Wednesday 6 June 2018

Inter-Orbital Kinetic Energy Exchanges: Part I

Electrical power can be transferred between planets using high velocity masses. Kinetic Energy Exchanges are an efficient concept that can output more energy than it consumes and only gets better with distance.
Guest writer Zerraspace (Zach Hajj) works out the details and reveals just how impressive the concept is. 

This blog post was written by Zach Hajj, who provided descriptions, workings and calculations. He is also known as ZerraSpace and is part of the team behind the very promising hard science-fiction game Starfighter Inc (@StarfighterInc). Find his works on DeviantArt and come have a chat with us on the ToughSF Discord.
This concept was based on discussions in the earlier "How to Live on Other Planets" entries for Jupiter and Saturn, detailing the possibility of energy exchange from the outer worlds to inner ones via orbital mass transfer, what might also be called interorbital kinetic energy exchange.
Diagram of a simple Inter-Orbital Kinetic Energy Exchange between Saturn (top) and Earth (bottom).
In summary, a projectile is launched retrograde from a high orbit, such that it can reach a near standstill relative to the sun. At this point it will plummet towards the inner solar system, trading its initial gravitational potential energy for kinetic energy, thus speeding up as it falls farther. With a carefully placed catcher to intercept, this kinetic energy can be harnessed as electricity, and may be many times that required for launch.

The key to this is the relative velocity at each location. Were we to launch such a projectile from Saturn orbit, we could cancel its initial orbital velocity with a 9.7 km/s retrograde boost, enabling freefall. Via energy conservation, we can determine the velocity developed as it falls farther and farther:
G is the gravitational constant (6.67408 × 10^-11)
M is the mass of the sun (1.989 × 10^30 kg)
a_0 is our semi-major axis at the fall point (km)
a_1 the axis at the point of study (km)

Thus, falling from Saturnian orbit at 9.6 AU, by the time our projectile has reached 1 AU, it will have accelerated to a full 39.8 km/s. Supposing we have timed this to encounter the Earth on its fall, the planet will be moving orthogonal to it at 29.8 km/s along its orbit, thus the projectile’s relative velocity can be determined via Pythagorean sum to be 49.7 km/s. 

A catcher so located would then intercept it at 5.1 times the initial boost velocity; that is to say, for an initial 47 MJ/kg investment of kinetic energy, we could receive 1.235 GJ/kg, 26 times what we started with

This on its own seems quite impressive, but it makes a large assumption – that the projectile velocity on either end is relative to that of the relevant planet. This would be the case if we launched from a space station in a similar orbit to Saturn, and received at another in a similar orbit to the Earth, but not if we were to launch and receive from within the spheres of influence of the planets themselves. 
There are two more factors that must be accounted for there, and as it turns out, we can utilize these to radically improve our figures.

The first thing to understand is that the projectile does not maintain its velocity while passing by a celestial body. Much like it falls towards the sun, it also falls towards the planet and is sped up as it draws closer. This can be more easily understood via energy analysis in the planet's frame of reference – the projectile does not gain or lose energy, and so coming closer to the body, it exchanges its gravitational potential energy for kinetic.  

Again, we can demonstrate through conservation of energy:
V_inf is the hyperbolic excess velocity
V_e = sqrt(2*G*M/r) is the planetary escape velocity

A similar equation can be used to derive the Oberth effect. 

The dependence on escape velocity is very important here, as the escape velocity varies with distance from the body. As we get deeper within the planet’s gravitational well, escape velocity increases, and so too must our object velocity increase. Clearly, the greatest speedup occurs when the escape velocity is significantly higher than the hyperbolic velocity, so for high relative velocity, we want massive bodies and very low orbits.
Around Earth, escape velocity at a 400 km LEO is 10.8 km/s (the often-cited 11.2 km/s is at its surface), so for our originally determined hyperbolic excess velocity of 49.7 km/s, velocity at periapsis becomes 50.9 km/s. This may not seem like a significant increase, but it makes quite a bit more difference at Saturn: assuming we wanted to launch from Titan orbit, local escape velocity is 7.9 km/s, which is more comparable with the intended V_inf of 9.7 km/s, giving a periapsis velocity of 12.5 km/s.
The second thing we must now account for is that the relevant velocity is not relative to the planet, but to an object along a point in its orbit. Depending on the point selected, we can utterly change the direction of motion, and thus the magnitude of the relative motion as well.
A catcher station in Earth orbit can add or decrease its orbital velocity to the intercept velocity.
Consider our catcher at 400 km LEO: orbital velocity here is roughly 7.9 km/s, so if our catcher were to intercept the projectile while it is moving in the same direction as its orbit, the orbital velocity would be subtracted for a relative velocity of 50.9 – 7.9 = 43 km/s. On the other hand, if the projectile were to arrive moving opposite the catcher, orbital velocity would be added, yielding 50.9 + 7.9 = 58.8 km/s. At Saturn, the effects are more notable: taking into account the 5.6 km/s orbital velocity at Titan orbit, launching in the direction of the catcher will yield a relative velocity of 6.9 km/s, while launching against it requires 18.1 km/s.
Clearly, to maximize gain, we wish to maximize the relative velocity on the receiving end and minimize it at the launching end. Thus, we should launch when the launcher is moving in the same direction as we intend for our projectile, and we should receive when the catcher is moving opposite its intended arrival. Getting the exact windows would require precise timing, but this doesn’t necessarily have to be factored entirely at the launch site. The projectile could feasibly feature a small propulsion bus, triggered to fire just at the edge of the destination body’s SOI, where only a minor adjustment would be needed to correct the intercept.
Earth's Sphere of Influence extends out to 1.5 million km. 
Thus applied, we have reduced the initial launch investment to 23.8 MJ/kg and increased the received energy to 1.729 GJ/kg, roughly 73 times what was needed to start. We have nearly tripled our relative energy multiplier. 
However, we have neglected another important dimension of the problem: what goes for the planets goes too for their moons.
By launching from the low orbit of a moon such as Titan, additional free energy is available.
Earth is sadly lacking in natural satellites at 400 km LEO, but at Titan, a 1000 km orbit corresponds to an escape velocity of 2.2 km/s (we could go lower but risk significant atmosphere drag from the low scale height). 
Titan around Saturn.
Here the hyperbolic excess speed is the same as the periapsis velocity we expected around Saturn, 6.9 km/s if Titan is moving in the desired direction, so the periapsis velocity at the moon itself can then be determined to be 7.2 km/s. Launching in the direction of station motion, we can shave off its orbital velocity of 1.6 km/s, and hence further reduce launch velocity to 5.6 km/s.

