Saturday, August 27, 2016

Pluto Charon Elevator

Double Tidal Locking

Pluto and Charon are mutually tidally locked. That is, they both present the same face to the other planet all the time. They hover motionless in each other's sky. Pluto is in Charon synchronous orbit and Charon is in Pluto synchronous orbit.

A tether could be extended from Pluto's near point to Charon's near point. Since the orbit is so nearly circular, there would very very little flexing of this tether.

Minimum Tether to Remain Aloft

To remain aloft, a tether anchored to Charon would need to extend past the L1 point more than 10,000 kilometers to within nearly 2,500 kilometers of Pluto's surface.

This tether would be more than 15,000 kilometers long. Using Wolfe's Spreadsheet we find Zylon taper ratio is 1.13. Tether to Payload mass ratio is .88. This is with a safety factor of 3.

All The Way To Pluto

Extending the tether an additional 2,500 kilometers anchors it to Pluto's surface.

Taper ratio is about 1.7 and Tether to Payload mass ratio is 14.36.

Still acceptable but dramatically different from a tether only 2,500 shorter. This is because we dropped the tether foot into a much steeper part of Pluto's gravity well.

Net acceleration is .62 meters/second2 at the Pluto end of the elevator. Very close to Pluto's surface gravity. At the Charon anchor net acceleration is -.28 meters/second2. Very close to Charon's surface gravity. It is negative to indicate it's in the opposite direction from Pluto's gravity.

At L1 net acceleration is zero.

It's easy to see most of the stress newtons come from the close neighborhoods of Pluto or Charon. It might be worthwhile to build standard compressive towers at the elevator anchor points.

What's The Point?

Pluto's surface escape velocity is 1.2 km/s. Charon's surface escape velocity is .6 km/s. It's not that hard to get off the surface of Pluto or Charon. So what's the point of an elevator?

Space craft with very good ISP have meager thrust. With such space craft soft landings on Pluto or Charon would not be possible. Nor could they leave the surface of these planets.

But a low thrust craft could dock with the elevator at L1.

From L1 a small nudge could send passengers or cargo towards Pluto or Charon. And gravity would pull it the rest of the way down.

I believe Pluto Charon L1 would become  a major metropolis on the corridor between two major city states as well as a port to the rest of the solar system.

Will humans reach Pluto?

The Edge of Sunlight

Sunlight falls with inverse square of distance from sun. Asteroids 3 A.U. from from the sun will receive 1/9 of the insolation we enjoy on earth. Sun Jupiter Trojans at 5 A.U. will get 1/25 the sunlight. We could compensate by constructing large parabolic mirrors to harvest sunlight.

Giant parabolic mirrors could harvest sunlight for spin habs.

But Pluto  has a 30 A.U. by 49 A.U. orbit. And most of the time it dwells in the neighborhood of aphelion. 1/492 = about 1/2400. Mirrors for the KBO nation states would need to be vast. Mike Combs wrote a neat story featuring these sorts of mega mirrors. As much as I enjoy Mike's story, I don't think such monster mirrors are practical.

Fusion Power?

Will our technology achieve practical fusion power plants? Maybe. If so, that would vastly expand our possible frontiers.

The 4th Space Frontier

There's nothing like logistic growth ceilings to motivate opening a new frontier. As we settle and fill up one frontier, we start looking over the horizon. I'm going to make some wildly speculative predictions. This is a science fiction blog, after all.

1st space frontier: NEAs, Luna, Mars, Phobos and Deimos. This would give us one or two millennia of unrestrained growth.

2nd space frontier: The Main Belt. Three millennia of exponential growth. Ceres will be the capital of this United Federation of Main Belt Nation States. This frontier will open within a century or two after we establish a strong foothold on Mars/Phobos/Deimos.

3rd space frontier: The Sun Jupiter Trojans. The Hildas will be our ride from the Main Belt to the Trojans. It will take five hundred years to fill the Trojan petri dish.

4th space frontier: The Kuiper Belt as well as the icey moons of Saturn, Uranus and Neptune. As mentioned earlier, this would require practical power sources other than sunlight. Pluto will be the capital of the United Federation of Kuiper Belt Nation States. This frontier will take 10 millennia to expand into.

