Mini Solar Systems

Edit as of 6-23-2016. Many of our gas giant moons seem to have have internal liquid oceans. Liquid water  suggests regions with comfortable temperatures. These strata might also have human friendly pressures. There would certainly be lots of in situ water and organic compounds. I am becoming more interested in icey moons as potential homes for humans.

Originally I had pointed to Jupiter and Saturn suggesting similar moon systems in other star systems would make good science fiction settings. But perhaps the gas giant moons within our own system could provide such a setting. A moon need not reside within the "Goldilocks Zone" in order to accommodate humans.

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Most pulp science fiction of yesteryear relies on fast paced story lines that take place over a short time. Not plausible in our solar system where Hohmann launch windows are years apart and trip times between planets are months to years.

A setting Retro Rockets suggests is a mini solar system where trip times and time between launch windows are on the order of days instead of months or years. The "mini solar system" proposed is a gas giant with a family of moons, all orbiting in a star's habitable zone.

This is a plausible setting in my opinion. This spreadsheet shows travel between the moons of Jupiter or Saturn can occur at a good pace. The interval between launch windows is called synodic period.

The gas giants in our solar system have respectable families of moons and many are a comparable size to Mars and Mercury. Here's a graphic comparing some gas giant moons to rocky bodies in our inner solar system:

Retrorockets notes that while mini-solar systems allow a story with an exciting tempo, delta v (needed change in velocity) is still high. But a setting with much less delta V is plausible.

Many of the gas giant moons  in our solar system are tidally locked with the planet they orbit. That is, they always present the same face to the orbiting planet. From the surface of a tide-locked moon, the planet-moon L1 and L2 regions remain in the same part of the sky, much like geosynchronous satellites appear to hover motionless when viewed from the earth's surface. For tide-locked moons, L1 and L2 are possible centers for a space elevator.

Between two moons there exists an elliptical transfer orbit whose apoapsis angular velocity (ω) matches that of the upper moon and whose periapsis ω matches the angular velocity of the lower moon. If the moons are nearly co-planar, trips can be made between the moon's elevators with very little delta V. Here's an illustration showing tide-locked moons Phobos and Deimos:

Expressions for transfer ellipse's eccentricity, apoapsis, periapsis are shown above. They can be generalized to any pair of tide-locked, coplanar moons.

Transfer ellipses between Saturn moon beanstalks:

Tranfer ellipses between Galilean Moon beanstalks:

Something to watch out for is the planet-moon L1 and L2 locations. If L1 and L2 aren't well below the departure arrival point on the beanstalk, the influence of the moon's gravity might substantially alter the shape of the transfer orbit. In the case of Jupiter's and Saturn's moons, the L1 & L2s are well below the tether tops.

Another thing to watch out for is gas giant rings. The chunks of ice in Saturn's rings might well be a debris field that would quickly cut some of these beanstalks.

It is a convention to label a tide-locked moons closest point as having 0 degrees latitude and 0 degrees longitude. For a civilization evolving on a tide-locked moon, I would predict religious significance being attached to 0º, 0º point. A viewer standing at this location will see the gas giant hovering in the sky's zenith. The far and near points will gain additional military and commercial importance when they anchor beanstalks going through L1 and L2.

Our earth globe has non-arbitrary features: the north pole, south pole, equator, tropic of Cancer and Capricorn and the arctic and antarctic circles. Cartographers of tidelocked moons will have additional non-arbitrary markings: A band separating the near side from the far side. I'd also expect a circle containing the near and far points as well as the north and south poles.  A simplified globe would look like a spherical octahedron:

Here is a painting I had done of Gielo (Giant In Earth Like Orbit) and Elm (Earth Like Moon):

A very interesting setting with lots of possibilities. I hope science fiction writers will do stories of habitable moons orbiting a gas giant.

Deboning the Porkchop Plot

Changing direction causes ΔV (change in velocity), often more than a change in speed. Compare the velocity vectors below. When going the same direction, the difference is 1 km/s. When at right angles the difference is 5 km/s. We know this from driving in traffic. Two cars going almost the same speed hit each other. If they’re in the same lane going the same direction, it’s a mild bump. If one car runs a red light and T-bones a car in cross traffic, the impact is serious: 

This is the strength of a Hohmann transfer orbit. Velocity vectors are pointing the same direction at departure as well as destination. No direction change is needed, only a speed change:

Note the Hohmann transfer path moves 180 degrees about the sun:

A Hohmann transfer assumes the departure and destination orbits are co-planar. But what if the destination orbit is inclined?

Orbit Planes and Spherical Trigonometry

A plane passing through a sphere’s center cuts the sphere along a great circle. A group of planes all sharing a common point can be represented as great circles on a sphere. Since every orbit about the sun is a conic section having the sun as a focus, each orbital plane shares the sun as a common point. Representing the orbital planes as great circles is convenient. There are already a lot of theorems in spherical trigonometry which gives us a suite of tools for looking at angles between orbital planes.

The shortest path (or geodesic) along a spherical surface between two points is an arc of a great circle. If we set the sphere’s radius to be 1, the arc length is also the angular separation in radians.

A familar group of great circles are the longitude lines on a globe. The equator is the only great circle among the latitude lines. All the longitude lines are great circles passing through the poles.

Let’s use the equatorial great circle to represent the departure plane. Recall the Hohmann transfer moves 180 degrees about the center. In this illustration, latitude and longitude for departure and destination is (0º, 0º) and (7º, 180º). The only great circle connecting these points is a polar orbit nearly 90º from the departure and destination planes! Big plane changes at departure and destination destroys the virtue of a Hohmann orbit.

I’ve also tried to demonstrate this in this video:

The big delta V needed for large plane changes makes the ridge in a porkchop plot:

(image courtesy NASA)

Porkchop plots are drawn by doing iterations of various Lambert Space Triangles. Lambert iterations give polar transfer orbits when departure and destination longitudes differ by 180º.

Does this mean Hohmann transfers are no good if the destination orbit’s inclined? No, the big plane changes can be avoided with a mid course plane change. Here is a broken plane transfer where a plane change burn is done at the ascending node:

The line where the destination and departure planes intersect form the ascending and descending nodes. Starting in the departure plane and doing a plane change at the node avoids the two major plane changes. The departure and destination planes differ by an angle called i, for inclination.

Changing a vector by an angle i takes dv of v * 2 * sin(i/2).

The Vis Viva Equation tells us v = sqrt(μ(2/r - 1/a)). So v ranges from sqrt (μ((1-e)/(a(1+e)))) at aphelion to sqrt (μ((1+e)/(a(1-e)))) at perihelion. Let's look at a Ceres transfer orbit. An ellipse with a 1.88 a.u. semi major axis and eccentricity .47 will have speeds ranging from 36 km/s (at perihelion) to 13 km/s (at apohelion). Inclination's about 10.6 degrees. So plane change ranges from 36 km/s   * 2 * sin(10º/2) to 13 km/s   * 2 * sin(10º/2) or from 6.7 to 2.4 km/s. Is the a 2.4 km/s plane change at aphelion the best we can do?  No, it's possible to have less plane change expense.

Launch is at the perihelion of an outbound Hohmann orbit. If the launch coincides with a node, the entire plane change can be done during earth departure or at arrival. Then the delta V entails a speed change as well as a direction change. Doing a single plane change/speed change burn saves delta V as shown by this diagram:

Law of cosines tells us for a triangle a, b, c, a² + b² - 2ab cos(i) = c². In this case, i is the angle between a and b and c is the delta V needed from the combined plane change and speed change.

At aphelion, a combined speed change/plane change only costs .76 km/s more than the speed change alone.

When launching deep in earth’s gravity well, we enjoy an Oberth benefit. Ceres' gravity well lends a little Oberth benefit at the destination. If the line of nodes coincides with transfer orbit's line of apsides, plane change can cost as little as .52 km/s extra.

