Wish list for space video games.

Kerbal Space Program

The Kerbal Space Program has demonstrated video games can be a very effective teaching tool.

It used to be very frustrating trying to talk about orbital mechanics. Use a word like "perigee" and eyes would glaze over as the audience tunes out.

But now there are many KSP players who are comfortable with terms like The Oberth Benefit, Bi Elliptic Transfers and other what use to be arcane, esoteric notions.

I'm hoping for more scientifically accurate games to make their way into pop culture.

Wish Number 1: Shotgun N-body simulations

Readers of this blog may know I'm a little obsessed with EML2 (Earth Moon Lagrange 2).

Many of my delta V numbers from EML2 assume dropping from EML2 using the Farquhar route and then insertion to a transfer orbit when moving ~11 km/s at perigee.

The Farquhar Route

However Farquhar's well done graphic is a simplification. A ship departing from from the EML2 region would not depart from a point. Rather it would drop from a halo or lissajous orbit about EML2. There are a multitude of possible orbits in this region.

Dropping from different parts of a halo orbit will result in different longitudes and latitudes for a perigee. And if you're doing a perigee burn for injection to a Mars transfer orbit, you want to be at a specific location and heading a specific direction when making your burn. 

Years ago Tom Powell helped me build a shotgun Java n-body sim from Bob Jenkins' code. blast many pellets in the general direction of your target. See which pellets pass closest and then narrow the shotgun blast.

Above is an attempt to show the shotgun concept. A fellow going by the handle "Impaler" was annoying me in a space forum. First I blast the varmint with broad scattering of buckshot. Then I more thoroughly pepper his backside by narrowing the blast between pellets 5 and 7.

By successively narrowing buck shot from earth to EML2 I found this route 3.1 km/s route from LEO to EML2:

The sim included earth, moon and sun. A lunar swing by boosts apogee on the way out. And then sun's tidal influence serves to raise perigee to EML2 altitude.

There are some serious limitations to my shot gun sim. There are only a few very limited scenarios that Tom Powell and I set up, very specific times and places. I would like to be able to have the user get location and velocity of a body at any time. I under stand there's software called SPICE that does this but I don't know how to use it.

Also JAVA seems obsolete. It's very difficult for me to use my own pages any more.

And my sims cans only specify the initial burns. Once you have a transfer path to a location it'd be nice to be able to do burns to park at that location.

I would use such a tool to learn how to move between different loosely bound lunar orbits.

Perhaps dropping from one EML2 halo orbit during a launch window wouldn't put the perigee in the right place for an injection burn. How much delta V would it take to move to a more favorable halo orbit?

Supposedly there are heteroclinic paths between halo orbits EML1 and EML2. A shotgun sim might help a player find these paths.

Halo orbits about EML1 and EML2 are part of a family of orbits that also include Near Rectilinear Halo Orbits (NHROs). If a lunar gateway is placed in an NHRO, it'd be fun and useful to explore different lunar orbits you could enter from an NHRO.

Wish Number 2: Tunneling on small bodies

For planets and large moons we are limited to exploiting only the thin outer shell of a body. Heat and pressure prohibit us from tunneling deeply.

But the entire volume is accessible for a small body.

If we could exploit the entire volume of Ceres, the dwarf planet could make Trantor look like Dogpatch.

I am hoping some planetary scientists and geologists could build tools to guesstimate how deeply we could tunnel given a body's surface temperature, radius and mass.

Wish Number 3: Tensile towers on small bodies

Also known as space elevators.

I'd be so happy to see a world building game use something like Wolfe's spreadsheet to examine effort and materials needed for various elevators. The user could input tensile strength, planet's angular velocity and body mass to examine various scenarios.

For example given Ceres' high angular velocity and shallow gravity well, Ceres synchronous orbit is only 706 kilometers above Ceres' surface. Materials needed for a Ceres or Vesta elevator are only a tiny fraction of what a Clarke Tower from earth or Mars would need.

Besides elevators from synchronous orbits it would also be good to enable users to build from planet-moon L1 and L2 points. 

The Mars Phobos and Mars Deimos are the moon elevators I like most. But elevators from L2 or L2 are usable in any family of tide locked moons.

Various tethers enabling ZRVTOs between Saturn's moons.

A gas giant's family of moons with tethers could be a rich setting for dramatic stories.

Hohmann trip times and launch windows between moons are on the order of days and weeks so it'd be possible to have a fast paced story without resorting to implausible engineering.

