A tether needs to be substantially more massive than it's payloads. Else a catch/throw would wreck the tether orbit.
In my last post I described how near earth asteroids parked in retrograde lunar orbits might be used as anchors and momentum banks for lunar orbital tethers.
What could we use to anchor a vertical tether in earth orbit?
When a satellite in geosynchronous orbit satellite dies, it's sent to a graveyard orbit about 300 km above geosynch. According to IO9 there are more than a hundred sats in this graveyard. There will be more as time goes on.
Boost one of these dead sats 25 km higher than the graveyard orbit and dangle a 25 km tether. The tether foot will be moving about 10 kilometers/hour or about 5.5 mph with regard to the sat graveyard. As satellites are caught, momentum can be added via ion engines. With an ion engine's high ISP, the satellite collector's reaction mass can be small with regard to the mass of the satellites collected.
There's little plane change delta V since most the GEO sats are equatorial.
This would cleanse the geosynch neighborhood of orbital debris. When the dead sats are collected into a single mass, cross section is much smaller than a multitude of satellites. Thus likelihood of debris generating impacts is much smaller.
Some parts of these dead sats may be salvageable. Many may still have working solar arrays, for example. Although it is possible salvage issues could be a road block to this scheme. Those parts not salvageable would still have value just as a source of orbital momentum.
Boost this ball of dead sats to an orbit 10,000 km higher than GEO and extend a tether 10,000 km up and 7,000 km down. Now we have a well anchored 17,000 km tether. Tether foot is 3,000 km above geosynch so there's no chance the foot will hit an GEO sat. There is also less chance of tether damage from an impact with orbital debris.
A payload released from this tether top will reach the moon.
If we use Kevlar with a tensile strength of 3.6 giga pascals and density of 1.44 grams per cubic centimeter, taper ratio for this tether is 1.18. Tether to payload mass ratio is less than 1.
The tether center is moving about 2.78 km/s. Grave yard sats move about 3.06 km/s. So delta V to raise the ball of sats is only .28 km/s.
From LEO it takes around 3.2 km/s to rendezvous with this tether foot. About what it takes for a normal Trans Lunar Insertion from LEO. This was disappointing to me.
However this tether could receive mass from an asteroid parked in a lunar orbit. It could then send asteroidal mass to lower orbits.
If lower tethers were receiving mass from above as well as from earth, it might be less costly to give the lower tethers a substantial anchor mass.
Here are three possible tethers: the super GEO tether already described, a sub MEO tether and a super LEO tether:
Tether to payload mass ratio is also less than one for both the Super LEO and sub MEO tethers.
The apogees and perigees of these red ellipses match the tether velocities at rendezvous. So almost no propellent would be used for catches and throws.
From LEO it takes .5 km/s to reach the Super LEO Tether. From there the relay of tethers can deliver spacecraft to the moon.
Once In The Moon's Neighborhood...
The Super GEO tether tosses payloads to a 384,400 km apogee. 384,400 km is the moon's distance from earth. Velocity of this ellipse's apogee is about .54 km/s while the moon's speed is about 1.01 km/s. Vinf with regard to the moon is about .48 km/s.
In my earlier post I described an asteroid anchored tether that could toss stuff from the moon with a Vinfinity of 1.6 km/s. Tether to payload mass ratio would be around 3. If we only need a Vinfinity of .48 km/s, a less massive tether would do:
Tether center's 24,200 km from the moon's center. Tether foot 13740 km, tether top 39000 km. If we use Kevlar with 3.6 giga pascal tensile strength and 1.44 g/cm^3 density, the tether to payload mass ratio is less than 1/4.
Dropping from this tether foot, a payload would impact the moon at 2.23 km/s.
It'd also be somewhat easier to park a near earth asteroid in this higher lunar orbit. See the Keck Report for a proposed method to park rocks in lunar orbit. For asteroids with orbital energy just above zero it is doable to park them in an high lunar orbit.
Up Momentum as a Valuable Commodity
Catching from a lower orbit and throwing upwards will sap a tether's orbital momentum. Earlier I had mentioned that ion engines using xenon as reaction mass could restore momentum.
But asteroidal mass from above is a source of up momentum.
With two way traffic, the need for xenon is reduced. Momentum boosting maneuvers could be balanced with momentum sapping catches and throws. The need for reaction mass would be largely eliminated.
An asteroid anchored tether in lunar orbit would be helpful in capturing more asteroids to lunar orbit. There's a lot of near earth asteroids in accessible orbits, so there's a massive source of up momentum.
How about using Lorentz force to change orbital momentum? As an electron moves up (away from earth's center) it passes through earth's magnetic field and the tether is pushed east, boosting momentum. Sending electrons down will give a westward push, reducing momentum.
But this relies on one way current. If the circuit is closed, electrons move up as well as down and there's no net Lorentz force.
The ionosphere can close a circuit in low earth orbit. The tether can pick up electrons from the ionosphere as well as discharge electrons into the ionosphere.
But the tethers described here are above the ionosphere. Using Lorentz force doesn't seem to be an option.
But I don't know that much about electrodynamic tethers, I could be wrong. If someone corrected me, it'd be a pleasant surprise.
Why I Don't Like Rotovators
Why my obsession with vertical tethers? Yes, rotovators could be shorter. But there's several reasons I don't like rotovators.
Taper Ratio and Tether to Payload Mass Ratio
Tension in rotovators comes from so called centrifugal force, ω2r. At the Space Stack Exchange 2012rcampion takes a look at a sling's tether taper ratios. Campion's results look a lot like Moravec's equations.
As tether tip speed grows, taper ratio soars. Short tethers capable of a good throw would be quite massive. According to this Tether.com pdf, a LEO to GTO rotovator capable of tossing 5 tonne payloads would need to mass 50 tonnes (3rd paragraph, page 4). A 10 to 1 tether to payload mass ratio.
In contrast, a vertical tether's tension comes from centrifugal force and gravity, ω2r - μ/r2. Gravity mitigates stress from centrifugal force and taper ratio grows a lot more slowly. All the vertical tethers described in this post have a tether to payload mass ratio less than 1.
Vertical tethers do need an anchor mass. But anchor mass can be very useful. I'd like to see lots of solar arrays at the tether centers. Solar arrays could power electrolysis plants to crack water into bi-propellent, move elevator cars up and down, and occasionally power Hall Thrusters to adjust the tether's orbit.
A rotovator is good for catches and throws when it's vertically aligned. But it's well aligned only for a very brief time during its spin. The rotovator must be correctly positioned when a launch window occurs. Ditto for catching from a Hohmann orbit.
Catches are harder. As a payload approaches a rotovator, the tip remains on its path for a brief time and then either zooms up or down (from the payload's point of view). In contrast, the tips of a vertical elevator remain at constant altitude.
A vertical tether stays vertical due to tidal acceleration gradient. It seems to me a rotovators attitude would need to be adjusted from time to time.
Possible Imports to Earth and LEO
I believe the most important import from asteroids will be water.
My last two blog posts are more or less in response to Jon Goff's The Slings and Arrows of Outrageous Lunar Transportation Schemes: Part 1 - Gear Ratios. Goff pointed out that only a small fraction of propellent mined at the lunar poles could be delivered to LEO.
Ever since Goff wrote that, I've been trying to think of ways to deliver extraterrestrial propellent to where it's needed.
"Wait a minute," you might be thinking, "This guy has just described a transportation system using momentum exchange and ion engines. Why is he still stuck on stone age chemical propellent?"
I believe the biggest obstacle to fully reusable spacecraft is an upper stage's 8 km/s re-entry. Hall Thrusters decelerate too slowly to help with that plunge.
A tether foot low enough to drop payloads into low velocity suborbital paths would be vulnerable to collision. Below 1000 km, space is full of sats and debris.
What the Super LEO tether could do is deliver propellent to LEO. An ellipse from the Super LEO foot would take .5 km/s to circularize at perigee. And some of that .5 km/s might be accomplished by aerobraking.
An upper stage refueled at LEO could do a healthy burn to lose most the 8 km/s. The upper stage might also beef up it's dry mass with structural support and TPS, also from asteroids. Given these options, upper stage re-use is very doable. If upper as well as booster stages can be economically re-used, the dream of cheap space access is realized.
Many asteroids have high concentrations of the platinum group metals. Right now these are precious due to rarity. But should they become more available, there are numerous ways they can be used.
Rare earth metals have many uses. Rare earths actually aren't rare. But they're hard to mine in an eco-friendly way. I would much rather see them mined on a lifeless, barren rock than in earth's biosphere. An asteroid in lunar orbit would make the moon's KREEP more accessible. Besides rare earths, KREEP also contains uranium and thorium, possible sources of energy.
As mentioned earlier, imported uranium and thorium could fuel terrestrial power plants.
The earth intercepts only .45 billionths of the sun's light. We're using only a tiny fraction of possible solar energy.
If we use solar energy to refine extra-terrestrial ore and import commodities to earth and LEO, in a sense we're importing energy.
Besides energy for refining, imported commodities would also require energy for transportation. To get a kilogram from just above C3 to LEO takes about 512 mega-watts. Tether momentum exchange could accomplish most of this. But it's energy used, regardless of source.
A source of up momentum would be a major game changer. A first step towards acquiring this source would have been the early version of the Asteroid Redirect Mission (ARM). This is doable. But for now it looks like popular opinion will keep this from ever being funded.
I'll continue singing the praises of asteroids and ARM. God willing, my small voice will have some influence.