This indicates as much plane change as possible should be made at departure and arrival. What sort of plane changes should we make to minimize the angle of the midcourse plane change?

The fattest part of an orange slice is right in the middle:

The angular separation at launch has to be some part of the orange slice. To minimize the angle between transfer plane and destination plane, the angular separation at launch should be in the middle. Having the transfer plane intersect the destination plane 90º from launch minimizes plane change angle.

An object on an elliptical path moves slower as it moves further from the sun, so doing plane changes further out are cheaper. The 90º from launch is a minimum. There will be a larger plane change angle 100 degrees from launch, but velocity will be slower. Also plane change lessens as flight path angle increases. I hope to talk about this more when I have time.

But for now I believe this shows that the Lambert iterations greatly exaggerates plane change expense for a Hohmann path where departure and destination points are 180º degrees apart. Most of that plane change expense can be eliminated by choosing a good place to do a midcourse plane change.

A PDF on Broken Plane Maneuvers Fernando Abilleria of NASA Jet Propulsion Laboratory

Beanstalks, Elevators, Clarke Towers

Planetary Beanstalks

Arthur C. Clarke well described a space elevator in his novel The Fountains of Paradise:

In the very decade that the first satellite was launched ... one daring Russian engineer conceived a system that would make the rocket obsolete. It was years before anyone took Yuri Artsutanov seriously. ... 

Go out of doors any clear night and you will see that commonplace wonder of our age — the stars that never rise or set, but are fixed motionless in the sky. We ... have long taken for granted the synchronous satellites ... which move about the equator at the same speed as the turning earth, and so hang foerever above the same spot. 

The question Artsutanov asked himself had the childlike brilliance of true genius. A merely clever man could never have thought of it — or would have dismissed it instantly as absurd. 

If the laws of celestial mechanics make it possible for an object to stay fixed in the sky, might it not be possible to lower a cable down to the surface, and so to establish an elevator system linking earth to space? 

When you build a bridge, you start from the two ends and meet in the middle. With the Orbital tower, it would be the exact opposite. You have to build upward and downward simultaneously from the synchronous satellite, according to a careful program. The trick is to keep the structure's center of gravity always balanced at the stationary point. If you don't, it will move into the wrong orbit, and start drifting slowly around the earth.

Besides popularizing the notion of Artsutanov elevators based on geostationary orbit, Clarke also invented geostationary communication satellites.

What is the altitude of a stationary orbit? Speed  of a circular orbit is (Gm/r)^1/2. Speed is also ωr, where ω is angular velocity in radians. For a geostationary orbit, ω would be 2 pi radians/sidereal day. Using these two equations we can find radius of a body's stationary orbit:

ωr = (Gm/r)^1/2
ω²r² = Gm/r
r³ =  Gm/ω²
r = (Gm/ω²)^1/3

Altitude of the stationary orbit is the orbit's radius minus the body's radius.

Stationary orbit altitudes of a few inner system bodies:

Body	Stationary Altitude
Vesta	265 km
Ceres	706 km
Mars	17030 km
Earth	35784 km

Vesta has a low stationary orbit because of it's low mass and high ω.

There are two accelerations at play: gravity and inertia in a rotating frame (the so-called centrifugal force).

Centrifugal acceleration is ω²r and gravity is Gm/r². We can choose our units so that Gm as well as ω are 1. Then the acceleration gradient can be graphed like this:

The slope is steeper below the geostationary orbit. For the above and below portions to balance, the pink area must equal the blue area. Assuming uniform thickness, the blue lengths above need to be longer than the red lengths below geostationary orbit.

A friend pointed out "But why assume a uniform strand? The part near synch has the most tension, and so is thickest in most designs,"  Thickened portions can be modeled as several strands. Each strand would need to be asymmetrical to balance.

A 108,000 km strand above geostationary would counterbalance the 36,000 km strand from geostationary to earth's surface.

