Thursday, June 15, 2023

Orbital Tethers as Momentum Capacitors

Some years ago I was knocked off my chair when I was soldering a flash for our camera. The flash was powered by two AA batteries. How could such a dinky power source pack such a wallop?

It was because of the flash's capacitors. A capacitor will build up a charge over time and then release the accumulated charge suddenly. In this case the flash would deliver a very bright and brief flash of light when the camera shutter was open.

The orbital tether as a capacitor for momentum.

An ion engine can have an exhaust velocity of ~30 kilometers per second. That is nearly eight times that of the best chemical exhaust, around 4 kilometers per second. That means a much smaller exponent in the rocket equation. When we're taking exponents, scaling by 1/8 can make a huge difference in delta v delivered per kilogram of propellent.

The problem is the ion engine's dinky thrust. A chemical rocket can slam you back in your seat with 4 or 5 g's. But an ion engine's delicate push is barely perceptible, like the push of a feather. It takes a long time to build up delta V which makes it difficult to enjoy an Oberth benefit. It can also mean a trip lasting months for a trip that would take hours via a chemical rock

But a tether with an ion engine can take months or weeks between catches or throws to build up momentum.  So while it takes a long to build up momentum, it can release or impart it suddenly with a Catch or a throw.

So a tether can impart a brief and powerful change in momentum even with the ion rocket's barely perceptible thrust. It is like a capacitor but for momentum instead of electricity.

More tether stuff

It's been a long time since I did a post on tethers. So I'm going to toss in some other random bits that have accumulated in my head over the years.

Musk and Carmack on orbital tethers.

Back in 2016, shortly after SpaceX had landed a booster on an earth platform, John Carmack tweeted:

Elon replied:

I was delighted to see this exchange. I've been hanging around spaceflight forums since the 90s and Carmack has long been a big name in new space. Carmack and Armadillo Aerospace were X-Prize winners in 2006. I don't think I need to review what Musk has been doing.

Carmack, Fear and Dread

Carmack and ID software made a very successful computer game set on the Martian moon Phobos. The names of the Martian moons (Phobos and Deimos) means Fear and Dread. Which is very appropriate for the computer game Doom.

I love the idea of using the Martian moons as settings for science fiction stories. I believe they will be great assets in humanity's effort to settle the solar system. I've done a number of blog posts on Phobos and Deimos:

Phobos, Panama Canal of the Inner Solar System.

Upper Phobos Tether

Lower Phobos Tether

Deimos Tether.

But if I'm trying to sell Phobos and Deimos maybe I shouldn't be mentioning Doom. Oh well.

ZRVTO between Phobos and Deimos

Thinking about elevators anchored on Phobos and Deimos it occurred to me there would be a Zero Relative Velocity Transfer Orbit (ZRVTO) between the moons' tethers.

The transfer orbit's velocity at periapsis matches the speed of Phobos' tether top. Velocity at apoapsis matches the foot of the Deimos tether. Thus passengers and cargo could be exchanged between the moons using very little propellent.

I hope this idea will eventually be used.

ZRVTOs in other settings

There can be ZRVTOs in other settings. The tether anchor masses need to be tide locked in circular, coplanar orbits. Which describes a lot of the moons of Jupiter, Saturn, Uranus and Neptune. I look at this in Mini Solar Systems.

In Trans Cislunar Railroad I look at ZRVTOs between possible tethers in earth orbit:

In some ways tether mass is like propellent mass in the rocket equation — tether mass goes up exponentially with increasing delta V.

But tossing payloads between tethers breaks the the delta V budget into chunks. And thus greatly reduces the needed tether mass.

How much mass is saved with with ZRVTOs?

The above system tosses payloads up to the moon. For kicks I decided to see what would happen if I made a single LEO tether long enough to throw payloads to the moon.

I placed an anchor mass 1000 kilometers above earth's surface and tweaked tether length until the apoapsis of a flung payload was a lunar distance (384,400 km).

Taper ratio about 35. The tether would need to be about 106 times as massive of the payload it throws given a safety factor of three. It would need to about 1,842 kilometers long.

