Mars' orbital ring

Mars' radius is 3389.5 km and its present atmo and magnetic-field would certainly allow for 3500 km semimajor, especially given Birch I.3.3-4. Mars' ring at slightly more than half Birch' proposed semimajor requires slightly more than half the mass. Can pull more mass for the tether, too. As with all things Bagestan, I borrow here from Warhammer 40k, in this case the Ring of Iron. I assume the first iteration be equatorial since the Martians want it for the Deimos trade.

Oh right: and because it has to be built in the first place. That'll require Mars' other equator-circling satellite. In all Phobos' 10.6 billion kilotonnes, I am asking the miners to dig out ninety kilotonnes of useful metal. Per 10.1038/s41550-021-01306-2, Phobos and Deimos were once one body from beyond Deimos' orbit; so, I must assume, came that parent's impactor. These two satellites today are rubble-piles not easy to ascertain what elements make up their rubble. Since Birch was writing we've found plenty of superconductors which will be little trouble keeping cool in near-vacuum at 586.2 W/m² only half the time. Pace the Games Workshop I have no great hopes for iron (nor bismuth). I have higher hopes for rare-earths.

UPDATE 1/6/22: The workers dropping the material between Phobos and ring-altitude can be protected: by still more Phobos ejecta. I don't think we need sweep up much of the junk; it's a layer of redundancy, never unwelcome.

More: spewing out Phobos material and dropping more material to 3500 km semimajor would, by Newton, further help to even up Phobos' eccentricity if not to boost its orbit. And (if equatorial) this solves DuPont and Murphy's question of where to put that ring to protect the atmosphere; it gets the terraforming started. Where the ring doesn't pay for itself over Earth, over Mars the Congressional Republic is going to give serious thought to this idea.

Paul Birch

Paul Birch proposed in 1982 that where we cannot have practical geosynch space-elevators, we might try "Orbital Ring Systems and Jacob's Ladders".

[ADVISORY! The pagination is wrong between I.3.3 and I.3.4. p. 482 is 483; 483, 482.]

And yeah: Inyalowda cannot have an elevator. Deimos, even if it's in synch, cannot dangle a ladder past Phobos' ap'ares; must make do with a shorter tether. Earth's proposal keeps butting against ... what material can bear 35,786 km of its own mass. And then we got Venus, our own Moon, and Mercury which all spin so slowly they have no synchronous orbit. Ditto Jupiter's inner moons which (like Mercury) have prohibitive delta-V and radiation, anyway. We're stuck with Ceres down here.

And then, in 1982, came Paul Birch, to save us. Rather: to save Mars. But we'll get to that.

Birch figured Earth, at least, will have no worry if we had a series of interconnected stations all in LEO, chained together. The stations move; the circle doesn't. The circle is, further, magnetic. Magnetise a Ring Station and that station just ... sits there. It dangles its tether down to wherever on Earth you want it. That's not 35,786 km; that is more like 600 km, depending on how far out you put the ring, presumably beneath Van Allen thus protecting the magnet. 600 km of rope is as nothing to tether-enthusiasts.

The problem thus shifts away from "unobtanium" and toward - who gets to pay for 180 kilotonnes of various pricey metals in LEO (semimajor 6678 or 6978 km). Also minor issues like space-junk and other satellites. Reading Gregory Leal's 2018 lecture, I cannot see Earth agreeing to this in the near future... before seeing how it works already. Just look at Elon's Starship today (well, in 2023); it inspires us because it has been showing results. So, for the orbital ring, we need first to see it work on some other planet.

The Federation in Starship Troopers paid for Birch II.3.5 - a smaller version, ringing our Moon.

Leal recommended to do this for Venus, also. That is a harder sell in that, although Venus is only 6051.8 km around, its atmo extends much higher and, in fact, blows out a coma on the night side. Birch wouldn't worry about drag and needn't worry about Venus' magnetic field (there isn't one) but he might worry about ions. The wind will push out the ring... but, I fear, to bend the ring into an oval if all goes uncorrected (Birch I.4.1). So if Venus gets an orbital ring I should run it at the same 6678-978 km semimajor. Venus gets its materiel from asteroids.