Ratio of tether thickness at stationary altitude to thickness at planet surface is called the taper ratio. Taper ratio varies depending on Gm, ω as well as tensile strength and density of tether material. This Wikipedia chart gives tensile strength and density of various materials. Equations from this The physics of the space elevator by P. K. Aravind can be used to find altitude of the elevator top as well as taper ratios.

Body	Stationary Altitude (km)	Top Altitude (km)	Taper Kevlar	Taper Bucky Tubes
Vesta	265	665	1.01	1
Ceres	706	1922	1.02	1
Mars	17030	65774	45	1.1
Earth	35784	143772	2.6e8	1.62

Tide-locked Moons

It is also possible to build bean stalks from tide-locked moons. For tide-locked moons, the stationary starting points would be L1 and L2. Here are some tide-locked moons sorted by altitudes to L1 and L2:

Body	L1 (km)	L2 (km)
Phobos	3.25	3.27
Deimos	16.63	16.64
Io	8655.52	8831.64
Europa	11987.17	12172.28
Ganymede	28737.39	29362.77
Callisto	49749.25	48241.32
Luna	56292.23	62789.73

These numbers come from equations on pages 133 to 138 of Szebehely's "Theory of Orbits - The Restricted 3 Body Problem".

With tide-locked moons, there are three accelerations: 1) gravity of central body, 2) inertia in a rotating frame (aka centrifugal force, 3) gravity of moon.

The angular velocity ω is 2 pi radians/moon's orbital period. We can set time unit as orbital period/(2*pi), length unit as moon's orbit radius, and mass unit as mass of central body. Then ω and Gm are 1 and the accelerations can be graphed like this:

The constant k is ratio of moon's mass to central body mass. On the left side of moon orbit, moon pulls away from earth so moon acceleration is shown as positive. On the other side, the moon pulls stuff towards the earth, so moon acceleration  is negative.

To counterbalance, the blue strands extending away from the moon must be longer than red strands dangling towards the moon. the asymmetry is even more pronounced on the EML2 beanstalk.

A length extending 234,000 kilometers from EML1 earthward would balance a 57,000 kilometer length from EML1 to the moon's surface. Liftport proposes a Lunar elevator somewhat like this. An 11 tonne Zylon tether would extend 264,000 km from the moon's surface earthward. That's a little shy of the length needed but their diagrams indicate a counterweight at the earthward tether end. 

Here's a picture of the Liftport proposal:

Speed at apogees of red ellipses match ω * r. So virtually no delta V is needed for rendezvous with tether at apogee. The tether is within 3 km/s of Low Earth Orbit (LEO) and 1 km/s of Geosynchronous Earth Orbit (GEO).

Jerome Pearson et al have talked about lunar elevators. They point out a counterweight near EML1 has few newtons per kilograms, so a weight in that neighborhood would need to be quite massive. The chart on upper right of page 7 of this pdf indicates the counterweight mass at 60,000 km would be between 100 and 1000 times the tether mass. Here is a more detailed lunar elevator pdf by Pearson and friends.

Phobos Elevator

At 1.08e16 kilograms, Phobos is a large momentum bank. A Phobos tether could catch or fling many payloads with little effect on its orbit.

Mars fans like to point out that Mars' shallow gravity well allows a beanstalk made of conventional materials like Kevlar. They suggest a Mars elevator could be a gateway to the resource rich Main Asteroid Belt. To sling payloads to Ceres, a Mars elevator would need to be at least 46,350 kilometers tall. Taper ratio for Kevlar would be 45.

In contrast a Phobos tether less than 14,000 km can fling stuff to Ceres.

Kevlar taper for a Phobos tether is about 8, less than 1/5 of the Mars tether's taper.

Here is a graphic comparing taper and length of Phobos and Mars elevators capable of slinging payloads to Ceres:

A Phobos elevator accomplishes many of the same goals for a small fraction of the materials. It doesn't descend to Mars' surface, however. The Phobos tether foot is moving about .6 km/s wrt Mars' surface. So a small suborbital hop would be needed for a Mars ascent vehicle to rendezvous with the Phobos tether foot.  A Mars lander departing from the tether foot would need to shed .6 km/s, much less difficult than the typical 6 km/s.