Let's compare that to my system of tethers in the Tran Cislunar Railroad:

So my system of tethers is actually about 5,000 kilometers longer than LEO tether capable of slinging payloads to the moon. That's a little disappointing. But tether to payload mass is less than 4.

So there is more than a 25 fold savings in tether mass. That is gratifying.

"Would only matter if it was extremely big"

Recall Musk's reply to Carmack was "Would only matter if it was extremely big".

The tether anchor would need to be a lot more massive than the payloads it handles. Or else the act of catching or throwing a payload would destroy the tether's orbit.

That's not an issue for tethers anchored on planetary moons. But it seems like a show stopper for tethers in earth orbits. Or maybe not....

Big Balls of Dead Sats

There is a lot of dead sats that could be harvested for a momentum bank. As of 2015 it was estimated that there were 670 tonnes of dead sats in the graveyard orbit just above geosynchronous orbit. 

Gathering these into a single anchor mass would vastly reduce their surface area and those lessen the likelihood of impacts generating orbital debris.

Many of them still have solar panels that can provide electricity. There are high gain antenna dishes. Some of the harvested momentum mass might even be useful.

What about LEO?

In 2016 I was wondering how we could provide a massive anchor for a LEO tether. But since then Elon Musk and SpaceX have been launching StarLink, a huge constellation of communication satellites.

I expect at the present time the plan is send an aging StarLink satellite down to the upper atmosphere and let it become a shooting star. But couldn't satellites in similar orbits be gathered together to form a momentum bank? If so, Musk has already made huge deposits into an LEO momentum bank.

And the StarLink satellites have a lot of solar panels as well as ion engines that could be salvaged.

Some ZRVTO equations

Some equations to figure lengths of tethers that accomodate Zero Relative Velocity Transfer Orbits. 

Lower tether length would be L1((1+e)^(1/3) - 1).
Upper tether length would be L2(1 - (1-e)^(1/3))

Momentum Exchange

At the outset of this post I mentioned tethers could impart momentum gradually built up by ion engines whose exhaust velocity is a lot higher than chemical rockets.

If there is downward traffic as well as upward that could greatly reduce the argon or xenon propellant used by the ion engines.
Momentum boosting maneuvers
Catching payloads from above or dropping them into lower orbits
Momentum depleted maneuvers
Catching payload from below or tossing them into higher orbits

These could be balanced to achieve most of delta v needed, in my opinion.

Propellent Mass as cost driver?

Reducing propellant mass should be a top priority. In even the best circumstances Gross Lift Off Weight (GLOW) from earth's surface will be dominated by propellant.

Charlie Stross was indignant when I was ridiculing space naysayers. He said he wouldn't dignify my criticisms with a public response. But then proceeded to make several thoughtful public responses. Link. I quote:

"My cost estimate was for near-future transport to LEO.

"Contemporary civil airlines' operating costs are on the order of triple the cost of fuel. (Equal shares: fuel, airframe depreciation and maintenance, and crew/ground support costs.)

"If you want to do it for less than triple the fuel cost, you need to beat the standards of a viciously competitive industry that's been trying to pare costs for around a century.

"SpaceX currently cite the cost of fuel for a Falcon 9 as ~$200,000. So my BOTE would get us to $600,000 for a ~20 ton payload. I gather they're currently quoting about $60M, so there' someroom for improvement."
That's from a comment Charlie made in 2018. And I would agree that spaceflight dominated by propellent cost is optimistic. You would also need very durable, reusable rockets that don't require a great deal of maintenance.

What could we import from above?

For a momentum exchange tether to work you need two way traffic. So what mass from above could provide up momentum?

Lunar propellent might be the first import from above. In 2010 India's lunar orbiter Chandrayaan 1 found evidence of massive ice deposits on the lunar poles Link. The late lunar geologist Paul Spudis would argue an off earth source of propellent could confer a commercial and military advantage to the power that controls it Link. Former NASA administrator Jim Bridenstine also made the same argument Link

Jon Goff voiced some objections to lunar propellent. Given the delta V between the lunar surface and and earth orbits, only a small fraction of lunar propellent would arrive to supply propellent depots in earth orbits. If propellent were delivered by conventional rockets. 

However more would arrive if lunar propellent were delivered via momentum exchange tethers. And they would provide up momentum for the momentum exchange tethers and reduce the need for propellent mass. 