From Mars to Phobos?

A year-and-half back I went looking up Tsiolkovsky dodges and turned up the space fountain. I took this seriously for Aphrodite Terra if we find our way around the corrosive clouds. Let us talk about Mars, which Weinersmith is taking rather less seriously.

Here's the fun part about Mars - besides that it starts with negligible atmospheric drag and 3.721 m/s². The shuttle back to interspace just has to hit Deimos. Here's the even funner part: we expect the shuttle, someday, can grab a chain dangling from (5989 km) Phobos. Hollister David for the chain allows 1400-4300 km before it starts dragging the present atmo and (more to the point) groaning under its own mass so let's start at the low end: 4589 km altitude. (UPDATE 2 PM MST - and leaving alone the orbital ring.) Give or take Phobos' eccentricity, which we are also hoping to correct.

MIT's original fountain scheme was for a permanent fixture, for Earthlings to get into (the lowest) orbit. Over Mars, the fountain exists to inject cargo into a 100 km altitude which thence blasts Herr Hohmann to 4589 km.

Downside: a constant tower needs a constant source of energy. Venus has this, in its eternal heavy winds. Earth will have this in geothermal sites, looking especially at such tropics as Indonesia; SpaceX photovoltaics also look good at this timescale. I do not find anywhere in Mars where the energy is renewable, constant, and sufficient. Is there a budget for hoisting a fountain for "only" a century at a time?

How about not building a fountain. Instead: ad-hoc boost a platform to 100 km at 6.1 m/s², at which altitude said platform fires its rockets. Boost this at night so superconductors give you the magnetism. That's a lot of bullets and casing to clean up afterward; but Rocket Lab can take the casing, and magnetic bullets are literally dirt cheap on Mars. Comparing the energy-budget for all this, with the budget for making hydrogen-heavy explosive chemicals; on Mars, that might be a wash, especially given Mars is low on volatiles.

On Mars, Lofstrom's Launch-Loop or the Bifrost Bridge look better as permanent structures. Once the orbital ring is up, I'd honestly file all these as local solutions: get ores and (maybe especially) water-ice off the more-polar regions, into the equator. Ditto for the Moon given what a joke the pogo turned out to be.

WTF is Polarised-Cardio

Mikhail Cernovich dropped a term on us today that I had to look up: "Polarized Cardio".

His fanbase flooded the place with comments about THE CLOT SHOT. Why?, Cerno should ask. But anyway; I actually agree that spike proteins are bad, and that the shot is dangerous. I just happen to believe, also, that THE VAXX is less dangerous (because throwing out fewer spikes) than... the disease itself. Because I am not a damned fool. I am not a conservative. But, I repeat myself.

I took the two [Pfizer] jabs April / May. Will take the booster, if/when it's good to keep off the B'529. I've been doing daily walks, workouts, walks since el Cinco; with a small walk interrupting the weightlifts.

To that end: among the srrvative chaff was this grain of wheat.

I'd really like to have this broken down for plebeians who are either too dumb to understand it, and/or are too interested in anything other than it. This "Polarised Cardio" stuff from Cerno sounds, to me; like one of my lectures on Dyotheletism or Kepler's equations would sound, to him.

Tolimán alone

This being Thanksgiving we should all pause to reflect on what is most important to us ... colonialism.

Some while ago I was musing about Alpha Centauri. Probably not inhabited. Probably not a good idea to inhabit except by Beltalowda in O'Neills around, oh, Centauri-Proxima L4 and L5 and even those will need to make their own fuel. Although I did wonder if the Alpha Centauri / Tolimán interspace hath Hilda.

I was reminded of this when peeking in at Centauri Dreams. They noted that Proxima is going to be a flare-star for a long time. I am pondering now Tolimán, aka the Ẓalīmān, aka "B". It's a K type, supposedly ideal. If it weren't being roasted by the local Alpha.

