is far less than the propellant orbited by a rocket launch, but launch loops may orbit billions of tonnes per year someday, and millions of tonnes of orbiting propellant atoms is unacceptable.
Over time, we should strive for even faster thermal velocities (and correspondingly less reaction mass), and move towards multiday construction orbits, with lower apogee velocities, lower escape velocities, and smaller plane change velocities. That will require larger passenger vehicles and larger launch loops for a comfortable multiday launch ride and return.
Landing with Nets: Arrival Thrust at the Construction Station
The vehicle will arrive approximately collinearly with the construction station orbit, requiring up to 150 m/s of speedup delta V for "late capture" into a one day construction orbit. That would require a LOT of laser ablation thrust; there's a better way, which ablates nothing and puts no unwanted material into orbit.
Consider the arrest cables on an aircraft carrier; heavy aircraft land with a tailhook dragging the deck and snagging one or more cables. The cables are pulled by the aircraft, and roll past brakes (?) in the carrier to dissipate the vehicle's kinetic energy. Planes land at perhaps 135 knots, or 70 m/s, and slow down within 150 meters of deck, averaging 1.7 gees and peaking at much higher gee forces.
Station "landing speeds" are higher - but we can do this without the cable and without the deck. Vehicles do not need the support of a deck, nor do they need air for lift or even a limited-length "runway", Here's how:
Changing vehicle velocity by 200 m/s at 10 m/s² (∼1 gee) can be done with a 4000 meter "runway". We won't use cables, we won't use propellant; instead, the station will launch a stream of mesh-elastic nets at the arriving vehicle, which arrives tail first, so the thrust direction is the same as the 30 m/s² launch thrust.
The numbers below are crude estimates, a differential equation will be better ...
If the vehicle is 2 meters diameter, and the nets are 10 meters diameter and arrive centered and perpendicular to the vehicle, the vehicle will speed up a little, and the net will slow a LOT, wrapping around the vehicle in a fraction of a second. If the net masses 2 kg, and the velocity difference of the "collision" is 250 m/s, then the vehicle increases speed by 0.1 meter per second during the 20 millisecond "wrap". If it hits 100 nets per second (spacing 2.5 meters), that averages to 10 m/s².
The station deploys perhaps 2000 nets at 50 m/s in advance of vehicle arrival, perhaps 80 seconds deployment time to spread the nets into a 4000 meter row. The vehicle decelerates in 20 seconds, so 75% of the nets were in flight when it hit the first one, the last 25% before it "lands". The last 20 m/s of slowdown will probably be into a large net affixed to the station itself, with about two tonnes of net wrapped around the front of the five tonne vehicle.
Bring vehicle with accumulated nets into a processing area on the station. Peel off the nets one by one, repair and straighten them, and load them onto the net launcher for the next incoming vehicle.
No gram left behind, except for some vehicle and net abrasion.
The station will slow down; 1e6 kg-m/s of momentum was transferred to the vehicle. The station is presumably massive, 2000 tonnes or more, but it will slow down by a large fraction of a meter per second while launching nets. Some of those thousands of tonnes are solar panels and batteries, like the ablation laser stations, and some are multiple-redundant electric rocket engines (for example, VASIMR ) and the propellant for them. If the station makes up the thrust during net launch, and uses 20 km/s electric thrusters to do it over an average of 40 seconds (multiple arriving vehicles), it must manufacture 25000 Newtons of thrust, expend 1.25 kg/s of propellant, and use more than 250 MW to do so. That is more than 1250 tonnes of solar panel, or, as before, the discharge of 500 kg of lithium battery per second. Capturing for 1000 seconds, 500 tonnes of battery.
Double that to 1000 tonnes of battery; the net collisions dissipate energy. But if the batteries last 6 years (with on-orbit repair and refurbishment), they can capture 200 times their mass, perhaps 200,000 tonnes of incoming cargo, net after consumables and propellant and cargo shell recycling.
In the coming decades
One launch loop can support nearly 100 construction stations, in orbits spaced 900 seconds apart. Millions of tonnes of cargo per year. If some of that is converted into space solar power satellites, also at 200W/kg, that is 200 GW per year of added SSPS capability.
In six years, launch loops and cargo vehicles will scale up, perhaps by a factor of 10 if we can emulate the scaling practices of the semiconductor industry before 2000 AD. The loops can launch their own power supply. It may take less than 2 decades to deploy and use 50 TW of power satellites; if 10 of those terawatts are used for loop launch, that is 6 billion tonnes to orbit per year, five times current ocean cargo shipping rates. It is imperative that we do so with the absolute minimum of propellant atoms remaining in orbit, so obsessive focus on ultra-low exhaust orbital capture systems will be essential to the long term usability of cis-lunar space.
Thousands of million-tonne-scale construction stations orbiting through the van Allen belts will eventually intercept and "de-fang" most of those particles as they hit the stations. Soon, the van Allen belts will disappear, and their side effects (such as coupling solar storms to the Earth's magnetic field and to the global power grid) will disappear as well.
There are thousands of tonnes of orbiting debris today - we will need ultra-low exhaust systems for deorbiting that. We will also need to capture the exhaust propellant molecules the stations orbit through,rather than add additional sputtered surface atoms to the garbage that is already there. We should leave space cis-lunar space cleaner than it was before Sputnik.
Millenia from now, the propellant atoms we launch to earth escape will accumulate in solar orbit into a serious nuisance. We will need capture systems for those atoms, eventually. Due to conservation of angular momentum, we must drop mass into the Sun, or launch it to solar escape, However, "cis-asteroid-belt" space is a billion times the volume of cis-Lunar space, which in turn is 1000 times the volume of cis-GEO space, which in turn is about a 1000 times the volume of low-earth orbit, which is 1000 times the volume of the Earth's atmosphere. There is plenty of room for growth, if we clean up as we go.
No gram left behind!