5th space frontier: The Oort. The nation states of the Oort will be separated by vast distances. They will be more isolated than even the nation states of the Kuiper. There is a strong incentive to become less reliant on trade and more self sufficient. 20 millennia of unrestrained growth. By the time we reach the outer Oort, nation states will be self sufficient biomes. There would be nothing preventing an outer Oort nation state from achieving solar escape velocity and leaving our sun's sphere of influence.

The Outer Oort Nation States will be natural generation star ships.

Charon Elevator through L2

Enough wild eyed fantasy. Back to mundane stuff like space elevators in the Kuiper Belt.

To maintain tension and remain , an elevator from Charon's far point through the Pluto Charon L2 would need to extend 41,000 kilometers. With a safety factor of 3, Zylon taper ratio would be 1.14. Tether to Payload mass ratio would be  about .3.

Small Problem: Styx

Pluto's moon Styx orbits at a distance of 42,600 kilometers from Pluto. Charon orbits at about 20,000 kilometers from Pluto. So a tether from Charon's far point can only extend about 22,000 kilometers before it runs the risk of an impact with Styx.

A counterweight would need to be placed on the elevator somewhere below the orbit of Styx. If placed just below the orbit of Styx, the tether top could impart a velocity of about .5 km/s. Which would be helpful for injection into heliocentric transfer orbits to other destinations in the solar system.

This elevator could also help with transportation between Charon and the other moons of Pluto: Styx, Nix, Kerboros and Hydra.

An ion craft could also dock with Pluto Charon L2, so L2 could also serve as a port to the rest of the solar system. There are heteroclinic paths between L1 and L2 so transportation between the two elevators would be easy.

Pluto And I Share An Annivesary

Clyde Tombaugh discovered Pluto on February 18, 1930. February 18 is my birthday! So I guess it's only natural I'm interested in this body, we're practically twins.

Wednesday, August 17, 2016

Three Orbital Tethers

This post revisits Orbital Momentum As A Commodity. But now I will examine these tethers using Wolfe's spreadsheet.

I envision 3 equatorial tethers to move stuff back and forth between LEO and the lunar neighborhood:

The location of these vertical tethers avoids zones of orbital debris:

The orange regions, LEO, MEO and GEO, have high satellite and/or debris density. Thus tethers in those regions would be more vulnerable to damage from impacts.

Unless elevator mass is lot more than the payloads, the acts of catching or throwing could destroy the tether orbit. At first it looks like the need for a substantial anchor mass is a show stopper. But there are a large number of dead sats in equatorial orbits. By one estimate,  there's 670 tonnes in the graveyard orbit above geosynch.

The dead sats gathered might have functioning solar arrays. According to this stack exchange discussion, solar arrays degrade by 2 to 3% a year due to radiation, debris impacts and thermal degradation. Thus a 20 year old array could still be providing 50% to 66% of the power it delivered at the beginning of its life. The parabolic dishes for high gain antennas might also be salvageable.

Whether functioning or not, solar arrays as well as other paneling might be used as shades to keep propellent cold. If our tethers receive propellent from the moon or from asteroids parked in lunar orbit, shades would help with cryogenic storage.

Consolidating dead equatorial satellites would reduce their cross sectional area and help solve the problem of orbital debris.

Super GEO tether

The circular orbit pictured above is 10,000 km above Geosynchronous Earth Orbit (GEO). The lower part of the tether has a length of 7,000 km and the upper tether is 10,340 km in length.

A Space Stack Exchange answer estimates there are 670 tonnes of dead sats in the geosynch graveyard orbit.

Delta V to raise the dead sats to this higher orbit is about .28 km/s. This might be accomplished with ion engines. Also the elevator could be used to send some to the sats towards the lower MEO tether. This would help with the .28 km/s delta V budget.

Upper Super GEO Tether, 10,340 km long
 Safety Factor 3 Zylon taper ratio: 1.38 Tether to payload mass ratio: .78 Tether top radius 62,504 km Tether top speed: 3.3 km/s Tether top net acceleration: .07 m/s2 (.007 g) Payload apogee: 384,400 km Payload apogee speed: .53 km/s

The payload apogee is at lunar altitude and the payload's moving .53 km/s. The moon moves at about 1 km/s. So Vinf with regard to the moon is about .47.

