Monday, August 8, 2016

Lunar Sky Hook

Kim Holder has been urging me to do this blog post. Her comments in various forums have been helpful in thinking about this.

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.

Travel About The Moon

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.


Chris Wolfe said...

Apologies in advance for this giant comment...

Sounds clear and rational. The material demands for a travel tether sound easily achievable with current technology. An SEP asteroid retrieval vehicle is within the range of our current capabilities. Let's do it.

A 20,000 km lunar orbit has a v of 495 m/s and a period of 70.487 hours, a bit under 3 days. The anchor would complete 9.3 orbits for each lunar orbit around the Earth, so each orbit would precess 38.7° westward around the equator.

The down side is that due to precession any given spot on the surface would only have a perfect launch opportunity every ~2.5 years. If the launch system has enough dV to deviate by about 17° (which is an attainable amount for chemical systems but a value of concern for fixed-position mass drivers) then they get a launch opportunity once per lunar month (27.3 days) at the equator. Higher latitudes allow more frequent opportunities, while sites near the poles (meaning at a latitude no less than 90 - launch inclination range) would have opportunities every orbit (every 7 hours). However, the vector of launch may be important for polar sites depending on the mechanism of capture; a chemical system or a sling launcher would have no trouble but a fixed rail installation could have problems.

Matching inclination with the tether from the surface would require up to a 20° plane change (about 172 m/s for a circular orbit) at rendezvous. The tether could potentially absorb this energy at capture but it would tend to deflect the path of the tether 'horizontally' and induce oscillations. I know that one of the points of a tether is so that the payload doesn't have to circularize itself, but not every use case will have the payload at zero effective speed at capture.

If the anchor was used to service specific surface bases, let's say at 30° intervals around the equator, the altitude would have to be fixed such that the anchor completes 12 orbits for each orbit of the Moon around the Earth. That would be every 2.277 days, radius of 16,877.792 km, velocity of 539m/s and longest shadowed time of 107 minutes. There are solutions for any integer factor or multiple of 360°, but not all of the resulting orbits are stable. If 20,000 km is the upper limit then 36° / 10 orbits per month is the slowest stable configuration. Mascons reportedly allow a stable orbit at 86° down to ~100km altitude (r=1,836km, t=1.96 hours, p=1.076° per orbit), so the lower limit of stability is likely to be ruled by the dV requirements for parking the anchor mass.

Rok said...

On topic of upcoming rotovator post. Has it been ever considered to use angular momentum of the rotovator to lessen the drop in orbit of the system?

The thought i had without doing any math was to catch the payload and then extend the tether so that rotation matches orbital period. Basically levelling the tether in an orbit that was the center of mass after payload capture.

If it actually weighs any less and or is actually possible for LEO.

Force on tether would be less than full rotovator, and presumably half of rotational energy would go to brakes of some kind.

DougSpace said...

I have seen a number of posts on various sites about tethers to transfer payloads from and to various locations. But it seems to me that this is one of those ever-future things without a clear near-term point when it is likely to be built by someone specific. Is there something about the concepts which makes them unlikely to be realize in the near future?

Hop David said...

Doug, pop wisdom tells us tethers have been tried but failed in spectacular fashion. At least I think that's the common perception. While some tether missions have failed, some have been successful. Here's a Wikipedia article on tether missions. Japan hopes to do a tether mission in the near future.

Another problem is I believe people conflate tethers with the much less plausible Clarke elevators anchored to a planet surface.

Kirk Sorensen was pushing for NASA investment in momentum exchange tethers during his 10 year stint at the agency. I don't know if it's a priority at this time. Sometimes it seems to me NASA's real purpose is to provide employment in certain congressional districts.

There are a couple of commercial entities researching tethers: Liftport and Tethers Unlimited. A few new space companies might have healthy revenue streams. But outfits like Blue Origin or SpaceX are the exception rather than the rule. Most new space workers labor hard and long for little or no money, living on idealism. I regard these folks as 21st century saints.

I believe space tethers are technically doable. Devoting even a third of the SLS/Orion budget to this technology would likely give us a number of game changers. Unfortunately, I don't see this coming to pass.

These tether scenarios I'm describing are merely the daydreams of an old space cadet.

DougSpace said...

Has there been a demonstration of momentum exchange using tethers on Earth that is clearly applicable to space? When I Google Images "space elevator challenge" I find lots of demonstrations. But I can't seem to find anything but diagrams and illustrations for "momentum exchange tethers" or "demonstration".

It looks like Tethers Unlimited is now known more SpiderFab and LiftPort has done only elevator demos and, as far as I can quickly tell, not demonstrated (angular) momentum exchange as such.

It seems to me that, for example, a rotovator could be demonstrated on Earth using a horizontal orientation.

Rok said...

Testing it on Earth wouldnt do much else than confirm how momentum works.