Now initial investment is 15.7 MJ/kg, increasing our energy multiplier to 110. We have more than quadrupled our original estimate.

Such a system makes for potent gains, but comes with a huge catch: exchange can only happen at appropriate intervals, where the inner planet will end up right beneath the projectile as it crosses its semi-major axis. These small windows are separated by the two worlds’ synodic period, the time necessary for them to repeat their relative positions. For far apart worlds, this is much closer to the inner world’s period than the outer, since the outer world barely moves relative to the inner, so for Saturn and Earth, the synodic period is just slightly longer than an Earth year.
Synodic periods of the planets relative to Earth.
This may seem bearable, but the wait quickly becomes prohibitive for farther out pairs; for Jupiter and Saturn, the synodic period is 19.9 years; for Uranus and Neptune, it’s an agonizing 171.4 years! Even for shorter durations, it becomes difficult to utilize this setup as a continuous energy source. In order to do that, we need to find ways to launch and receive outside our original window, and we can do that by adjusting our launch velocity.

As we reduce our initial boost, we maintain an increasing aphelion velocity, and our projectile changes from a straight-line fall into a highly eccentric orbit. With some proper care and adjustment, we can tailor this to intersect our destination’s orbit at any point. The greater the angular offset from our freefall point, the less boost we need, and this applies whether said angle is ahead of or behind the original point – the projectile orbit is symmetric, and so will eventually reach either side. The greatest slowdown will be necessary to access the point directly opposite the freefall point, where our projectile’s periapsis exactly matches our destination’s semi-major axis. In this case, we’ve launched it into a regular Hohmann transfer orbit.
Hohmann transfer velocity from Saturn to Earth is 5.4 km/s, requiring a Titan launch velocity of merely 3 km/s, 4.5 MJ/kg. This will reach a relative velocity of 10.3 km/s to the Earth, and relative to our LEO station, up to 22.8 km/s, 260 MJ/kg, for an energy multiplier of 25.7. This is far less than we’d have received from freefall, but it does represent the lower limit for potential gains. For the rest of the year, figures will be between this and freefall.  

We could also apply this same principle another way. Consider that for freefall, we’ve pushed our projectile to a near standstill. With a little extra boost, we could then regain an aphelion velocity, but moving retrograde around the sun, effectively doing the same trick in reverse. Now greater speedup leads to less eccentric higher-reaching orbits, until at maximum boost, the projectile would reach the inner world at perihelion, but moving in the opposite direction – a retrograde Hohmann transfer orbit.
For a Hohmann transfer from Saturn to Earth, solar velocity at aphelion is 9.7-5.4 = 4.3 km/s, so to reach this velocity moving retrograde to Saturn, we must then boost by 9.7+4.3 = 14 km/s. Optimized launch velocity from Titan then becomes 10.3 km/s, and velocity at perihelion will be 40.1 km/s. 

Here is where the advantage of this technique becomes apparent: because we are moving in the opposite direction to the Earth, we add its full velocity to our relative motion, rather than the Pythagorean sum, yielding an incredible 69.9 km/s at planetary periapsis, 78.6 km/s relative to our LEO station. Our launch investment has drastically increased to 53 MJ/kg, but so too has the received energy at the Earth, now up to 3.089 GJ/kg. The energy multiplier has dropped to 58, but energy per launched mass is far greater, almost double what we had from freefall. 

Launching from a low velocity to high velocity planets allows the difference in orbital velocities to be exploited.
Again, we have bound potential energy gains depending on the time of year, but in the other direction. Now freefall is our lower limit, and full retrograde is our maximum.

With this, the energy transfer system can be made to run regardless of the relative position of the planets involved.

However, thus far only one side has really benefited. Titan has to expend energy to send the projectile, whereas Earth gets both the free energy and the material of the projectile to boot. Earth could share back some of its dividends via laser and cargo shipments, but there’s an easier way to send up what was given, and that is by using the system itself.

Thus far, we have only focused on a projectile falling from the outer solar system towards the inner. By playing this game in reverse, launching projectiles outwards as well as inwards, we can ensure those farther reaches receive their due energy as well.
Railgun launcher from The Expanse. It could be used for peaceful purposes.
Launching a projectile along the launcher’s orbit, at 400 km LEO a boost of 7.3 km/s for 26.7 MJ/kg is sufficient to reach out all the way to Saturn. Conversely, we can receive this same projectile at Titan moving opposite its orbit and a local catcher, at a relative velocity of 15.2 km/s for 115.5 MJ/kg. This is more than twice the 53 MJ/kg needed for a retrograde Hohmann launch, and four times the 23.8 MJ/kg for a simple freefall. Earth’s investment is a drop in the bucket next to the potential 1.729 to 3.089 GJ/kg it can receive.

