Guest Post: Orbital Momentum as a Commodity

Hello, everyone! Today I have a guest post by my friend Eamon K. Minges, author of the upcoming novel Paradigm’s End from Kindle Direct Press. He’ll be examining various energy-efficient methods of orbital launch, comparing their merits, and discussing their possible applications. With no further ado:

Part 1: Tsiolkovsky’s Tyranny

For over sixty years, humans have been launching liquid fueled chemical rockets to send their numerous payloads and live human astronauts into space. The advantages of chemical rockets are numerous. Liquid fuel chemical rockets rely, after all, on cryogenic volatiles that for the most part are both easy (from a chemical engineering perspective) and inexpensive to produce. Nevertheless, the payload they can deliver to orbit is limited to a small fractional percentage of the rocket’s liftoff mass, On average an orbital chemical rocket gross liftoff mass is 93-95% fuel and oxidizer. Why is this? About 120 years ago, a Russian/Soviet scientist and pioneer of modern astronautic theory, Konstantin Tsiolkovsky, figured out through rigorous research and experimentation the fundamental factors that limit a rocket’s total change in velocity (delta velocity, or delta-v). In 1896 he synthesized the final form of his rocket equation, and the news for chemical-fueled launchers wasn’t good.

The rocket equation. I used to have this framed on my wall.
A graph of the Tsiolkovsky rocket equation. On the bottom axis is delta-V as a multiple of exhaust velocity, and on the vertical axis is the mass ratio.

What Tsiolkovsky figured out was that as you increase the fraction of a rocket’s mass that is fuel, you get diminishing marginal returns on your delta-v. In the Tsiolkovsky equation the total delta velocity a rocket system can achieve is calculated by multiplying the rocket’s exhaust velocity by the natural logarithm of the rocket’s mass ratio, which is rocket’s fully-field mass divided by its unfueled mass (sometimes referred to as the wet mass over the dry mass). 

Unfortunately for orbital rockets, Earth has a thick soupy atmosphere and relatively high surface gravity compared to most bodies in our solar system. This means that it takes about 9,400 m/s of delta-v to achieve a circular 350-km orbit once gravity losses and drag are factored in. This amount of delta-v is punishing for chemical rockets looking to achieve Earth orbit, because it consigns the lion’s share of the rocket’s liftoff mass (93-95%) to fuel and oxidizer whilst leaving only a small pittance for payload allowance. Overall, the “tyranny of the rocket equation,” as some engineers refer to it, has severely impeded the infrastructure and space based economy needed for the settlement of cislunar space and the solar system as a whole. One solution would be to raise the exhaust velocity of our orbital class rockets, but unfortunately there is a hard limit on exhaust velocity of chemical rockets.

Operationally, the highest exhaust velocities for existing orbital rockets are around 4,400 m/s, Hydrolox engines like the Space Shuttles RS-25 and the Delta IV Rs-68a, as well as the Atlas Rs-25 and Blue Origin’s Be-3u, are capable of achieving exhaust velocities of around 4,100 m/s to 4,450 m/s, while the highest ever exhaust velocity by a liquid fueled chemical rocket was 4,900 m/s, which NASA achieved on a test stand with a experimental engine powered by a tri-propellant of liquid hydrogen, fluorine and lithium, clearly untenable because of toxic exhausts as well as fuel costs. 

As I see it there are two solutions to this problem: the first would be to raise the exhaust velocity of our orbital rockets, which would require that our launch vehicles leave the realm of chemical reactions and enter the higher-energy world of nuclear physics. This solution, however, is not practical in the short or even medium term for two reasons. Firstly there is the obvious regulatory problem. What government would allow an agency or company to launch vehicles that could spread vast amounts of nuclear fallout in the event of a launch failure? Secondly, all of the nuclear thermal fission-based rocket engines we have built have pitiful thrust, incapable of overcoming gravity losses.

My second solution might seem like a bit of a head scratcher at first, but hear me out. What if we could dramatically lower the delta-v required for rockets and space planes to reach orbit? And no, I’m not talking about messing with the laws of physics and destroying the planet in the process, I’m talking about something much more practical and near term. In my opinion, the first piece of space infrastructure necessary to get millions of tonnes into orbit is a large fleet of rotating skyhooks. What is this, you may ask? Let me explain this wonderful concept in more detail.

Part 2: Hooked from above

Many of you reading this post may be familiar with the concept of the space elevator, the idea of tethering a point at the Earth’s equator to a station in geostationary orbit. While this is a good idea in theory, the practical engineering challenges of building such a structure on Earth have yet to be overcome, the main problem being that we don’t have any materials that could support their own weight across 35,000 km. Even carbon nanotubes look to not be strong enough to build a space elevator on Earth. Despite this, a space elevator is possible on both the Moon and Mars due to their proportionally lower gravities. But what if we could make the tether shorter on Earth so that it could support its own weight? Well, it turns out that this is possible with another well known launch assist system: the skyhook.  

This is how it might work. As the radius of your orbit increases, your orbital velocity relative to the surface of the Earth decreases in an inversely proportionally way, and due to this principle it would theoretically be possible to hang a long tether that would orbit at the orbital velocity at the point of its center of mass.