Lower Super GEO tether, 7,100 km long
 Safety Factor 3 Zylon taper ratio: 1.21 Tether to payload mass ratio: .47 Tether foot distance from earth 45,000 km Tether foot speed: 2.4 km/s Tether foot net acceleration: .07 m/s2 (.007 g) Payload perigee: 21,450 km Payload perigee speed: 5 km/s

The tether foot drops a payload to rendezvous with the MEO tether.

Sub MEO Tether

The circular orbit of the Sub MEO anchor mass is has a radius of 19,425 km. To get satellites from the super synchronous graveyard orbit to this orbit takes about 1.4 km/s. Some of that 1.4 km/s might be accomplished with the super GEO tether. Sending mass downward would help push the remaining GEO sats upward.

Upper Sub MEO Tether, 2,050 km long
 Safety Factor 3 Zylon taper ratio: 1.30 Tether to payload mass ratio: .61 Tether top distance from earth 21,450 km Tether top speed: 5 km/s Tether top net acceleration: .3 m/s2 (.03 g) Payload apogee: 45,000 km Payload apogee speed: 2.4 km/s

The payload apogee radius and speed matches the foot of the super  GEO tether's radius and speed.
The top of this tether's radius and speed matches the payload perigee and speed sent from super GEO tether. The Sub MEO and Super GEO tethers can exchange payloads with minimal delta V at tether/payload rendezvous.

Lower Sub MEO tether.
 Safety Factor 3 Zylon taper ratio: 1.35 Tether to payload mass ratio: .78 Tether foot radius 17,375 km Tether foot speed: 4.1 km/s Tether foot net acceleration: .38 m/s2 (.038 g) Payload perigee: 9,680 km Payload perigee speed: 7.3 km/s

The Low Sub MEO tether sends and receivse payloads to and from the upper Super LEO tether.

Super LEO Tether

The anchor mass is in a circular orbit of radius 9300 km.

Upper Super LEO Tether, 765 km long
 Safety Factor 3 Zylon taper ratio: 1.4 Tether to payload mass ratio: .84 Tether top radius 10,065 km Tether top speed: 7.1 km/s Tether top net acceleration: .11 m/s2 (.011 g) Payload apogee: 17375 km Payload apogee speed: 4.1 km/s

The payload apogee is at lunar altitude and the payload's moving .53 km/s. The moon moves at about 1 km/s. So Vinf with regard to the moon is about .47.

Lower Super LEO tether, 450 km long
 Safety Factor 3 Zylon taper ratio: 1.13 Tether to payload mass ratio: .29 Tether foot distance from earth 8,844 km Tether foot speed: 6.2 km/s Tether foot net acceleration: .7 m/s2 (.07 g) Payload perigee: 6,778 km Payload perigee speed: 8.3 km/s

Perigee altitude is about 300 km. Circular orbital speed at this atltitude is about 7.7 km/s. To send a LEO payload on it's way to the Super LEO tether would take about .6 km/s.

Sending a payload from the tether to LEO can take less than .6 km/s as the delta v needed for circularizing can be provided by aerobraking.

Total Tether Mass to Payload Ratio

We've looked at a total of 6 tether lengths, the upper and lower parts of 3 vertical tethers.

Tether Mass to Payload Mass Ratios & Lengths
 T/P Length (km) Upper Super GEO .78 10340 Lower Super GEO .47 7100 Upper Sub MEO .61 2050 Lower Sub MEO .78 2050 Upper Super LEO .84 765 Lower Super LEO .29 450 Total: 3.77 22,755

Thus 38 tonnes of Zylon could accommodate 10 tonnes of payload. That's not too bad.

A much larger problem is the anchor mass needed for each tether. There are lots of dead sats just above GEO that could be gathered for the Super GEO tether anchor mass. But anchor masses for the sub MEO and super LEO tethers will be more expensive. This is a possible show stopper.

Facilitating Momentum Exchange

Using Hall Thrusters to restore momentum.

Sending mass from LEO to a lunar height apogee saps our tethers' orbital momentum. The momentum hit is somewhere around payload mass * 4 km/s. Orbital momentum can be restored gradually with ion thrusters. Hall Thrusters can expel xenon with a 30 km/s exhaust velocity.

Plugging these numbers into the rocket equation:

Propellent mass fraction = 1 - e -4/30 = ~.125.