A Mars elevator would need to avoid Phobos as well as Deimos. Not a problem with a Phobos elevator. The top of the Phobos elevator is below Deimos' orbit. And of course a Phobos elevator doesn't have to worry about collisions with Phobos.

Given a Phobos tether and a Deimos tether, it is possible to travel between the two moons with virtually no delta V. If a payload is released 937 kilometers above Phobos, it will follow an ellipse whose apo-aerion is 2942 kilometers below Deimos. At this apo-aerion, the payload is traveling the same speed as the Deimos tether at that altitude.

The eccentricity of this ellipse is (1 - (ω_Deimos/ω_Phobos)^1/2) / (1 + (ω_Deimos/ω_Phobos)^1/2).

Ellipse Peri-aerion is (1 + e)^1/3 * Phobos orbital radius.

Ellipse Apo-aerion is (1 - e)^1/3 * Deimos orbital radius.

Given two co-planar tide-locked moons orbiting a planet, there can be similar transfer ellipses between tethers. I like to imagine a system of tide-locked moons about a gas giant using such tethers. The tethers would need to lie outside of the gas giant's rings, though. Else the debris flux from the ring would likely cut the beanstalk.

A little bit of nay-saying (added 11-18-2012)


I'm not embracing elevators as the panacea that will open the cosmos. There are problems. Problems should be examined. 

Throughput

A Spaceward article The Space Elevator Feasibility Condition looks at throughput. Elevator cars and their cargo add to elevator mass but not tensile strength. So unless the cars are a tiny fraction of elevator mass, they'll boost the taper ratio. How fast can the elevator cars move? If their horse power comes from solar arrays on the car, they may move fairly slowly. The distances are huge, it could easily take a car months to climb to its destination.

Initially the space elevator material must be delivered with rockets. If the mass delivered by rockets is hundreds of times the mass an elevator can deliver in a year,

The Space Elevator Feasibility Condition notes that throughput might not be enough to even maintain an elevator.

The longer the elevator, the more serious the throughput problem. It'd be much less of an issue in the shorter elevators like the Phobos or Ceres elevator.

Debris

Orbital debris could sever an elevator. This is a big problem for an earth surface to GEO elevator. This elevator passes through LEO which has a high debris density and this debris is moving about 8 km/s with regard to the elevator.

Tether Experiments is a page listing various tether missions. One of the missions was SEDS-2, a 20 kilometer tether deployed "to see how long it would remain intact in the face of collisions with space dust and other orbital debris. ... it was cut after only four days"

The other elevators I've looked at occupy volumes with a lower debris density. And the orbital velocities are more leisurely so the debris flux is more tolerable. But even if an impact is a long shot, it's a concern if a very large investment is at risk.

Balancing act during construction

This is mostly directed at the Lunar elevator. The Liftport elevator starts at EML1 and sends tether ends simultaneously moonward and earthward. A slight nudge from EML1 can send a mass along a chaotic orbit, sometimes wildly chaotic. Station keeping is important. During construction, this balancing act must be maintained while one end is traveling approximately 200,000 kilometers and the other end 60,000 kilometers. After the elevator is anchored to the lunar surface, this station keeping isn't necessary but it's unclear how long it will take for the anchor to reach the moon's surface. If the anchor impacts the lunar surface at near lunar escape velocity, it would likely vaporize. If the lunar anchor is lowered gently, the duration of the balancing act would be prolonged.



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I'm not attacking these notions. Quite the contrary, I believe criticisms from a thoughtful Devil's Advocate can help a worthwhile idea more than cheer leading.

Mf is a Mofo

The Tyranny of the Rocket Equation is an excellent article by astronaut Don Pettit written while he was aboard the I.S.S..

The foundation of the article is this version of Tsiolkovsky’s rocket equation:

Mf = 1 - e^{-delta v/v_exhaust}

Mf is the fraction of the spaceship’s mass that is propellant.