The local Alpha won't be with us forever. Actually the whole system will eventually run by us, so - this is looking to the long-term. Alpha bears 1.1 Solar masses which, by the handy equation M^-2.5, means its total lifespan is 0.788 Solar lifespans. Our sun approximates, what, 1E+10? so, 7.88 beellyion years of which Alpha (and Tolimán) has/have already used 5.3.

A lot can happen in 2.5 billion years. By then of course our own Earth won't be liveable, whatever we do, whatever this liar says. More to the point our whole galaxy will be sucked into Andromeda. Although, that won't affect the mutual dance between Tolimán and Alpha. Might budge Proxima.

When Alpha goes red-giant, this will bake off whatever volatiles are in the Tolimán / Alpha Hilda. Good news: when Alpha falls back to white-dwarf, more volatiles will be spilled out - a lot of them, I think, to be drained into Tolimán. And maybe into Proxima if it's still around, although if so I bet Proxima is taking her leave at this point.

Anyway Tolimán should have another 4.96 billion after Red Alpha bombards it, although depending on how much mass Alpha bestows upon it, that number might go down.

The hydraulic pogo

Here we are not trusting Hop's equations for time-of-flight, but trusting the basics for commutes local-enough to redo them linearly.

Notion is: power-source on the pogo pushes against the surface. Up you go into space. Expend more power: wind back the spring. Down you go onto the surface. Boing again. Repeat. Eventually you've got enough stored momentum that your last kick back can be at an angle. Orbit!

Oh what fun. Now, let's get started on something "practical". Say we want lunar pogo-bounce as does 200 meters at a time for about 28 mph sideways; hitting the ground at a 45° angle for 40 mph, each bounce. First let us anticipate the question - who wants this.

First answer: whoever hated those MAKO missions in the first Mass Effect. 45° will clear many obstacles. Maximum height won't be that full cos(π/4) x whatever-meters up; but with a 40 mph initial velocity-budget, you can adjust angle accordingly.

Also the mechanism can store and expend energy per bounce. Say the problem is 200 m out. You plot 100 m, 50 m, 25 m. Next jump can be more than 40 mph. This before we get into battery-storage perhaps with solar panels.

I'd assume the computer would auto-plot the best route in advance. Or at least assist you.

Major issue: safety. The inner cabin needs to cushion the blows. Start with Earthlings, Luna's first (so seasonal) visitors. We like it 9.8 m/s². As the pogo hits the ground, we exert 8.18 m/s² upward, to turn the 28 down mph into 28 up again whilst delivering that 9.8 m/s² to the passengers. So, about 6.9 seconds of upthrust.

Three and a half seconds away at maybe 18 m/s along this diagonal end of its arc means the pogo's "stick" has to extend 62.3 meters out. So a third of its time pushing up, a third swinging around the extended piston to point forward (1/6 to apex, 1/6 going down), last third pushing down. Will need to expend energy moving the piston.

I am thinking less "coiled metal spring" and more "hydraulic". Do we own a fluid that can compress 65 meters in 3.5 seconds, and bounce back? Probably; but how much total length would be needed? It would be a cylinder, so we'd also ask diameter. 20x150 m? Superheavy is 9 x 68 m; Empire State is 380 m. Why not.

Inertia of this mass filled with hydraulic fluid plus, you know, cargo will be an issue. Once set on its route, it cannot easily change said route. In case of emergency, dump the fluid and eject the passengers. (Loonies don't use parachutes; they use inflatable cushions.)

I already did the maths to pogo a mile at a time on the Moon: a full kilometer of pure hydraulics. LOL! But . . .

Ceres and Callisto let you boiiiing that mile faster and I think the angle be lower. And if they wanted total 9.8 m/s² they could get that with more upward force than 8.18 m/s². So less time to upthrust; less length of hydraulic.

I think the pogo is "feasible" on the Moon for 200 m at a bounce. Callisto and more so Ceres are looking good for 500 m bounces. And from Deimos... well, that station will be docked to it, not on it.

UPDATE 12/13: ... for certain values of "feasible". Dude. Just use electric-augmented trampolines. Or even Elon's vacu-suck.