Dramatic situations might include missing a tether catch and being trapped in an orbit that won't rendezvous with a  tether catcher until the passengers have died from using up air, food or water. Or terrorists could sever a tether. There are many possibilities.

Wish Number 4: Compressive towers on small bodies.

Given lower gravity it's possible to build taller structures even given constraints imposed by a material's compressive strength. Likewise, sky scrapers are less plausible if a body has greater surface gravity.

I'd like the user to be able to specify a material's compressive strength and body gravity to get maximum plausible height for structures.

This would be especially useful for elevators between mutually tidally locked bodies like Pluto and Charon. Compressive towers built from the surfaces of Pluto and Charon could extend a fair distance towards Pluto-Charon-L1 and the also the Pluto Charon barycenter. This would considerably reduce the stress on the elevator and thus reducing the mass of the materials needed.

Wish Number 5: Thermal management.

This section dded on 9-8-19 on the suggestion of Winchell Chung and other thoughtful readers. There's three thermal management subjects I'd love to see a game address.

Limits to population growth

Earlier I mentioned a fully exploited Ceres volume could be a megapolis that makes Trantor look like Dogpatch. In the comments below Jim Baerg noted big populations generate heat. How would a growing population dump heat?

A good world building sim would take thermal management into account as a barrier to population growth.

Stealth

Infra red signature could make military craft visible. A topic Chung talks about in his Atomic Rockets page.

Rocket propulsion.

Nuclear power electricity generation for ion propelled rockets would generate considerable waste heat. Dumping waste heat requires big radiators which make for a poorer power source alpha. There are other heat sources that need radiators to dump waste heat. These should be counted when calculating mass requirements for a space ship.

Any other ideas?

Well made multi user games could be a way to educate as well as stimulate interest in space exploration. If a reader has any other suggestions please comment. I screen comments for spam but I eventually post what I believe are worthwhile comments. It's unlikely an actual video game developer will ever read these but there's no harm in day dreaming.

Zylon Mars Elevator

Mars Elevator With Conventional Materials

Mars spins nearly the same rate as earth (about a 24.62 hour day). Mars has about 1/9 earth's mass. At 17,000 kilometers, altitude of Mars synchronous orbit is less than half the altitude of geosynchronous orbit (about 36,000 kilometers).

These considerations have led some Mars enthusiasts to claim a Mars elevator made of conventional materials is possible. No bucky tubes or other science fiction material is needed, Kevlar will do. Is this true? I will take a look using Chris Wolfe's spreadsheet.

Safety Factor

In earlier blog posts using Wolfe's spreadsheet I used a safety factor of 1, a razor thin margin. The slightest scrape or nick will make the tether break. This is like drawing a pentagram to summon the demon Murphy's Law. No sensible entity would risk expensive payloads on such a narrow margin. Much less human lives. I hope to revise my earlier blog posts to include more sensible safety margins.

In later blog posts I looked at scenarios using a safety factor of 3. With this margin a portion of tether can lose up to 2/3 of it's mass without breaking.

In this post I'll use tables looking at a range of safety factors.  With a safety factor of 2, I cut tensile strength in half. A safety factor of 3 cuts tensile strength to a third. Which is a lot like cutting exhaust velocity in the rocket equation. Increasing an exponent can make tether thickness sky rocket.

Mars Equator to Mars Synchronous Orbit

This is the lower part of a Mars elevator. It exerts downward newtons that need to be balanced with upward newtons from elevator mass above Mars synchronous orbit.

Safety  Factor	Zylon Taper Ratio	Tether to Payload  Mass Ratio
1	13	154
2	162	3191
3	2016	51824

Payload is mass of elevator car as well as elevator car's contents. The elevator car will need to include motors and power source.

Mars Synchronous to Sub Deimos Elevator Top

Elevator top is set 50 kilometers below Deimos' periapsis. This is to avoid collision. The counterweight and tether above Mars synchronous orbit must counterbalance the downward force of the lower elevator.

Safety  Factor	Zylon Taper Ratio	Tether to Payload  Mass Ratio	Counterweight to Payload  Mass Ratio
1	1.02	38	1200
2	1.03	955	14800
3	1.05	1761	180000

The Whole Shebang

Safety Factor 1

Assuming lifting a 10 tonne elevator car and contents from Mars' surface and given a safety factor of 1, we'd need 10 * (38 + 154) tonnes of tether material. That'd be 1,920 tonnes of Zylon. Perhaps worthwhile if the elevator had a vigorous through put. I think these are the numbers Mars enthusiasts are talking about when they talk about Mars beanstalks made of Kevlar.