V_exhaust for chemical propellant ranges from 3 to 4.5 km/s. Delta V to get into orbit is around 9 km/s.

Plugging these in we can see a spaceship must be more than 80 percent propellant. Pettit notes The 3-stage Saturn V rocket was 85 percent propellant and the Soyuz rocket 91 percent.

Pettit explains this sort of mass fraction is very challenging and drives up engineering expense:

If a vehicle is 10 percent propellant, it is typically made from billets of steel. Changes to its structure are possible without detailed engineering anyalysis: you simply weld on another hunk of steel to reinforce the frame according to what your intuition might indicate. I can easily overload my three quarter ton pick-up truck by a factor of two... 

Once vehicles become airborne, engineering structures become more serious. Lightweight structures made of aluminum, magnesium, titanium, and composites of epoxy-graphite are the norm. To alter a structure requires significant analysis: one does not simply weld on another chunk to your airframe or drill a hole though some convenient section if you want to live. ... Overloading an airplane by a factor of of two results in disaster. Even though these vehicles are 30 to 40 percent propellant (and thus, 60 to 70 percent structure and payload), there is eough ‘wiggle rooom’ to comfortably operate aircraft, which is how we have a robust, safe, and cost effective aviation industry.  

Rockets at 85 percent propellant and 15 percent structure and payload are on the extreme edge of our ability to fabricate, not to mention pay for. They require constant work to keep flying. The seemingly smallest modifications require monumental analysis and testing of prototypes in vacuum chanbers, shaker tables and test launches... 

The common soda can... is 94 percent soda and 6 percent can by mass. Compare that to the external tank (ET) for the space shuttle at 96 percent propellant and thus, 4 percent structure. The ET is big enough to hold a barn dance inside and contains cryogenic fluids at 20 degrees above absolute zero pressurized to 60 pounds per square inch, four times atmospheric pressure...”

ET photo courtesy of NASA

One very expensive aspect of Mf Pettit didn’t talk about: Delta V budgets for reaching low earth orbit and beyond strongly encourage multi-stage expendable rockets. Here is a video explaining how multi-stage rockets are a way to deal with large delta V budgets. Expendable is another word for disposable. After transporting it’s payload, much or all of the engineering marvel is typically thrown away. Imagine how expensive a transcontinental plane ticket would be if we threw away a 747 each trip.

Pettit suggests a way to break the tyranny of the rocket equation:

A rudimentary and basic skill to master is to learn how to use raw materials of space to create new capabilites there. Our nearest planetary neighbor, the moon, is close and useful – it contains the material and energy resources we need to build a permanent space transportation system. Extracting and producing useful materials useful products from the raw materials of the Moon (particularly water, useful for life suport, rocket propellant and many other space applications) would relieve us from the need to drag everything we need in space from the bottom of Earth’s deep gravity well. This eventuality would significantly alter the consequences of the rocket equation in our favor.

I’d like elaborate on this. Here's a delta V map of our neighborhood, cislunar space:

A propellant tanker from the Moon to EML1 would have a round trip delta V budget of 5 km/s. Mf is 67 percent (assuming hydrogen/oxygen propellant).

A propellant tanker from EML1 to LEO would have a round trip delta V budget of 4.5 km/s. Mf is 63 percent.

A tanker from EML1 to GEO would have a round trip delta V budget of 2.6 km/s and a 43 percent Mf.

With propellant available at these locations, vehicles for moving about cislunar space would have mass fractions ranging from 25 percent to 58 percent

No herculean feats of engineering needed to meet these mass fractions. And they allow single stage reusable vehicles.

Lunar water isn’t the only way to cut Mf. Planetary Resources wants to move a water rich asteroid into high lunar orbit or EML1. Whether propellant comes from the Moon or a Near Earth Asteroid, it would revolutionize space transportation in our own neighborhood as well as deep space destinations such as Mars or asteroids.

Pettit's article appeared in the Fall 2012 issue of Ad Astra published by the National Space Society.