Problems needed solving are control, stability and economics...

Anonymous said...

What about a flyby rotovator? An asteroid bola lowers a backspun asteroid fragment to the surface (refined product) the other end tows heavy object up and away from the Moon?

Hop David said...

Anonymous, please give yourself a label. Several people labeled "anonymous" can lead to confusion when holding a conversation.

Three reasons I prefer vertical tethers over rotovators.

1) Marking a catch is somewhat more difficult with rotovators. Best time to make a catch is when the tether is near vertical which is only a small fraction of the time.

2) For vertical tethers gravity gradient keeps the tether aligned to local vertical. I believe control of a rotovator would be much more difficult.

3) With rotovators taper ratio sky rockets as angular velocity and tether radius go up. With vertical tethers the gravity gradient somewhat mitigates the acceleration from centrifugal force. The taper ratio doesn't shoot up as fast with vertical tethers.

That said, rotovators are interesting. I hope to look at some rotovator scenarios. But I will be honest and confess that I haven't built a satisfactory model of a rotovator. Not only centrifugal force but tidal force needs to be accounted for. I didn't even the make the model for vertical tethers, I stole it from Chris Wolfe. I think I can adapt Wolfe's spreadsheet to rotovators but haven't had the time or energy.

Unknown said...

Hop, you have given me a reason to download Kerbal Space Program again and spend some time on it, so i can get a feel for the factors you mention here. I have no sense of how changes in orbital inclination affect delta V, and i'm struggling with some other things, too.

So, a vessel at the upper end of the tether is dragged by the whole tether at a higher orbital speed than the orbital speed at that altitude, so when it is released, it will move further outwards into an elliptical orbit, right? I had to struggle for a while to get that. So if it is released at the right moment, it's arc will intersect with EML1, or EML2, and then it brakes to enter a halo orbit there or dock with a station. Ok, i think i get that now... So, i guess that release also need to happen when the alignment is right for launch to Earth...

My head is full of thoughts now, so i think i'm going to post a series of comments to try to make this more organized. For now, i'm thinking about Chris Wolfe's comment above. I had thought a bit about this issue too (with much less sophistication). The tether of this kind i had originally proposed was only 3000 km long, and i didn't even think about an upper tether, i was just looking for a way to get stuff between the poles and the equator in high volume as cheaply as possible. That allows for passes close by the equatorial colony much more often.

Now, i know you try to design for the real world (you poor thing), but i was vaguely playing with the idea of putting in 2 tethers to make a complete system - a polar orbit tether, and an equatorial orbit tether. Might that make sense? The 3000 km figure was sort of picked out of the air, it allows for hopping between pole and equator for less than a third of the delta V. Another tether orbiting the equator also with a COG at 3000 km, and an upper tether of length sufficient to put a released vessel into a transfer orbit to EML2, say, seems like it might be pretty sweet.

That didn't occur to me until long after i'd posted about this on space.stackexchange. The Keck style mission you mention is of course awfully expensive to do twice for this, but the upper stages used to get the payloads to Lalande crater could be used for the equatorial tether, if you could manage to shepherd them together. I don't know how the quantity of Zylon in this polar model would compare to the scheme i'm talking about... in fact i realize this is would require a lot of calculation to consider, i just felt a need to throw it out there.

An ion-drive cargo ship from Earth could dock with that equatorial tether if it had a reasonable complement of maneuvering thrusters, right? The polar tether could be almost entirely for local transport. For my particular purposes on Moonwards, that makes sense. For the many cases that assume the base is at the poles, maybe it doesn't. Then again, even launching to the polar tether, braking and landing on the surface, and then launching again to meet the foot of the equatorial tether is still around half the delta V needed to launch from the surface towards Earth from the pole, and you can do it at any time.

Thanks a million for this post Hop, it is a big help to me :)

Unknown said...

I have one question - You are talking here about sky hook's, which means rotating structures ? Not stationary cables placed in LSO ?

Hop David said...

Wojtek, (Googling...) It seems sky hook is usually used as a word for rotovator. So I guess I have abused the term.

The structure I'm looking at here rotates once orbital period, about 70 hours. Which means it remains aligned to the local vertical.

My apologies for sloppy terminology.

Unknown said...

No problem,
I got interest in sky hook's after SevenEves lecture (they were named "Hanger" there) and Your blog is great source of informations about them ;)
If I can ask one more question:
Let say we have rotovator - maybe in LLO. Would it be possible, to change the structure length (fold the wire) to alter ships trajectory and speed? Lets say this way:
1. ship start from Moon Surface.
2. He goes to LLO and dock to rotovator.
3. During the rotation, we start to fold wire - the length of the structure reduce, but we gain speed - same like ballerina folding here arms
4. Ship leaves the doc and goes to destination (LEO, GEO, Mars)

Would this resolve at least some problems with launch window, or delta v budget ?