Also needed would be a 12,000 tonne counterweight. That's about thirty times the mass of the I.S.S.. This to lift a 10 tonne elevator car from Mars' surface? The need for a stud hoss counterweight sinks the argument for a Mars elevator, in my opinion.

Safety Factor 2

10 * (162 + 955) = 11170. About 11 thousand tonnes of Zylon to lift a 10 tonne elevator car and contents.

We'd need a nearly 150,000 tonne counterweight.

I think it's pretty obvious a Zylon Mars elevator with a safety factor of two isn't worthwhile. I'm not going to bother looking at a safety factor of 3.

Benefits

The elevator top is moving at about 1.7 km/s. It needs another 1.6 km/s to achieve Trans Earth Insertion (TEI). From the surface of Mars it takes about 6 km/s for TEI. So the elevator cuts saves about 4.4 km/s off of trips to earth.

Obstacles

Given a sensible safety factor, a Zylon tether would need to be much more massive than the payload. The counterweight mass would dwarf the payload mass.

Mars neighbors the main asteroid belt. Some rocks from the belt make their way to Mars neighborhood. Collision with asteroidal debris could cut the tether. Given this elevator's 20,000 km length and healthy taper ratio, there is a large cross sectional area. This increases likelihood of an impact.

Also there is a chunk of Debris named Phobos which crosses the elevator's path every 10 hours or so.

Comparison to Phobos Elevator

A Phobos elevator dropping to Mars' upper atmosphere and extending to Trans Ceres insertion is about 13,700 km. This about 6,000 km shorter than the Mars elevator described above. It also has a smaller taper ratio. This makes for a smaller cross sectional area to intercept debris. Being anchored at Phobos, this elevator won't collide with Phobos. The top is well below Deimos. orbit.

This tether can provide Trans Ceres Insertion as well as Trans Earth Insertion.

It takes about a .6 km/s suborbital hop for a Mars ascent vehicle to rendezvous with this tether foot.

Using a safety factor of 1, the upper Phobos tether has a 3.21 payload to mass ratio. The lower Phobos tether has a tether to payload mass ratio of about 16.1. So from top to bottom, about twenty times the payload mass is needed in Zylon.

The Phobos takes about 1/10 of the Zylon mass for a mars elevator with a safety factor of one.

A sub Deimos Mars elevator can't throw payloads above Mars escape velocity.

But with higher taper ratio, it'd take ten times as much zylon mass than a Phobos elevator.

This is with a safety factor of 1.

A Zylon Mars elevator with better safety factors is impractical.

I hope to revisit the upper Phobos tether and lower Phobos tether pages and include safety factors of 2 and 3. I suspect with a higher safety factor that a Zylon tether from Phobos to Mars upper atmosphere may not be feasible.

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.

What is more, the orbit is very nearly circular.

From Stern et al's 2015 paper:

(Thank you to Dr. Kirby Runyon for pointing me to this paper).

A tether could be extended from Pluto's near point to Charon's near point. Since the orbit is so nearly circular and obliquity is tiny, 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.

Upper Phobos Tether

This is third in a series of posts that rely on Wolfe's model of tethers from tide locked moons. As with the Lower Phobos Tether post, I will look at possible stages of this tether examining tether to payload mass as well as benefits each stage confers.

7 kilometer upper Phobos tether - tether doesn't collapse but remains extended

I used Wolfe's spreadsheet to find location of tether top where tether length Phobos side of L2 balances the length extending beyond L2. This occurs 6.6 kilometers from the tether anchor. Having the tether extend 7 kilometers is sufficient to maintain tension.

Safety  Factor	Zylon Taper Ratio	Tether to Payload  Mass Ratio
1	1.01	.04
2	1.03	.06
3	1.04	.09

Benefits
Docking with a facility at the L1 or L2 regions is easier than landing on Phobos. In the words of Paul451: "Instead of a tricky rocket landing at miniscule gravity on a loosely consolidated dusty surface, you just dock with the L1-hub of the ribbon (same as docking with ISS), transfer the payload to the elevator car and gently lower it to the surface. Reverse trip to bring fuel from Phobos to your ship (Assuming ISRU fuel is available on Phobos.)"

Also this small tether can serve as scaffolding on which to add longer tether lengths.

937 kilometer upper Phobos tether - transfer to Deimos tether

Given tethers from two coplanar moons tidelocked to the same central body, it is possible to travel between the two moons using nearly zero reaction mass.

Above I attempt to show how peri-aerion and apo-aerion of elliptical transfer orbit matches velocity of the tether points this ellipse connects. Tether Vs are red, transfer ellipse'sVs are blue.

Above I try to explain the math for finding the tether lengths from Deimos and Phobos.

Trip time between the two tethers is about 8 hours.

Safety  Factor	Zylon Taper Ratio	Tether to Payload  Mass Ratio
1	1.02	.035
2	1.04	.070
3	1.05	.107

With a safety factor of three, one tonne of Zylon could accommodate about 9 tonnes of payload.

I look at the Deimos tether here.

The notion of a ZRVTO between Deimos and Phobos tethers is not new. Above is a diagram from an article by JPL engineer Paul Penzo. Page 70 of the 1997 publication Tethers In Space Handbook. Penzo came up with this idea in 1984 (I believe).

Penzo's 940 and 2960 km lengths aren't that far from my 937 and 2942 numbers. It is reassuring that an aerospace engineer's numbers are close to my own.

Benefits

Easy travel between Deimos and Phobos is a benefit in itself. 

But this would be a huge help to ion driven Mars Transfer Vehicles.

I like the notion of reusable ion driven MTVs. Ion engines have have great ISP thus allowing a more substantial payload mass ratio. However they have pathetic thrust. Andy Weir's fictional Hermes spacecraft can accelerate at 2 millimeters/sec^2. Which actually is very robust ion thrust. However ithis is only medium implausible. Low thrust means little or no planetary Oberth benefit. Plus a lo-o-o-ng time to climb in and out of planetary gravity wells.

From Mark Adler's explanation on how to model ion rocket trajectories: 

300 km above Mars surface in low Mars orbit, gravitational acceleration is about 3 meters/sec^2. For a 300 km altitude low earth orbit, gravitational acceleration is about 9 meters/sec^2. 2 mm/s^2 acceleration is less than 10^-3 of the gravitational acceleration at initial orbit velocity in both these case. However I will be kind and go with Adler's .856 * initial orbit velocity.

At 2 millimeters/s^2 it would take Hermes 38 days to spiral out of earth's gravity well from low earth orbit and 17 days to spiral out of Mars gravity well. Most of the slow spiral out of earth's gravity would be through the intense radiation of the Van Allen belts.

I was very disappointed when Neil deGrasse Tyson's trailer had Hermes departing from low earth orbit and arriving in Mars' orbit 124 days later.

Besides adding 10 km/s to the delta V budget, climbing in and out of gravity wells would add about two months to Hermes' trip time. Tyson's video describes an impossible trajectory.  I wish he'd fact check himself with the same enthusiasm he applies to others.

It would be much better for Hermes to travel between the edges of each gravity well. At least as close as practical to the edge. In earth's neighborhood, Hermes could park at EML2 between trips. In Mars' neighborhood, parking at Deimos would save a lot of time and delta V. From Deimos, astronauts and payloads can transfer to Phobos and then to Mars surface. In this scenario, Hermes' 124 day trip from earth to Mars is plausible.

2345 kilometer upper Phobos tether - Mars escape

If anchor in a circular orbit, escape velocity can be achieved if tether top is at a distance 2^(1/3) anchor's orbital radius. I try to demonstrate that here. Phobos is in a nearly circular orbit. To achieve escape, the tether would need to be 2435 kilometers long.

Safety  Factor	Zylon Taper Ratio	Tether to Payload  Mass Ratio
1	1.11	.204
2	1.22	.436
3	1.35	.700

A 7 tonne Zylon tether could deal with a 10 tonne payload, even with a safety factor of three.

Benefits:

Achieve mars escape.

6155 km kilometer upper Phobos tether - To a 1 A.U. heliocentric orbit

A tether this long can fling payloads to a 1 A.U. heliocentric orbit, in other words an earth transfer orbit.

Safety  Factor	Zylon Taper Ratio	Tether to Payload  Mass Ratio
1	1.80	1.57
2	3.24	4.77
3	5.82	11.16

With a safety factor of three, an 11.2 tonne elevator could lift a one tonne payload. Not great, but it'd be worthwhile if we were tossing lots of payloads earthward.

Benefits

Catch/throw payloads to/from earth. Phobos is about 24º from Mars orbital plane. Mars orbit is about 1.5º from the ecliptic. So there may be some plane change expense.