Inflated Delta Vs

"What's delta V from Earth orbit to Mars orbit?" -- a common question in science fiction or space exploration forums. The usual answer given is around 6 km/s, the delta V needed to go from a low, circular Earth orbit to a low, circular Mars orbit. A misleading answer, in my opinion.

There are a multitude of possible orbits and low circular orbits take more delta V to enter and exit. A science fiction writer using 6 km/s for Earth orbit to Mars orbit has a needlessly high delta V budget.

There are capture orbits that take much less delta V to enter and exit. By capture orbit I mean a periapsis as low as possible and apoapsis as high as possible. A capture orbit's apoapsis should be within a planet's Sphere Of Influence (SOI).

On page 124 of Prussing and Conway's Orbital Mechanics, radius of Sphere Of Influence is given by:

r_soi = ( m_p / m_s ) ^2/5 r_sp

where

r_soi is radius of Sphere Of Influence
m_p is mass of planet
m_s is mass of sun
r_sp is distance between sun and planet.

The table below is modeled after a mission table at Atomic Rockets, a popular resource for science fiction writers and space enthusiasts.

• Departure and destination planets are along the left side and across the top of the table.
• Numbers are kilometers/second
• Numbers below the diagonal in blue are delta V's needed to go from departure planet's low circular orbit to destination planet's low circular orbit. These are about the same as the blue quantities listed at Atomic rockets.
• Numbers above the diagonal in red are delta V's needed to go from departure planet's capture orbit to desitnation planet's capture orbit.

	Venus	Earth	Mars	Jupiter	Saturn	Uranus	Neptune
Venus		.7	3.6	5.6	6.7	7.5	7.5
Earth	6.8		1.1	3.5	4.6	5.3	5.4
Mars	7.9	5.7		3.0	4.5	5.6	5.8
Jupiter	25.8	24.0	21.8		.1	.3	.3
Saturn	20.0	18.1	16.2	27.8		.1	.2
Uranus	16.6	14.7	13.2	23.8	16.6		.03
Neptune	17.3	15.4	14.1	24.5	17.3	13.1

It's easy to see the red numbers are a lot less than the blue numbers. I used this spreadsheet to get these numbers. The spreadsheet assumes circular, coplanar orbits.

A  graphic comparing delta Vs from earth to various destination planets:

If a low circular orbit at the destination is needed, it's common to do a burn to capture orbit with the capture orbit's periapsis passing through the upper atmosphere. Each periapsis pass through the upper atmosphere sheds velocity, lowering the apoapsis. Thus over time the orbit is circularized without the need for reaction mass. The planets in the table above have atmospheres, so the drag pass technique can be used for all of them.

A delta V budget is from propellant source to destination. If propellant depots are in high orbit, the needed delta V is closer to departing from a capture orbit than departing from a low circular orbit.

Thus it would save a lot of delta V to depart from Earth-Moon-Lagrange 1 or 2 (EML1 or EML2) regions. The poles of Luna have cold traps that may have rich volatile deposits. This potential propellant is only 2.5 km/s from EML1 and EML2. Entities like Planetary Resources have talked about parking a water rich asteroid at EML1 or 2. Whether EML propellant depots are supplied by lunar or asteroidal volatiles, they would greatly reduce the delta V for interplanetary trips.

Mars' two moons, Phobos and Deimos, have low densities. Whether that is from volatile ices or voids in a rubble pile is still unknown. If they do have volatile ices, these moons could be a propellant source. It would take much less delta V departing from Deimos than low Mars orbit.

All the gas giants have icey bodies high on the slopes of their gravity wells. However the axis of Uranus and her moons are tilted 97 degrees from the ecliptic. The plane change would be very expensive in terms of delta V. So the moons of Uranus wouldn't be helpful as propellant sources.

Venus has no moon. So of all the planets listed above, only Uranus and Venus lack potential high orbit propellant sources.

Anyway you look at it, the blue numbers from conventional wisdom are inflated.