About 1/8. So to make up for the momentum lost throwing 7 tonnes of payload, we'd need a tonne of xenon. Better than chemical but still expensive.

Lunar or NEA propellent as a source of up momentum.

Some Near Earth Asteroids (NEAs) can be parked in lunar orbit for as little as .2 km/s. Carbonaceous asteroids can be up to 40% water by mass (in the form of hydrated clays). There may be rich water ice deposits in the lunar cold traps. So far as I know, these are the most accessible potential sources of extra terrestrial propellent.

Catching propellent from higher orbits would boost a tether's momentum. Dropping this payload to a lower tether would also boost momentum.

Thus up momentum can be traded for down momentum. Xenon reaction mass to maintain tether orbits can be cut drastically with two way traffic.

Jon Goff's gear ratios

Jon Goff has pointed out it take some delta V to get propellent from the moon's surface to LEO. Thus only ~10% of propellent mined lunar cold traps would make it LEO. See his blog post The Slings And Arrows of Outrageous Lunar Transportation Schemes Part-1 Gear ratios.

Well, lunar propellent could be a source of down momentum for the Lunar Sky Hook I described recently. And a source of up momentum for the Trans Cislunar Railroad this blog post looks at. NEA propellent could also be a source of up momentum for the Trans Cislunar Railroad.

Using propellent as a source of tether up momentum I believe it's plausible for 40% of the lunar propellent to make it to LEO. In which case it becomes plausible to use reaction mass to mitigate the extreme conditions of re-entry.

Breaking the Genie's Bottle

The human race is a genie in a bottle. Given Tsiolkovsky's rocket equation, it's enormously difficult to cross the boundaries that confine us. But given infrastructure and resources at our disposal, we can build bridges to larger frontiers.

Monday, August 8, 2016

Lunar Sky Hook

Vertical Lunar Tether In A Polar Orbit

This sky hook is a gravity gradient stabilized vertical tether. It's in a polar orbit so it will pass over the poles as well as the lower lunar latitudes.

Unlike an equatorial orbit, there are only two occasions during a lunar orbit where a tether's Vinf velocity vector is anti-parallel to the moon's velocity vector. So launch windows to earth would only occur each two weeks. That's still pretty often. These occasions are also good times to rendezvous with the tether.

Playing with earth moon three body simulations, polar orbits seem to remain stable up to a radius of around 20,000 kilometers. That is where I will set the anchor mass at the balance point of this sky hook. I believe this is far enough above the lunar surface that the mascons won't damage this tether's orbit.

Asteroid Anchor Mass Via a Keck vehicle

What to use for the anchor mass? With the asteroid retrieval vehicle proposed in the Keck Report, it is possible for a vehicle of moderate mass to retrieve a much larger mass to the earth moon neighborhood. The Keck authors believe a rock could be placed in high lunar orbit for around .17 km/s. A lunar orbit with a 20,000 km radius has a speed of around .5 km/s. I believe it would take around .7 km/s to park a rock in the orbit we want.

The Keck vehicle includes solar panel arrays and Hall ion thrusters. These would be great to have on a vertical tether. It takes awhile for ion engines to impart momentum, but given time they're about ten times as efficient as the best chemical rockets. A tether can build up momentum over time but release it suddenly. Thus they are a good way to enjoy an ion engine's great ISP and an Oberth benefit.

As well as adjusting the tether's orbit the Keck vehicle's solar arrays might also power elevator cars moving up and down the tether. If water is exported from from the lunar cold traps to the tether, the arrays might also crack water into oxygen and hydrogen bipropellent. There are a number of possible uses for this power source.

Upper Tether

The tether length above the anchor mass can be built in increments. I imagine the tether growing longer and more able with time. Here are three possible stages:

To EML2 or EML1

EML1 and 2 are about 65,000 km from the moon. To reach this apolune, we'd need an upper tether length of about 2700 kilometers. Using Wolfe's spread sheet, this tether length has a taper ratio of 1. With a safety factor to 3, tether mass to payload ratio is about .02.

This is pretty good. I believe this low stress tether length could accommodate copper wires to transmit power to the elevator cars.

Once at apolune, I believe it would take about .3 km/s to park the payload at EML2 or EML1.

EML2 is a good staging location should we want to travel to and from destinations beyond the earth-moon neighborhood.

To a Perigee at Geosynchronous Orbit

Transfer orbit from GEO to the moon is about a an ~36,000 x 378,000 ellipse. Apogee speed is about .45 km/s. The moon's speed is about 1.02 km/s. So the tether needs to hurl a payload to a Vinf of (1.02-.45) km/s or about .57 km/s.

To achieve this Vinf our tether needs to be 12,200 km. Zylon taper ratio is 1.09. With a safety factor of three, Tether to payload mass ratio is about .167. So a ten tonne tether could accommodate a sixty tonne payload. This is still pretty good. A power cable along this length is also doable.

Perigee velocity of our transfer orbit is ~4.13 km/s. Geosynch orbit velocity is ~3.07 km/s. If the transfer orbit and destination geosynch orbit are coplanar, geosynch circularization would be about 1.06 km/s. But I expect that would be the exception rather than the rule. If the orbit inclinations differ by 20ยบ, 1.6 km/s would be needed to park in geosynch.

To a Perigee at Low Earth Orbit.

A 300 x 378,000 km orbit has apogee velocity of ~.19 km/s. (1.02 - .19) km/s = .83 km/s.

To throw a payload to a trans earth orbit, our tether needs to impart a Vinf of .83 km/s. This takes a tether length of 19,200 kilometers. With a safety factor of three, Zylon taper ratio is 1.2. Tether to payload mass ratio is .38.

If perigee is through earth's upper atmosphere, aerobraking can provide a large part of the 3.1 km/s delta V for circularizing at LEO.

Lower Tether

Again, the tether length below the anchor mass can be built in increments. Incremental growth with time is more doable than trying to do the whole length in fell swoop. Here are some possible steps along the way.

To a Perilune at Low Lunar Orbit.

To drop a payload to a 90 km altitude perilune, length needs to be 7360 km. Given a safety factor of 3, Zylon taper ratio is 1.06. Tether to payload mass ratio is .15.

Velocity of transfer orbit's perilune is about 2.2 km/s. Low lunar orbit is about 1.6 km/s. It'd take about .6 km/s to circularize at low lunar orbit.

To the Moon's Surface, Impact Velocity 1 km/s.

If the tether is extended to a length of 17890 km, tether foot altitude is about 370 km. Dropping a payload from this tether foot would result in a 1 km/s impact.

Given a safety factor of two, Zylon taper ratio is 2.88. Tether to payload mass ratio is 26.87.

Note the safety factor is less than in the other scenarios. As we descend further into the moon's gravity well, stress climbs more rapidly. It would be more difficult to include copper wires for power along the lower parts of the tether.

To a Tether Foot Just Above the Moon's Surface.

Dropping the tether foot to an altitude of 10 kilometers gives us a length of 18,252 km. Safety factor of 2 and Zylon taper ratio is 3.72. Tether to payload mass ratio is  about 51.

Dropping from this tether foot, a payload would impact the lunar surface at .184 km/s.

A .2 km/s payload delta V budget for soft landing seems quite doable. Likewise it would take about .2 km/s to launch a payload from the lunar to rendezvous with the tether foot.

However dropping the tether foot this far is considerably more ambitious than the other scenarios described above.

Kim Holder noted such a tether might serve as transportation between locations on the moon.

Without a tether, going from pole to pole would take about 3.4 km/s: 1.7 km/s to launch and another 1.7 for soft landing. Going from equator to pole would take 1.53 km/s to launch and another 1.53 km/s for a soft landing, totaling 3.06 km/s.

So a 18,000 km lower lunar tether length would make travel about the moon easier.

A Location to Process Asteroid Ore

It takes about .6 km/s to park ore from some of the more accessible asteroids in 20,000 km lunar orbit. If rendezvous with the tether top is doable, it could take considerably less.

I envision infrastructure accreting about the tether anchor mass 18,262 km above the lunar surface. Water, platinum, gold, rare earth metals, and other materials could be extracted at the anchor. Refined commodities could climb to the top of the tether and then tossed earthward.

A Synergy Between The Moon and Near Earth Asteroids

Moon and asteroid enthusiasts are often at odds with one another. They should be allies. In terms of delta V, it's a lot easier to park asteroids in lunar orbit than lower earth orbits. And given growing infrastructure in lunar orbit, the moon's surface becomes more accessible.