Thus, with the projectile passed back and forth, both Titan and Earth can make gains, and moreover, the same mass can be recirculated and continually supply power.

Of course, this is the minimum required energy for transmission, and the minimum Titan can expect to receive. Can we boost further to reach the outer world at any time of the year? 

In this case, it’s not as useful a solution. Boosting up to even the local solar escape velocity will access less than half of the outer world’s orbit, and even infinite boosts along our planet’s direction of motion cannot access points behind it. To reach those, we need to boost radially to our orbit… and for points trailing, we must ultimately boost retrograde.

The velocities quickly become staggering and require massive setups. Because we can launch in the same direction as the launcher and receive moving opposite to it, we can always make sure that a retrograde launch is cheaper than a retrograde catch and thus net some energy, but it will still drain most of what we’d expect to gain from the partner. Whether this would be deemed an acceptable tradeoff depends on one’s priority. Do we want regular shortly-interspersed transfers, or maximum energy per transfer?
Mercury and the Sun.
In some cases, this is not much of an issue. Mercury has such a short synodic period with essentially any other world (on the order of five months with Venus and three/four months with anywhere else) that it would not be much trouble to simply wait for the optimal launch window and use inexpensive Hohmann transfers for launch while receiving the return retrograde. For other worlds, a compromise is possible: if we consider the reverse freefall as a practical upper limit, we make sure that launch is always cheaper than any reception regardless of the time of year.

Applied to our ongoing example, for our LEO to Titan launch, we can reduce the maximum (reverse freefall) velocity from the received 58.8 km/s, 1.729 GJ/kg to 43 km/s, 924 MJ/kg; in turn, we can expect 58.8 km/s to 78.6 km/s, 1.729 GJ/kg to 3.089 GJ/kg returns. Thus, we ensure that we will always make some gain, and still allow mutual launch for roughly three-quarters of the year.

Can we improve this even further?

We are essentially adding on the orbital velocity when receiving and subtracting it when launching, so to maximize the difference, it pays to increase the orbital velocity, and for that we must move deeper.

Mimas is the closest of Saturn's largest moons, and therefore orbits the fastest.
For Saturn, we’ll go as far as Mimas (there are other moons closer in, but they are blocked behind the rings). This deep in Saturn’s gravity well, orbital velocity is an impressive 14.3 km/s, and escape velocity is an even more substantial 20.2 km/s. Mimas itself has a low mass and miniscule gravity – at 100 km orbit, orbital velocity is a mere 92 m/s and escape velocity is barely 130 m/s – so we could feasibly ignore its gravitational contributions to the projectile. 
Mimas is tiny. 
As before, we want the catcher and moon to be moving in the opposite direction of the projectile when intercepting, which leads to a relative velocity of 35.3 km/s, 623 MJ/kg. For a full retrograde return, we can do with a velocity of 10.2 km/s, 52 MJ/kg is sufficient. Thus, where Titan can make 4 times what it must send, Mimas can make a more impressive 12.

How far could one go with this? 

For the highest possible relative velocities, we should drop from the highest possible location to the lowest possible location, from Neptune to Mercury. 

The lonely blue planet.
We have already discussed the advantages of Mercury, but as for Neptune, it is so high up, its orbital velocity is miniscule (a mere 5.4 km/s) making for cheap returns, and little extra investment is needed to boost from freefall to retrograde (the aphelion velocity for our projectile in this case will be a mere 0.9 km/s).
Neptune is very far away...
The initial projectile can be launched from Mercury at 17.0 km/s, 144.5 MJ/kg; intercepting at Triton yields relative velocity of 13.1 km/s, 85.8 MJ/kg. Triton can then launch it back at 3.7 km/s, 6.8 MJ/kg, so it will arrive at Mercury at a whopping 118 km/s, 6.962 GJ/kg. Relative to its own launch, Mercury has multiplied the energy 48-fold, while Triton effectively multiplies launch energy 12.5-fold, and from Triton launch to Mercury reception, we have multiplied the energy a thousand-fold.
The launcher has to take into account Triton's inclination.
Similar systems can be worked out for other worlds, with figures worked out below. Note these assume low orbit launch (400 km unless specified), and the moons of the gas giants used are Callisto, Titan (1000 km), Miranda (100 km) and Triton:
Find full file here: Google Document.
Energies involved depend on the direction of transfer. For outward transfers, the pattern is simple: energy required at the inner world always increases and energy received at the outer world always decreases for further spaced partners. 

For inward transfers, it’s more complicated. Hohmann trajectories are also more expensive with distance, while freefall velocity is invariant of the inner world, and retrograde transfers end up being less expensive since we’re aiming for a decreasing aphelion velocity. Generally speaking, all inward transfers become less expensive as we move farther out, owing to the lower solar system velocities involved, which might be enough reason to justify colonizing the Neptune system – not only do we get more energy, it’s easier to send. 

The different InterOrbital Kinetic Energy Exchange trajectories possible.
Interestingly, this choice makes little difference to the inner world, as far enough out, relative velocity and energy change only a little even with greatly increasing distance. This is because projectile velocity is bracketed between the planet’s own orbital velocity and local solar escape velocity, and with this, we could set bounds upon the expected energy.

For two-way transfers, what’s most important is the location of both bodies in the solar system. For the terrestrial inner worlds, solar velocity dominates all exchanges, and so there are orders of magnitude difference between the cheapest sendoff/returns (Hohmann) and the most expensive (retrograde).

While significant energy is gained, much must be committed, so the overall multiplier for the whole exchange is low, and the outer world will usually earn a small fraction of what was initially given. For the gas giant outer worlds, the high orbital velocities and low solar velocities allow for small differences between different sendoffs. Launch can be made much cheaper than reception, so the two-way energy multiplier is much higher, and energy can be multiplied going both inwards and outwards.

But the gas giants need not limit themselves to interplanetary transfers. The same factors we’ve applied to interplanetary transfers can also be applied to interlunar transfers, between moons of the same planet. High orbital velocities and deep gravity wells are needed to make this work, which is exactly what the gas giants provide. Here the deepest moons almost hug the planet and can reach near-planetary velocities, while there remain far out moons for high gravitational potential.
Jupiter's spaghetti-orbits of its multiple moons. 
For maximum benefit, we try between the closest and farthest possible moon, ignoring oddly inclined outer satellites. Around Jupiter, this gives us Metis and Callisto. 
Callisto would make for an ideal colony location.
Launching from Metis at 11.6 km/s, 67.3 MJ/kg, we can receive the projectile at Callisto at 7.3 km/s, 26.6 MJ/kg. Launching it back at 9.8 km/s, 48 MJ/kg, it will be received at Metis going 74.6 km/s, 2.783 GJ/kg, 41.3 times what it cost to send.
Saturn has a huge collection of moons to choose from.
Around Saturn, we exchange between Mimas and Titan, again ignoring deeper moons within the rings (Hyperion might make a better choice than Titan in terms of distance, but Titan’s significant gravity gives it a greater advantage for changing velocities). Mimas sends out at 4.5 km/s, 10.1 MJ/kg, to be received at Titan at 5.1 km/s, 13 MJ/kg; launching back at 7.1 km/s, 25.2 MJ/kg, it is received at Mimas going 33.3 km/s, 554.4 MJ/kg, 55 times what it cost to send.
Similar systems could be set up around Uranus and Neptune, but would suffer due to the lower velocities and smaller spacing between moons.
These could be the trajectories of projectiles between a Saturnian moon and a low orbit station.
In both these cases, the farther moon suffers a net loss, and must be resupplied by the inner moon. Though we could make Callisto and Titan break even by launching into freefall rather than retrograde Hohmann, this would significantly reduce the energy available to the other world. 

In this case, the shorter distances make energy transfer via other means more viable, so Metis/Mimas could have an easier time resupplying. Clearly, this describes an optimal window; launch at other times is possible, but in this case the synodic period due to the inner moon is short enough (a day or less) that there is really no point in doing so.

What does this mean for the solar system at large? 

For one, gas giants can be relatively self-sufficient in terms of energy. Once enough energy is stockpiled for the initial launch and a redistribution system is set up to make up for the losses at the outer moon, this original stockpile can multiplied again and again to sustain local colonies.

A kite-drawn wind turbine in Saturn's high velocity winds. 
Alternatively, if the outer moon has its own alternative means of producing energy, this orbital transfer system could be used to share it. One could easily envision this opening up the Saturn system – wind turbines on Titan powering launchers to all the inner moons, which receive many times what Titan had to put in.

Such a system requires trust on both ends. 

Mimas cannot produce energy if Titan is not willing to send mass back to it, but it also won’t have any reason (or indeed, the means) to beam back energy in turn. 

Where orbital transfer is the primary source of power, it could force partnership based on mutual dependence: however each side feels about the other, its needs the system for sustenance, contingent on the others’ cooperation, and so they will put aside their differences at least insofar as it enables them to continue working together.

This breaks down if one side has an alternative energy source, in which case it gains a measure of power over the other partner. 

Consider Titan, powering the Saturn system through its wind turbines. Since it can make do without the beamed returns, yet is critical to circulating mass, it could use this to force its influence on the other moons, threatening to withhold all launches if they won’t subject themselves to its demands.

Such trust becomes even more critical when it’s done between planets, where shipments must be planned years in advance. The same energy politics could be extended to the solar system at large, though in this case, the threat is slightly different: rather than stopping the mass stream, which would not be felt for years, one world could radio propellant busses near their destination to move off course, thus immediately denying the catcher. 

The passive move is to order the projectiles to miss. The aggressive one... is to hit. (by JimHatama)
Mercury would seem to be best situated to take advantage of this, since it is the best partner in terms of frequency and energy availability per transfer, but also has plentiful solar power it can turn to should the launches cease.

Of course, this assumes that each side controls transfer in only one direction. It would certainly be in one side’s interests to control stations on both ends of the exchange, and thus avoid having to make any concessions to the other party.

This does not necessitate hostile acquisition – such a situation could arise historically from one colonizing power providing stations to develop its new outposts, and another could even offer these services to a more developed world selling the energy in exchange for local goods. 

A Kinetic Energy Exchange can serve as a transport system that supplants freighters. 
Other forms of dominance would require significant disparity between the strength of the dominator and the dominated, as one side must be capable of maintaining forces far from home to reliably defend assets right above the surface of their opposition. Justifying such presence would likely require significant energy to be at stake, and it may well be that some worlds’ advantages position them to be taken advantage of: Mercury and Neptune could well benefit, but they could also be at risk from those vying for the unique capabilities they’d offer.  

Having said that, the orbital transfer system could be a means of independence as well as suppression, because there is one thing that it almost unique about it.

It is an effective low-investment means of providing energy in the outer solar system.

This is critical; although many other means have been discussed on this blog, they require either large structures or rare resources. 