7980 kilometer upper Phobos tether - to a 2.77 A.U. heliocentric orbit.

Safety  Factor	Zylon Taper Ratio	Tether to Payload  Mass Ratio
1	2.5	3.1
2	6.4	12.5
3	16.2	39.5

With a safety factor of three, it would take a 40 tonne Zylon tether to handle a 1 tonne payload. We would need to be tossing many payloads for this to be worthwhile.

Benefits:

2.77 A.U. is the semi major axis of Ceres. A tether this long could catch/throw payload to/from Ceres. But this doesn't take into account plane change because of Ceres inclination.

Even with plane change expense, this tether could be very helpful for traveling to and from The Main Belt.

This could also throw payloads into a faster than Hohmann transfer orbit towards earth.

Hope to resume space blogs soon.

I'm not dead. I've been up to my ears in alligators lately -- with paying projects (thank God!).

Hope to resume blogging soon. Some things I want to do:

Tethers and elevators

I'm eager to adapt Chris Wolfe's spreadsheet and examine a variety of tethers and elevators.

A few scenarios I want to look at:

Earth
There's a large population of dead sats in a graveyard orbit just above geosynch. These could act as a momentum bank for a vertical tether above geosynch.
I also want to look at a low earth orbit rotovator. It will be tricky adding tidal stress to the rotovator's stress from centrifugal force, but I think I can tweak Wolfe's spreadsheet to do the job.

Moon
Lunar elevator going from Mösting Crater through a balance point at EML1
Lunar vertical tether from an anchor mass at 30,000 km altitude

Mars
Phobos anchored vertical tether.
Deimos anchored vertical tether.

Ceres
Clarke style elevators from Ceres. Using Chris' spreadsheet I will be able to look at elevators of various lengths. Down the road a Ceres beanstalk might even throw stuff to trans-earth orbits.

Vesta
I want to examine Clarke style elevators from Vesta.

Boundaries of our bodies/extended phenotype

Awhile ago I reviewed a James Patrick Kelly story where a large fraction of the populace dwells in cyber-space. A trend in science fiction was been to explore artificial digital worlds rather than outer space. I opined that as telepresence improves, robotic avatars will become common place. The line between digital existence and meat space will blur.

Well, recently Kelly wrote an essay on prosthetics. It was a rich source of information, full of great web links (the norm for Kelly's Asimov articles). I want to talk about Kelly's essay. Also prosthetics and boundaries of our body. Many already regard dentures or lens implants as part of ourselves. I believe the same will become true of robotic arms and other body parts. And if we come to regard a prosthetic arm as an extension of our body, what is the difference between an arm attached to our shoulder or a robotic tele-arm thousands of kilometers away?

Robert Reed has written science fiction stories of god like beings whose minds and bodies extend throughout multiple star systems. That's not going to happen any time soon, but I do hope to see our "bodies" extend to the moon and near earth asteroids. In my lifetime.

I believe it will be advances in robotics that enable us to move beyond Cradle Earth.

Phobos--Panama Canal of the Inner Solar System

My post Orbital Momentum as a Commodity describes how a tether with a healthy anchor mass can catch and throw payloads. I tried to think of ways a tether might restore orbital momentum lost during a catch or throw. Two way traffic is one way to pay back borrowed momentum.

Well, Mars' moon Phobos masses 1.066e16 kg. With this huge momentum bank, catching and throwing payloads would have less effect than a gnat hitching a ride on a Mack truck. A Phobos anchored tether could catch and throw for millennia with little effect on Phobos' orbit.

The tether illustrated above doesn't suffer the enormous stress of a full blown earth elevator or even a Mars elevator. It could be made from Kevlar with a taper ratio of about 11.

Access to Mars

The tether foot pictured above moves about .6 km/s with regard to Mars surface. This is about 1/10 of the ~6 km/s the typical lander from earth needs to shed. Mars Entry Descent and Landing (EDL) would be vastly less difficult.

Some have suggested Phobos 1.88 g/cm³ density indicates volatile ices. If so, the moon could also be used as a source of propellent. A Phobos propellent source would make EDL even less of a problem. However Phobos' low density might also be due to voids within a rubble pile.