A photo of Starship thermal tiles from

The Starship upper stages will likely re-enter at a much higher velocity than the booster stages. 35 kilo pascals is typical max Q for ascent. But for for descent 90 kilo pascals is common. Will Starship be able to economically refurbish after re-entry? Unlike the Space Shuttle Starship has a stainless steel hull. It looks like the thermal tiles are mechanically attached rather than glued on.

SpaceX likely has improved on thermal protection since the Space Shuttle Days. But I still expect re-uses after an 8 km/re-entry to be difficult.

If the upper stage could refuel in Low Earth Orbit (LEO), the upper stage could re-enter with an even lower velocity than the booster stage. Re-use would be far less difficult.  Re-usability may even become so advanced that cost of transportation would be triple the fuel costs, as Charlie Stross imagines in his best case scenario.

The Heteroclinic Zone

There are a family of loosely bound lunar orbits where a little delta V and use of earth's tidal influence can make a big change to the orbit. It's possible to move from Earth Moon Lagrange 2 (EML2) to  Earth Moon Lagrange 1 (EML1) with only a tiny burn. These low delta V routes between lunar orbits are called heteroclinic paths. They talk about these paths in chapter 3 of Dynamical Systems, the Three-Body Problem and Space Mission Design by Koon, Lo, Marsden and Ross.

EML1 is around .3 km/s from the top tether I mentioned in ZRVTOs in Other Settings earlier in this post.

From EML it's easy to reach EML2

EML2 is only .9 km/s from Trans Mars Insertion using the Farquhar route.

I am a little obsessed with EML2. I have a post devoted to this Lagrange point.


Included in The Heteroclinic Zone are Nearly Rectilinear Halo Orbits NHRO. I like these orbits for a number of reasons.

The perilune of these orbits are near the lunar poles. The lunar poles and cold traps are where I daydream of lunar propellent mines. So orbital insertion from the propellent mines to The Heteroclinic Zone is quite doable. 

I like to imagine advanced propellent mines with a rail guns that launch propellent into NHROs. 

A distant apolune is at the other end of an NRHO. It travels slowly in this region giving it lots of hang time over the lunar poles. It can give long periods line of sight periods to the lunar cold traps. In some ways this is like an earthly Molniya orbit. This would be useful in the early stages of a propellent mine when construction is being done by remotely controlled robots.

Phobos lending a hand with Mars EDL

A 1340 kilometer tether from Phobos could drop payloads into periaerion skimming Mars atmosphere. The payload would enter Mars atmosphere at about 3.6 km/s. Entry from an Earth to Mars Hohmann would be about 5.5 km/s. (3.6/5.5)^2 = ~.43. So less than half the kinetic energy to be shed.

And it may be doable to mine oxygen from Phobos minerals so propellent could also lend a hand in shedding velocity.

A 5680 km/s tether from Phobos would allow entry to Mars atmosphere about about .6 km/s However a Phobos tether going deep in Mars' gravity well is more difficult. Given Zylon and a safety factor of 3, taper ratio would be 84 and tether to payload mass ratio would be 640. See my lower Phobos Tether post.

Park Trans Planetary Vehicles at the edge of gravity wells

Vehicles that can keep humans alive for months must be massive. Vehicles for shorter trips can be much smaller.

What is the point of launching a trans Mars vehicle from earth's surface and landing it on Mars' surface? It would be like using a huge Mac truck to deliver a pizza from a restaurant to a customer's front porch.

Far better, in my opinion, to park trans planetary vehicles at EML2 or Phobos. Then there is no need for a thermal protection system to endure re-entry. And there is no need for the ship to be 90% propellent to climb up steepest slopes of planetary gravity wells.


Massimo said...

I'm so glad to see you posting again, and about tethers! Your tethers series has been a great favorite of mine.

Darayvus said...

It strikes me that as long as we're being told that the ISS is unsalvageable and that we must must must let it fall into the atmosphere ... maybe we could just use its husk as a big dumb tether-anchor

Matter Beam said...

I'm very happy to see you post again. This blog is where I really understood the capabilities of orbital tethers. I'll be sure to share this widely!