Wind turbines on a massive scale could be built within the atmospheres of the gas giants themselves, harnessing their powerful convective currents, but these would require delving straight into their deep gravity wells and creating structures in mid-air capable of surviving the harsh local conditions. 

Huge installations would be needed to extract significant energy from Enceladus's heat.
Large geo (luna?)-thermal plants could be built on Europa and Enceladus, making use of the temperature gradient between their frozen surface and subsurface ocean, but these would require digging tens to hundreds of kilometers through their crusts. 
Electrodynamic tethers can be used in reverse to produce electricity.
Electrodynamic tethers could be launched at the gas giants themselves, obtaining power as they de-orbit within each planet’s magnetic field, but these would require regular consumption of metal, a resource that is in short supply in the largely icy outer solar system.    

This far out from the sun, it’s most likely early colonies would rely on nuclear power, and to get that, they would need regular shipments of fissionable material from the inner solar system. At least for a while, they would be dependent on them for all their energy needs.

The orbital transfer system provides an alternative, both via interactions between moons and the planets themselves. It is not necessarily a good means of sending energy from the inner solar system to the outer, given how little energy is received relative to the cost of launch outside of optimal windows (as little as 2% for a retrograde Mercury-Neptune transfer), but it is great for sending energy from one gas giant to another, seeing as the high orbital velocities mean that is increased both ways.

If the inner worlds threaten to withhold shipments a little too often, Jupiter and Saturn could quickly set up networks within their own moon systems, having to hold on only long enough to get the launchers and receivers set up before they could power on and manage on their own. 

In the longer term, these two gas giants could set up exchanges between one another, forming the basis for further development. The turbines on Titan could be used to set up metal mines on Callisto, providing both with energy and metal, and in one fell swoop, they would cover two of the greatest limitations to their worlds’ self-dependence.
Suffice to say, the interorbital kinetic energy exchange allows for many different paths of development, making for a more interesting image of the solar system.


  1. Holy crap orbital mechanics allows for some crazy shit. I am shocked at that power multiplier, and that it can generate power on both ends even without the best of alignments! I've built up a good understanding of orbital mechanics in Kerbal but damn...
    Has anyone else made these kinds of suggestions before?

    1. The concept has probably been thought up be someone else before (as most ideas are), but it has only been considered in terms of propulsion concepts, and never with a focus on power transport or power generation.

      So, yeah, this is original.

    2. Jesus, holey mary of all spess cheese, that's incredible!!!....o____________O

    3. Thanks andrew. A lot of the credit goes to Zerraspace.

  2. Where is the energy actually coming from, though, in the conservation of energy sense? Are we moving net mass down well or slowing orbits of the main bodies?

    In a possibily related question, how much energy will it take to keep the orbit of the launcher platforms drom decaying?

    1. Both come into play; motion down the gravity well is responsible for the change in velocity between the catcher and launcher, but momentum exchange is more significant at the ends themselves. Technically, the mere passage of the projectile affects the body's orbit as well, but this is where we have the most dramatic and sudden change.

      Stationkeeping of the launcher/catcher platforms will be a significant issue, given the velocities involved. We do have a few solutions, but will go into detail in the following post. That being said, one of our followers on Reddit arrived to a similar conclusion - using slower exhaust at the launcher/catcher, you could use more propellant but at lower energy (since energy scales to the square of velocity, but momentum scales linearly). For his scenario, it was possible to hold up the station with some 7.5% of the energy received.

    2. Could you use an efficient thruster like an ion thruster or the like, or would the propulsion need to be concentrated in time to when the projectile is launched? If efficient high isp thrusters are viable for this use case you could potentially see some of the largest engines in the solar system involved in this scheme.

      Also, how would catching work without nuclear-level blasts? Throwing grains of sand and using them to heat up water to produce steam? Throwing specialised packages that can be caught electromagnetically?

    3. You need to burn in roughly the same location as you launch/catch to avoid creating a lopsided orbit, so time concentration would be preferred, though long term thrusters could still work by intermittently burning around the desired location and splitting it up across several burns.

      That being said, this is a possibly unique case where you want lower exhaust velocity, rather than higher. This is because momentum and energy both scale linearly with mass, but momentum scales linearly with velocity and energy scales to its square. Basically, when you increase exhaust velocity of the propellant, you'll get more momentum out of less propellant, but you'll also end up using significantly more energy, taking up a greater fraction of what you gained. In fact, it can proven that the only way to make gains at all is if your exhaust velocity is lower than your launch/catch velocity, which means you'll need to expel more propellant than you launch/catch. This does require cheap and easy access to propellant, or a local store (say, if your station is bolted to an ice asteroid), but we may have determined a way around this (we'll keep you posted).

      The catcher is actually fairly similar to the electromagnetic launcher, using the same effect but in reverse. It requires that the caught/launched object is conductive, but once the mass passes through, it can be braked magnetically and its kinetic energy stored.

  3. Very good. Little nagging however: I think 'freefall' is used to describe any situation in which the gravity is the only force acting on the body, so Hohmann transfer is just as freefal as the straight-fall degenerate orbit you described as 'freefall'

    1. Well, we do what we can with the limits of the vocabulary that is available!

  4. I had thought that simply sending unmanned and unpowered cargo pods via mass driver would be an efficient use of resources, but this turns it from a way of minimizing resources and costs into a pretty large profit centre as well.

    1. It solves a lot of the energy issues with colonizing Jupiter and Saturn too!

  5. This reminds me of the system Paul Birch formulated for moving planets around, the link to his papers are below:

    This seems to be a similar concept to Birch's article, but in reverse: subtracting energy from the system, instead of adding it. Makes me wonder if, on a large enough scale, over a long time, how this would move the planets. My intuition says it would cause the inner planet to spiral inwards, and the outer planet to spiral outwards, but I could be wrong. Maybe governments would try to enact laws to stop the solar system from spiraling apart.