On page 2 of the Acceleration of the Human Exploration of The Solar System with Space Elevators Marshall Eubanks takes a look at how the foot of Phobos-Anchored Martian Space Elevator (PAMSE) might interact with Mars' atmosphere:

The orbital eccentricity of Phobos amounts to 283 km, which is by coincidence comparable to the effective depth of the Martian atmosphere for satellite drag (typically ~ 170 km, but subject to variations due to atmospheric events such as dust storms). The average relative velocity between the lower tip and the surface of Mars is only 534 m/sec, roughly Mach 2 in the cold Martian atmosphere, and slow enough that it should not cause significant heating of the tip. This raises the interesting possibility that the PASME tip could dip down deep into the atmosphere to leave or recover payloads or perform reconnaissance, acting as a supersonic airplane for the period near periapse when it is near the surface.

Eubanks' 534 m/sec is a little slower than the .6 km/s of my tether tip. This might be because I had placed my tether tip 300 km/s above Mars' surface thinking atmospheric friction would destroy a lower tether foot. Eubanks' analysis has changed my view.

In the Facebook Asteroid Mining Group, Eubanks noted:

The orbit of Phobos is equatorial, and there is a big mountain in the way, Pavonis Mons, the middle of the Tharsis volcanoes, straddling the equator and by far the highest obstacle in the path of the elevator tip. Maybe a railroad on top of the volcano could match speeds with the elevator tip, once every 3 days or so (when the orbit and volcano aligned). If so, you would have up to 3 minutes to shift cargo on and off. 

as well as

…the cool thing is that the tip can be something like a tethered airplane (with wings and flaps, etc.) and you should be able to use that to control oscillations. I was hoping to get money to begin actually "testing" this (i. e. in simulation), but, alas, not so far. 

Remember, too, with the PAMSE the counterweight has ~ infinite mass, and so any oscillations have to end there. (of course, anchoring a PAMSE in Phobos is left as an exercise for the reader.)

If Phobos is indeed a loose rubble pile, anchoring the elevator would be difficult. So while Eubanks eased my anxieties on oscillations and atmospheric friction, he calls my attention to a problem I hadn't thought of.

Access to Earth

6155 km above Phobos the tether is moving faster than escape velocity with a Vinf of 2.65 km/s. This is sufficient to toss a payload down to a 1 A.U. perihelion. This could provide most of the delta V for Trans Earth Insertion.

A ship coming from Earth would have a Vinf of 2.65 km/s and so rendezvous with this part of the tether might be accomplished with little propellent.

Access to the Main Belt

7980 km above Phobos the elevator is moving with a Vinf of 3.27 km/s, enough to hurl payloads to a 2.77 A.U. aphelion. This part of the tether might send/receive payloads to/from the Main Belt. There are a lot of asteroids with healthy inclination, though. So there would be substantial plane change expense at times.

Possible Mars exports to the main belt

One thing about the Main Belt, the pace is much more leisurely. Ceres moves about 1º every 5 days. In contrast earth moves about 1º a day and a satellite in low earth orbit moves about 4º a minute.

So a month-long, low-thrust ion burn over there looks a lot more like an impulsive burn than it does in our neck of the woods. I believe high ISP ion engines are well suited for travel about the Main Belt.

The inert gas argon can be used as reaction mass for ion thrusters. Mars' atmosphere is about 2% argon. It is also about 2% nitrogen and 96% carbon dioxide with traces of oxygen and water. Mars also has respectable slabs of water ice at the poles.

Mars would be a good source of propellent for the entire belt as well as CHON for the volatile poor asteroids in the inner main belt.

Ion engines don't have the thrust to weight ratio to soft land on the larger asteroids. But asteroids often have high angular velocity (in other words, they spin fast). High angular velocity combined with shallow gravity wells make asteroids amenable to elevators.

For example the balance point for a Ceres elevator would only be 706 km above Ceres surface, that is the altitude of a Ceres-synchronous orbit. To provide enough tension to remain erect, the elevator would need to extend to an altitude of 2000 km. At 2000 km, the tether tip is moving about .46 km/s, a good fraction of the 2.82 km/s needed fro Trans Mars insertion. If this Ceres elevator is Kevlar, taper ratio would be about 1.02.

If extended to an altitude of 14,500 km, the Ceres elevator top would be moving fast enough for Trans Mars insertion. This would require a taper ratio of around 5 for a Kevlar tether.

Incremental Development

The tether pictured at the top of this post is ~14,000 km long with a taper ratio of 11 for Kevlar. While much smaller than a full blown Mars elevator, this elevator would still be a massive undertaking. But the whole thing doesn't need to be built overnight. Early stages of the elevator would still be useful.

Pictured above a Deimos tether drops a payload to a Phobos tether.