The Next Continent

Hard science fiction set in our solar system nearly died in the 1960s.

The Tigers of Barsoom were slain by Mariner Probes to Mars. The Jungles of Venus were defoliated by probes to Venus. H. G. Wells’ Selenites were exterminated by Apollo. The Mariner Probes as well as Apollo told us the neighboring islands are barren places inhospitable to life.

Science fiction moved from neighboring planets to neighboring stars. Stories told over time spans shorter than decades or centuries were forced to resort to faster than light travel. The Golden Age of hard science fiction passed away and so called science fiction became more about fantasy than science.

In the meantime space exploration has moved on.

We’ve learned water is abundant in our solar system. A multitude of icey bodies dwell in the Kuiper Belt in the outer system. The Sun-Jupiter L4 and L5 have healthy populations of small bodies thought to be icey. There’s evidence Main Belt asteroid Ceres has a liquid water ocean within. Four main belt asteroids have been seen outgassing, an indication of volatiles. A thin layer of volatile ices was detected on the surface of Main Belt asteroid 24 Themis.

We have learned Europa, Enceladus and other icey moons of gas giants may have liquid water oceans beneath their frozen crusts. Tidal flexing creates an internal heat source that could sustain ecosystems just as deep ocean ecosystems on earth are sustained by chemicals and heat from volcanic vents.

There are regions on the moon’s surface that never see sunlight. Temperatures in these lunar cold traps can be as low as 40 degrees Kelvin. Colder than Pluto. There are indications of large bodies of ice in these crater basins as well as an abundance of other volatiles including various compounds of carbon, hydrogen, oxygen and nitrogen. Neighboring some of these polar craters are plateaus that enjoy nearly constant sunlight.

It turns out our solar system is much more interesting and mysterious than we had imagined. I had hoped these revelations would result in science fiction re-embracing our local neighborhood. But the path of main stream science fiction remains dominated by inertia, little affected by the perturbations of new discoveries and ideas.

There are exceptions, of course. A lot of optimistic, hard science fiction is coming out of Japan. Haikasoru is a publishing house that translates Japanese science fiction for the English speaking market.

The Next Continent by Issui Ogawa is one of the Haikasoru books.

“The Next Continent” is earth’s moon.

Ogawa has done his homework. He has invested some time and effort learning the nuts and bolts of aerospace, life support and other engineering aspects of his story. I have reassessed that. See postscript at bottom of this post (spoiler). While scientifically plausible, the story is still entertaining, it doesn’t get bogged down in technical details.

The book revealed to me a chauvinism I didn’t know I had. Many stories by U.S. writers feature American heroes who are more tenacious and clever than characters from other nations. And I never notice. But it was jarring to see Ogawa’s Japanese heroes show up their U.S. counterparts. But it’s only natural a Japanese writer would put Japanese characters center stage. Which isn’t to say Ogawa is disrespectful of the United States. He portrays a mixture of international cooperation and competition that will propel humanity to space. But in this story the U.S.A. isn’t the first to establish a beachhead on an extraterrestial body.

At the rate we’re going, I wouldn’t be suprised if China, Japan or other nations establish a lunar base before the United States. If that comes to pass, I would be delighted. Humanity must break the boundaries that confine us to a single planet. Which nation leads the way isn’t important just so long as we do it.

Postscript (spoiler alert):

October of 2010 I e-mailed Haikasoru's Nick Mamatas, letting him know of an error. In the third part of Chapter 8, Sohya and Tae face almost certain death. But they seem to have found a way out! They can escape the sun's searing heat by making a break for it during an eclipse:

Except the moon doesn't orbit the earth at 1.68 km/sec. That's about the figure for low lunar orbit. The moon's average orbital speed about the earth is more like 1.022 km/s. Tae and Sohya would definitely have been cooked!

Sadly the above screen capture is from a Kindle book downloaded in July of 2015.

It is extremely disappointing that Haikasoru doesn't give a damn about scientific accuracy or getting the math right. I guess their science fiction is a lot more typical than I had thought.