    1. Well, you can consider the system as a rocket engine. Take the power contained in the mass stream, multiply by two, divide by the projectile's velocity and you get a 'thrust'.

      You'll notice that you need exorbitant amounts of energy to even move the planets by the smallest amount.

      100PW of power, 50km/s projectiles, gives us enough thrust to move mercury by 0.38 millimeters per second... per year.

    2. Ah, I see. Looks like getting putting Mars in a better orbit will have to wait for a few million years.

  6. I am incredibly impressed. What amounts of power are you talking about in some of these scenarios; i.e. what are realistic, extrapolatable levels of power generation based on the above calculations?

    1. Hi Keith.
      It will depend on how many resources are dedicated to the catcher station.

      Realistically, I expect 10kW/kg from the catcher station, meaning that a 10,000 ton station produces 100GW of power. There will be dozens of such stations, but only ten of them would be needed to supply the world's energy needs.

  7. Interesting idea, though I can only imagine what safety redundancies that would have to be put in place to prevent these exchangers from being used as orbital bombardment weapons, especially if they are automated and become routine.

    1. Well, two factors help prevent them from becoming orbital bombardment weapons, if implemented correctly:
      -The atmosphere around Earth prevents the masses streams from reaching the ground. When the relative velocities are measured in dozens of kilometers per second, the mass streams are more likely to explode in the upper atmosphere than reach the ground.

      -Default misses. The mass streams can be aimed to miss the catcher station, occupied orbits or the entire planet by a wide margin. Only when they get close to their target to they divert their course with onboard propulsion. This ensures that if the mass stream's electronics or controls fail during their long trip through space, it does not automatically lead to them colliding with something. They can also be given emergency maneuvering systems, perhaps even externally ignited, to force a miss at the last second if something goes wrong.

  8. An interesting article from Centauri Dreams, about the "Dipole" sail. While interesting in of itself, it also speaks to having a low mass, low "cost" add on to your cargo pod (or whatever else you are sending) on the energy "pipeline" in order to do those terminal manoeuvres for meeting the man decelerator.

    1. Thanks for sharing the link.
      I have been discussing actively propelled mass streams with Zerraspace, and that would be a good option.

  9. Interesting concept. Just checking: The point is to steal energy from 1. the gravitational potential energy of the projectile (minor); 2. the kinetic energy of the planets and moons (major); right? Once Earth LEO station catches the Pluto pellet, Earth gets slowed down a little and falls a little deeper into the sun's gravity well, and we steal that.
    I'm trying to imagine how a large crate moving at up to seventy kilometers per second be caught? Tether systems? A giant magnetic basket a hundred kilometers long?
    Launch windows are going to be problematic. Storing the terajoules is even worse (unless you're a tether - and since you're spinning around at seventy klicks per second - for the jupiter example - would carbon nanotubes cut it?). Giant lasers and PV panels seems easier to do.
    It seems to me that either system will have to be fixed to a moon - gravitationally or materially. If Pluto station keeps sending pellets down to Earth LEO, Earth LEO will eventually fall out of orbit unless it is attached to a mountain, or a space elevator, or a cheap source of mass to cheaply shoot the other way as rocket fuel. Or run it as a statite in a non-standard orbit, using the mass catcher in place of a solar sail for thrust. Is that at all possible?

    1. Hi!

      You are correct. The projectile is simply the vessel through which gravitational potential energy is taken from the launcher's planet and added to the receiver's plant.

      The payload is launched by a coilgun. At the 'catcher' station, it is intercepted by a 'reverse coilgun', that applies electromagnetic braking to slow down the projectile to a stop while extracting its kinetic energy in the form of electricity.

      You won't need a terajoule storage system if you divide your payload into a stream of small projectiles.

      The catcher station does lose momentum and orbital velocity as it catches projectiles. It can spend a small percentage of the energy is receives to accelerate some propellant to compensate for this, and the propellant can come from an orbital propellant depot, a captured comet or scooped up from the atmosphere.

  10. On a more near-term scale:
    If large cargo pellets (>30 tonnes) are launched in the billions of tonnes/year from the moon in the near future (the average O'Neill cylinder needs that, I think), and a substantial proportion of them are diverted to Earth to deliver raw materials or finished goods, it may be cost-effective to use the heat and light from re-entering cargo pods to melt sea ice to keep the Northwest Passage open.
    The energy from rocks dumped from the edge of the system might also be useful for terraforming Mars (not easy, even with unlimited energy). A few Chicuxlub-sized rocks impacting at retrograde velocities might be enough to melt the ice caps in one go. Back in the 80s, they talked about imaginary "nitrate beds" to vaporize with nuclear bombs, and rocks from the system's edge - part of this energy transfer system or a predecessor to it - might be just as good.
    I don't think terraforming has been discussed before on this site. From what I can tell, terraforming Mars will require delivery of large volumes of nitrogen and water, and that even if Mars were moved to 0.9AU tomorrow morning and given an artificial magnetic field, it would still be unsuitable for human habitation without extensive deliveries of materials. Has anyone heard anything regarding this speculation?

    1. Correct, terraforming hasn't been discussed in ToughSF, because I generally take it to require technologies too advanced to speculate accurately on. Moving planets is even more far fetched!

      If we could move plants, bringing a watery moon such as Enceladus closer to the Sun is much more interesting.