At apoapsis of the large ellipse, payload velocity matches the Deimos tether foot. At periapsis, the velocity matches the speed of the Phobos tether top. Thus payloads can be exchanged between these Martian moons using practically zero reaction mass.

After descending the Phobos tether, the payload can be dropped to a Mars atmosphere grazing orbit.

These tethers are a lot shorter than 14,000 km tether we were talking about and taper ratio is close to 1.

No Moons to Dodge

A full blown Mars elevator capable of throwing payloads to the Main Belt or even earthward would have to dodge Deimos as well as Phobos.

A Phobos elevator for flinging payloads to Ceres ends well below Deimos' orbit. And of course a Phobos anchored tether doesn't need to dodge Phobos.

Summary

Tsiolkovsky's rocket equation and big delta V budgets are touted as show stoppers for routine travel to Mars' surface or the Main Belt.

With judicious use of tethers and orbital momentum, rhinoceros sized delta V budgets are shrunk to hamster sized delta V budgets. No bucky tubes needed, ordinary materials like Kevlar can do the job.

Other Phobos elevator pages

Space Colonization Using Space-Elevators from Phobos by Leonard Weinstein - PDF uploaded in 2003.
Phobos as a space elevator for Mars.

Upper Phobos Tether.

Lower Phobos Tether.

Deimos Tether.

Mass parameter and ITN

It seems like every other post I'm singing the praises of EML2. I'm also enthusiastic about L1 and L2 necks for big moons orbiting gas giants.

So why do I diss the Sun Earth L2 or the Sun Mars L1? 

Robert Walker put it fairly well:

I've no idea why you think there's some essential difference between e.g. transfers between moons in the Jupiter system and transfer between planets around the sun. Mathematically it's the same situation, multiple masses around a central planet or sun. Obviously the moons of Jupiter are larger compared with Jupiter than planets are compared to the sun, and the orbits are far shorter. But they still have Hohmann transfer orbits, and hill spheres, and lagrange points, and these tubes, which lead out from the lagrange points. 

It's The μ

The big reason is mass parameter. This quantity is often denoted μ in discussion of 3 body mechanics.

It's common to choose units so that mass of central and orbiting body sum to one.

For example if central mass were 90% percent of the system's mass, central mass would be .9 and orbiting body would be .1. In this case μ would be 1/10.

The small the μ, the closer L1 and L2 get to the orbiting body.

What paths do payloads follow when nudged away from the orbiting body at L1 or L2? Well, we can notice a few things about L1 and L2:

The L1 and L2 have the same ω (angular velocity) as the orbiting body.

L1 and L2 are collinear with central and orbiting bodies.

It just so happens I have a diagram of collinear points all having the same ω. It's what I use to model vertical tethers. By scaling this diagram it could also be used to model space elevators. (Space elevators are a special case of vertical tether where the tether foot coincides with planet surface and circular orbit of the balancing point coincides with planet synchronous orbit):

Eccentricity Vertical Tether Conics = |1 - r³|

Release a payload from any point on the tether and the path will be conic section having eccentricity

|1 - r³| where distance from center to balancing point is 1 and a point's distance from center is r.

But this diagram was derived using 2 body mechanics. When nudged away from the orbiting body's Hill Sphere, the payload will quickly enter a regions where the central body gravity dominates and conic sections are fairly accurate.

But while in the neighborhood of the Hill Sphere, there's a short interval when the path should be modeled using both the accelerations of central and orbiting body:

While falling away from the moon near L1,  a payload surges ahead while the moon tugs it backwards and a little up. This has the effect of lowering the apo and periapsis as well as rotating line of apsides in a prograde direction. A payload nudged from L2 away from the moon will lag behind the moon. While in the lavender region, the moon pulls the L2 payload forward boosting peri and apo-apsis as well as rotating line of apsides forward. L2 necks throw higher and L2 drops lower than corresponding points from a vertical tether.

Here are orbital sims for various mass parameters where colored pellets are nudged with slightly different velocities from L1 and L2:

μ = .1

μ = .001

μ = .00001

μ = .000001

Notice as μ shrinks, the orbits get closer and closer to what the tether model would suggest. For μ = .000001, apogee is very close to point of release and eccentricity of ellipses is approaching |1 - r³|. As the Hill Sphere shrinks the lavender two body zone gets thinner and the 2 body model becomes increasingly accurate.

μ for sun-earth is .00000304 and μ for sun-Mars is .000000323. The paths from the planets' L1 and L2 necks don't go far and there's not much variation.