UPDATE 3/8/22: Keeping in mind that the Moon is dusty. Offroad driving has speedlimits. For ballistic bounce the only limit - the only speed - is from Kepler.

Bouncing off some ideas

Trollin' through Hop David poasts yesterday, I impacted the pogo. It's one more way around Tsiolkovsky, where the planetoid has low surface gravity and no atmosphere. If the maths added up . . . which we're here to check.

The maths aren't even about the pogo (I am preparing different maths for that); they're about getting off and getting back, by rocket if you have to. Hop has a spreadsheet, for the moon-intersecting ellipse. Travelling "just" 300 km means launching at 670 m/s and hitting the ground again at 670 m/s. Says he.

At stake here is if the ballistic jump will beat out an electric golf cart for that distance - especially if no roads. And it will all be even more feasible for lower-gravity worldlets like Ceres and Callisto.

Checking the spreadsheet, say you want to go one mile per leap, 1.60934 km. Hop claims 114 mph per impact; then, of course, you slow down until aposelene (r = a x (1+e)) and speed back to 114 mph on return. As a velocity this is exerted at a 45° angle. Cosine is 0.7071, so the horizontal vector started and ended 80.8 mph. So on a flat surface, which even on our small Moon we can assume paved for one measly mile, I should be taking 0.742 minutes.

Then I look at that "ToF" at cell D27. This has the flight taking 0.185726903 minutes. Where one mile / minute is 60 mph (famously), we've traveled that mile at 5.384 times 60 mph. A golf cart leaving and meeting the ballistic would be travelling an average 323 mph.

Too good to be true, I daresay. Something bad happened on the way to cell D27.

D15 e is the eccentricity and D16 a is the semimajor axis (in km) of my ballistic trajectory. Hold on to e; not using it yet, except to explain why a looks like only half the Lunar radius on a short hop.

Hop assumes a "planet" whose surface is a perfect sphere of wire mesh and whose whole mass is locked in a tiny ball in the centre. (As he should.) Let's grant to that core its actual 380 km radius. Now: consider falling through a hole in the mesh at a slight angle against that core. You drop 1360 km, blast past the core; get wrenched at a g high enough to break your Lunar-weakened bones and to send your internally-bleeding and concussed body back to the surface. That - Hop notes - is a Keplerian ellipse, eccentricity near 1 and the focus at the core. Contrast the Ceres airless mohole journey. That isn't Keplerian; the focus shifts as you fall, and the acceleration shifts (to zero), so your true a is diameter - not radius. Because... the mass of that 380 km radius isn't 100% of the lunar mass, it's 0.75–1.75%. But anyway: we're staying over the surface so don't touch D16.

If we don't touch D16 we move on to D17 surface velocity, in km/s. Here Hop, unbound by the Moon's internals, does vis viva SQRT($B$4*D9*(2/D10-1/D16)). $B$4*D9 is Lunar μ here 4900 km³/s²; 4904.8695 is the measured value but hey. D10 r = 1738 km which is where the Lunar disc intersects the ellipse; Hop doesn't want to be more precise than that in case of mountains and craters. D22 has the suborbital period, which is Kepler: =2*PI()*SQRT(D16*D16*D16/4904.8695) in seconds. For the near-perfect circle (so a=1738 km): D23 has 108.35 minutes. Lunar Reconnaissance Orbiter at 50 km so semimajor 1788 km, goes around at about 113 minutes (pdf). Kepler wins.

Time to look at D15, eccentricity. The equation checks out if I put 5458.5 (half circumference, as far as this XL will let me) as my travel-distance; it's almost a circle so e nears zero. And the time-of-flight is 54.17 minutes about half the suborbital period. Flight-time is bad only for short distances... meaning the distances we care about.

I take D26 to be the mean-anomaly against the mean-motion-constant. Last April I did some calculations starting with eccentric-anomaly at distance r given (cycler) orbits sent to Mars (and ideally back again). Hop instead has D26 = atan(sqrt((1-e)/(1+e))/e)/π, to be multiplied by the suborbital period. When it approaches a circle, this is very near 0.5; fine. Not so fine for a short hop. I have no idea whence Hop's D26 equation.