    2. Oh, I wasn't thinking of actually moving Mars. More like building seventy million square kilometers of foil mirror (keeping 'em flat is going to be non-trivial) and sticking it at the Mars-Sun L2 point to light up Mars's nightside.
      With Mars's surface area being 144 million square kilometers, this should be adequate to double insolation and achieve nicer temperatures.
      At 1 gram per square meter (easily achievable with solar sails), all you need is seventy million tonnes of material - non-trivial, but much less than the mass of Deimos.
      The point appears to be that Mars will not automatically become earth-like if we shine enough energy on it. And shipping trillions of tonnes of nitrogen (or more) in from the Outer System may well be much harder (methinks) than building seventy million square kilometers of foil mirror.

    3. The mirror is, of course, a constellation of smaller, much more manageable mirrors.

    4. For comparison, the world produces 1.6 billion tonnes of steel per year.

    5. Construction projects are best served by sourcing materials locally (from Mars's metal-rich surface) or from low-deltaV-cost sources (such as metallic asteroids). Sending materials all the way from the outer solar system does not seem reasonable.

      Nitrogen in the form of ammonia ice is plentiful. Comets are full of ices, and many can redirected at low cost to hit Mars, especially if the water ice on those same comets is used as propellant. Only if you're looking to fill up an entire planet's atmosphere with nitrogen do the comets start seeming insufficient.

      Mars only really needs enough sunlight to keep liquid water from freezing. No amount of sunlight will allow this while the atmospheric pressure is where it is. It is therefore necessary to increase the pressure to the point where the existing insolation can keep it liquid. For example, 10kPa and 10°C.

      Liquid water is great because it absorbs most of sunlight's energy and converts it into heat. Ice is bad because it reflects away sunlight.

    6. I enjoy reading speculations about terraforming Mars. Much like many magic tricks, most serious proposals usually can be summarized with "it's done with mirrors".

      Using the mirrors to focus gigantic amounts of solar energy on points not eh Martian surface could conceivably bill the oxygen out of the Martian rocks (which is probably the most energy intensive option possible). Using less energy could sublimate the CO2 in the Martian polar caps, thickening the atmosphere to the point that you could have liquid water on the surface. The water itself can be melted out of the remaining polar ice and from Martian permafrost, the issue here is there is no clear understanding of just how much water there actually is (estimates of Martian permafrost and trapped water are all over the place).

      Sending some comets to bring more water to the surface seems to be a pretty obvious step, although unlike Law Wong's posts above, I would not want the comets to arrive at interplanetary velocity, since the energy of the impact is likely to blow more material back into space than you receive. Slowing them down via solar sail or other sail technology, or capturing cometary material in a decelerator to gather the kinetic energy, then dropping them at mere orbital velocity seems to be a much safer and more controllable option.

      Sending cometary material to a mass catcher or other kinetic energy gathering device seems to be the best solution, you get both your water and other elements to create an atmosphere and fill the Boreal Ocean, and you get a supply of energy to power the industrial economy of Mars (or at least the part in orbit). And the captured materials are equally useful in space as on the planet, one possible "sub plot" for anyone contemplating worldbuilding on these lines is how to deal with the economic, social and political pressures to send materials to one or the other destination. IF Space industry can reliably outbid the Terraforming effort, but Teraforming is the centrepiece of the Martian Government's platform, we can see lots of rent seekers and political operatives struggling for control, making for an interesting setting.

    7. Interesting points. Catching cometary material de-orbited from the outer solar system, or ice launched from a moon, allows for vast amounts of energy to be gained. That energy can be applied to crack oxygen out of Martian rocks at a low cost and release the waste heat into the environment in a controlled manner, allowing you to deal with several problems at once.

      Even if we sublimated all of the frozen CO2 and melted all of the ice, we'd be left with a thin and toxic atmosphere, hence the need for the oxygen-releasing steps. Nitrogen is only about 5 times less abundant than oxygen in our Solar System, so getting a hold of it should not be difficult either.

      My issue with terraforming Mars is that the process is only worthwhile if you expect Mars to hold a very large population for a very long time, but whatever you do, Mars naturally wants to lose its atmosphere and return to its cold and dry state. It will have to be artificially managed to remain habitable, at which point it is not much better than artificial habitats.

    8. I mostly agree with you WRT the difficulty of maintaining a warm environment on Mars, but suspect that the motivations of the terraformers would be more akin to a religion than a technological project with a defined cost/benefit ratio. The people building the pyramids and other monumental architecture in ancient Egypt were skilled craftsmen and labourers who were evidently happy to build these things, even if a rational calculation would suggest building granaries and housing would be a far more effective use of their time. Builders of medieval cathedrals had similar impulses, embarking on projects which would take generations to complete.

      Of course in an SFnal setting, we can always apply various forms of handwavium to the problem (even if this isn't the purpose of your blog), including extended lifespans so people are willing to embark on 1000 year projects, artificial magnetic fields to protect Mars (a good use of the orbital kinetic energy) and even postulating an artificial diamond "shell" over the atmosphere to keep everything inside.

    9. Some popular theories indicate that most of Mars's carbon dioxide was lost to space (due to UV radiation and the solar wind) in the early stages of its history.
      As a result:
      The problem to me does not seem to be a lack of water, or oxygen (breathing masks are acceptable to most people).
      The problem seems to be a lack of carbon dioxide (this was assumed by many of the early terraforming theorists to be in abundance). Even if you build seventy million square kilometers of foil mirror to char-grill Mars and boil the ice caps with giant terawatt lasers and asteroid strikes, you only end up with less than 0.1 atmospheres (0.1 bar) of pressure or something like that. Add in the dry ice in the deeply buried permafrost - that'll take decades or centuries to heat up and maybe you can squeeze out half an atm (0.5 bar).
      Nitrogen is also a problem, as most people have noted.
      Water, on the other hand, seems to be in abundance everywhere under the permafrost and in the ice caps, although sea level may be disappointingly low, leaving most of Mars a desert.
      I'm also dreaming about positive/negative feedback effects and the effects of a terraforming project on existing settlements. In short, you do not want to live in a planetary construction site.
      A good model might be terrestrial arctic settlements built on melting permafrost. Sinkholes, bogs, and landslides might be a problem (I have no idea how wet inorganic sand/clay behaves).
      If too much water vapor saturates the atmosphere, we may end up with too much cloud cover, raising albedo and requiring even more mirror to heat Mars up.
      That same water vapor might alternatively create a strong greenhouse effect (think Venus). This might be desirable for steam-cooking Mars to get all the volatiles out of the permafrost (but see above point, I do not know how to model this). The mirrors can be turned off once Mars is well-done.

    10. I suppose, as suggested above, you could electrolyse enormous amounts of silicate sand and water to obtain 0.2 bar of oxygen atmosphere, but building the self-replicating factories to do that (on boggy terrain no less), and permanently sequestering the pure-ish silicon bars (or blasting it into orbit) is going to be a hassle. Are there plausible thermochemical methods?

    11. Thucydides: A quasi-religious motive might end up being the case, but it is irrational and hard to discuss objectively.

      Bubble atmospheres, where sea-level conditions of 1 atm are maintained inside enclosed volumes, is not a very far fetched idea!

      Law Wong: 100% correct. Building an atmosphere on Mars needs input from external sources on the order of 10e18 to 10e22 kg.

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  12. A bit more on electric sails. While the KE exchange revolves around dropping down the gravity well, a sail such as described here can be used both to control the descent (especially the fine aiming at the end to hit the mass catcher) and of course to go "uphill" against the gravity well:

    IF you don't have a handy mass driver in the orbit of Uranus, you could always use the sail to "kill" your orbital velocity relative to the Sun and then start your fall towards Luna or wherever your target mass catcher happens to be.

    1. Zerraspace and I are actually going through the benefits of using high-efficiency propulsion schemes on the falling payloads to significantly boost the energy in to energy out ratio.

      Thanks for the link!

  13. Always glad to help. Personally I would focus more on using the high efficiency drives to go "uphill" and let the gravity well do al the work on the downhill leg. All you would need is a drive with sufficient power to make fine corrections as you fall to hit the mass catcher, and everything else is a net positive.

    I'm not clear if you would recover *more* energy than you would input using a drive on the downhill leg (the Laws of Thermodynamics and Conservation of Energy would suggest that the extra energy input in accelerating downhill is not going to be fully recovered at the mass catcher).

    1. We're still working that out, but there's one obvious benefit to accelerating 'down' the gravity well: the travel times will be shorter. Most of the payload's time is spent slowly accelerating inwards from the Outer Solar System. A small kick to a higher initial velocity can drastically reduce the travel time and the 'set up delay' for any kinetic energy stream.

    2. Much of that really depends on the economics of the system, and to a lesser extent, the political situation.

      Once you start sending a steady stream of mass "downhill", you are essentially filling a pipeline. Once the pipeline is "full", then you can continue to run things with minimal input or fuss. I would think that if you need to reduce the set up delay, there is either some economic or political emergency which requires you to eat the extra costs, but then you would want to gradually reduce and eventually eliminate "boosting" payloads downhill to get an equitable cost structure.

    3. Simple financial incentives would give sufficient justification to speeding up the delay between setting up a 'pipeline' and receiving the goods at the other end. You have the time value of money, the compounding required rates of return and other time-sensitive factors that make you want to recover your investment as quickly as possible.

    4. Any plans for new articles on this blog soon, really liking what I've read so far.

    5. Soon! I am trying to find time to complete and post a few things.

  14. Can we do this with rotating tethers instead of coilguns?

    1. In principle, you could do this with a really massive set of rubber bands, all the is really required is a way to provide an impulse to the mass to get it into a transfer orbit, and a way to capture the mass and retrieve the energy. As a practical matter a massive rotating tether is great for flinging payloads and capturing them, but extracting "excess" energy is a bit of a chore.

      In real life, the tether is going to either gain or lose rotational energy (based on "flinging" or "capturing"), and can also express the energy by gaining or losing orbital altitude. As well, I suspect a lot of energy will be wasted by flexing and vibrations along the tether.

      Coilguns or mass drivers will have issues as well, but the major advantage is their energy can be fed or tapped as electricity, which is much more fungible. You can quickly take the electrical energy from an Earth orbiting mass catcher and use it to perform industrial work in orbital facilities, split water into H2 and O2, or charge up millions of Tesla cars. The mss drivers can be fed from fusion reactors, giant solar panels or other external sources of energy as well. Rotating tethers will likely need rocket engines to start the rotational process. with the issues that might cause.

      The final issue is where these devices will be placed. A mass driver can be on the surface of a moon or asteroid, as well as flying in orbit or deep space, while a tether will have to be in orbit or deep space, and if in orbit, in a high enough orbit to clear other structures and prevent orbital decay from causing it to crash to the surface (should there be a long delay in receiving incoming packages and gaining energy, for example).

      So in general, I would be more inclined to go for mass drivers or coilguns over rotating tethers.

  15. Any plans for new articles here soon? Great work.

    1. Yes! Sorry for the long delay. I think I've got something big coming within this week.