What About Gravity Assists? Just Look At Rosetta

"Well sure, nudging a payload from SEL2 doesn't get us much past a 1.07 A.U. aphelion" an ITN defender replies. "But earth gravity assists can boost that aphelion. Look at Rosetta's March 2005 gravity assist -- it boosted an earth like orbit to an aphelion past Mars."

So let's look at the Rosetta gravity assist.

We can see the March 2005 gravity assist gets Rosetta past Mars orbit. And the orbit from launch to gravity assist looks pretty earth like, right?

No. 

The orbit from launch to gravity assist is an ~.9 x 1.1 A.U. ellipse with an eccentricity of around .11. When r = 1 A.U., flight path is about 5 degrees. As it approaches earth, Vinfinity is about 2.6 km/s:

In contrast, Vinf of an orbit departing from SEL1 or 2 will be about .3 km/s. Rosetta's initial orbit couldn't be accomplished via a WSB from an L1 or L2 neck.

Further, a payload from SEL2 remains outside earth's orbit, it does not cross. The closest it comes it .01 A.U. during which time it's flight path is zero. The same is true of an orbit nudged from SEL1:

Synodic Period

Another thing to consider is synodic period. A way to think of synodic period is how often one runner laps another as they race about a circular track. If both runners are going nearly the same speed, it will take a long time.

Synodic period of orbiting bodies is |(T1 * T2)/(T1 - T2)| where T1 and T2 are bodies' orbital periods. Orbital period of a 1.01 x 1.06 ellipse is 1.053 years. Synodic period is 19.88 years. So the payload wouldn't even come close to the earth until almost two decades later!

When the payload finally does lap the earth 19.88 years later, it will be 43º from perihelion.

Instead of being .01 AU from earth, the payload will be more like .02 or .03 A.U. from earth. It won't get close to earth until nearly 8 synodic periods later. That's about 160 years.

The tinier the μ, the bigger the synodic periods of payloads released from L1 and L2 necks.

Synodic Period with a big μ

In closing I'll take a look at synodic period of something dropped with from Earth Moon L1. When it comes to μ's the earth moon's .012 is the 900 pound gorilla of the solar system. It's the biggest I know of except for Pluto Charon's .104.

Dropping from EML1, payloads fall into an approximately 100,000 x 300,000 km orbit:

Period is about 11 days. Synodic period is 20 days. So within a month's time these pellets will fly by the moon when they're near apogee:

EML1 and EML2 can do lots of stuff within a fairly short time. I have seen some crazy stuff running earth moon sims.

But zoom out and it gets boring. I've let sun earth sims run for centuries without seeing any drama. The L1 and L2 necks for the sun/rocky planets are a bunch of duds.

A few mass parameters

Here are a few mass parameters for central and orbiting bodies:

Pluto/Charon	1.043E-01
Earth/Moon	1.216E-02
Sun/Jupiter	9.545E-04
Sun/Saturn	2.856E-04
Saturn/Titan	2.374E-04
Jupiter/Ganymede	7.789E-05
Jupiter/Callisto	5.684E-05
Sun/Neptune	5.153E-05
Jupiter/Io	4.700E-05
Sun/Uranus	4.366E-05
Jupiter/Europa	2.526E-05
Saturn/Rhea	4.046E-06
Sun/Earth	3.039E-06
Sun/Venus	2.448E-06
Saturn/Dione	1.935E-06
Saturn/Tethys	1.091E-06
Sun/Mars	3.229E-07
Saturn/Enceladus	1.935E-07
Sun/Mercury	1.659E-07
Saturn/Mimas	7.037E-08
Mars/Phobos	1.682E-08
Sun/Pluto& Charon	7.149E-09
Mars/Deimos	2.803E-09
Sun/Ceres	4.741E-10

I hope I'll some time to play with the Pluto/Charon 3 body system. I believe there are some wonderful possibilities in this setting.

Does the ITN include Gravity Assists?

Given big enough  μ's, some WSBs can snake by another body which can lend a gravity assist.

Does that mean gravity assists are part of the ITN? No. We've been using gravity assists for many decades. They were in common use before Ross' or Belbruno's techniques came on the scene.

Some claim astrogators are now using Belbruno's or Ross' techniques to find opportunities for gravity assists. I haven't seen any evidence of this. So far as I can tell mission planners are still finding such opportunities the old fashioned way: looking for needles in a hay stack. In other words with persistence and hard work.