Skyhook1 / CC BY-SA (https://creativecommons.org/licenses/by-sa/3.0)

Now, imagine that the bottom of this long tether was just above the Karman line, say ~100 km. For simplicity’s sake let’s say that this long tether sat in a perfectly circular equatorial orbit and that its center of mass was at say ~350 km and another 350 km up was the tether’s release zone, at a low of orbit of around 800 km. Now imagine that a spacecraft was launched from Earth’s surface on a suborbital trajectory to catch up with and get hooked by the tether, then lifted up by a gantry or elevator mechanism at the release zone. This would allow the spacecraft to launch into an 800 km low Earth orbit for a considerably lower delta-v than from under their own power, because the skyhook transfers its overwhelmingly large orbital momentum onto the spacecraft it catches so as to assist it in reaching a final orbit. In the non rotating skyhook example (such as the diagram above) the delta-v to reach the skyhook’s lowest end would be only 4.7 km/s, as opposed to the brutal 9.4 km/s currently required to reach LEO—that is half the delta-v!

This design, however, can be even further improved upon. By rotating the tether around its center of mass in a counter orbital direction relative to the vector of the orbit, the skyhook could in theory effectively reduce its required capture velocity down to >1 km/s by taking advantage of the cardioid shape of its motion relative to Earth’s surface. Such a drastic reduction in Delta V would allow chemical rockets or space planes with mass fractions as low as 0.25 to launch into orbit. 

For a skyhook to be able to lift hundreds of tonnes of payload from the Earth’s surface, its mass would have to be proportionally over 1000 times that. Say 100,000 tonnes relative to a 100 tonne payload, this is necessary because each time the skyhook captures a payload there is a momentum exchange between the ship and the hook. The exchange is negative and leads to the hook losing orbital momentum. The more massive the hook the less orbital momentum it will lose when it captures a rocket or spaceplane. To compensate for losses in orbital momentum the hook may require a thruster system near its center of mass Another option to boost the hook’s orbit would be to use the concept of electromagnetic tethering, which has been used before in weather satellites to periodically boost their orbits. By generating a wide magnetic field of its own, the satellite or skyhook can effectively push off the Earth’s magnetosphere to replace lost orbital momentum. This is one of the few known practical methods of reactionless propulsion, besides solar or laser sails. 

Currently a skyhook is within reach for us to build if the cost to orbit goes down enough to make it affordable. Fortunately with super heavy lift reusable launchers such as SpaceX’s Starship as well as Blue Origins New Glenn and China’s Long March 9 on the horizon, this looks like a more likely prospect for the near future. A skyhook could theoretically be built with carbon composites since they have enough strength to bear the necessary force loads imposed upon such a structure. With reusable heavy lift launchers the skyhook’s structure could be built on Earth and then assembled robotically or remotely by drone pilots working on Earth over the course of a few years. Once fully assembled it could be spun up by thrusters mounted on either end of the tether. In the past I’ve read cost estimates that vary between about 100 and 350 billion US dollars to successfully build such a structure. While this cost may seem immense it is not outside the wealth of individual nations or even larger companies in the private sector.

The impact of a rotating skyhook to spaceflight would be immense. Its implementation would mean that a spacecraft with a mass fraction of .25 could effectively get to orbit just using chemical rockets. The combination of the reduction in required delta-v as well as the practicality and inexpensiveness of chemical rockets would cause launch costs to plummet, making possible a much larger build up of infrastructure and facilities in both low Earth orbit and in cislunar space. In my opinion, building rotating skyhooks would represent the first serious step to building large space colonies and settling Mars, as well as more easily getting access to Lunar resources.

Part 3: Beyond the skyhook

Once you have a rotating skyhook, many more possibilities open up. The skyhooks of Earth will be essential to interplanetary trade as the Panama canal is to international trade. The skyhooks would allow enough mass to affordably be moved to LEO to bootstrap an economy and more importantly an industrial capability. Factories in Low Earth Orbit could produce lunar landers to build up facilities on the Moon or perhaps rotating space habitats for tourists to visit in Low Earth Orbit. Once industrial capability exists in Low Earth Orbit mass can much more cheaply and easily be moved to the Moon. After a skyhook I’d anticipate a buildup in trips to the Moon focused on mining lunar materials and potentially extracting rare fusion fuels such a tritium and helium-3.

Eventually, with enough lunar industrial capability, a space elevator could be built on the Moon, since its surface gravity is low enough for a cable to be able to support its own weight all the way down to the surface.

A lunar space elevator would be tethered to the Moon’s equator with the additional possibility of a tether going to the south pole. Since the mining of Lunar resources is critical for building megastructures in space I personally assume that a lunar space elevator would perhaps soon follow a fleet of rotating skyhooks working on earth. The ability to ship millions of tonnes of lunar materials around cislunar space for relatively low costs would enable the dream of the late Princeton professor Gerard O’Neill to finally be realized. A lunar space elevator in tandem with rotating skyhooks would permit the construction of massive rotating habitats such as the O’Neill cylinder, Bernal Sphere or the Stanford Torus, as well as the economic vitality required to keep the populations of these space colonies employed.

In short: if we make the costly investment in building rotating skyhooks, and perhaps a lunar elevator, we will save drastically on the delta-v and overall energy required to bootstrap a space economy, allowing for settlements in cislunar space, on the Moon, on Mars, and potentially beyond.

Thank you for reading Eamon’s guest post! If you’d like more space and speculative fiction content delivered directly to your inbox, be sure to follow “Let’s Get Off This Rock Already!”; I’ll see you guys next week with my review of Interstellar (2014).

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

Powered by WordPress.com.

Up ↑

%d bloggers like this: