Could Starship lift mass to orbit (both low and geo-stationary) cheaper than a skyhook?

Question

In response to this question which appears to ask only about space elevators and not skyhooks, would Starship's cost per kilogram to LE or Geo-stationary orbits be lower than a skyhook's? I ask only because it appears that the tech for a skyhook is technologically feasible today even if clearing an orbit would be extremely difficult. While this question could inspire opinion based answers, since it is based on existing materials, at the very least, the answers could be more fact-based than the linked question.

Answer 1

No.

Since your question asked about “both Low and Geo-stationary” orbits (and becuase I'm a fan of using boolean operations when possible to save time) I'm just going to look at the geo-stationary case as it favors the skyhook.

Skyhook

The difference in energy between a kilogram on the surface of Earth and a kilogram in geostationary orbit is

$$\Delta E = E_{K0} + E_{P0} – E_{K1} – E_{P1}$$

Where:

$E_{K0}$ and $E_{P0}$ are the kinetic and potential energy on a kg resting on Earth, and

$E_{K1}$ and $E_{P1}$ are the kinetic and potential energy of a kg in GEO orbit.

The speed at the equator is 465 m/s. The speed at GEO is 3075 m/s. You can work this out with…

$$v = 2 \pi (r_{earth}+alt_{GEO}) / t_{siderealday})$$

Kinetic energy is...

$$E_K=1/2 mv^2$$

Potential Energy is…

$$E_P= -\mu m/r$$

The difference in energy is...

$$\Delta E = 108158+ (-62470418) – 4726751 – (-9449806) = 57.6 MegaJoules/kg$$

Getting to GEO involves imparting 57.6MJ of energy (per kg) to the object you want to place in GEO. If wholesale electricity costs 0.05 USD per kwh (0.0139 USD per MegaJoule), this works out to be about be just 0.80 USD per kg.

A 10m x 10m, 20% efficient, solar panel array in space will generate that much energy in about 35 minutes.

A Skyhook is a Momentum Exchange Tether, which means that you can swap momentum between two objects of the same mass (say a departing vehicle and a returning vehicle carrying orbital tourists) without having to replenish any lost energy. But if you’re only accelerating a payload up out of the gravity well, and there is no returning payload, then you will need to replenish the energy that the skyhook imparted to the payload. This can be done with a solar powered ion drive more cheaply than with a chemical rocket. If the ion drive’s exhaust velocity is 50 km/s, the same 57.6 MegaJoules of energy per kg of payload can be replenished by accelerating...

$$E = (1/2) m v^2$$

$$m = 2E/v^2 = 2(57.6)/50^2 = 0.046 kg$$

...of propellant. Ion drives have an efficiency of 60 to 80 %, (ref) so after factoring that in, each 10m x 10m, 20% efficient, solar panel array in space will be able to replenish lost momentum fast enough to launch about 1 kg per hour, or 8760 kg per year. For each kilogram of payload launched, 0.046 kg of propellant must be delivered to the skyhook ion drive’s propellant tanks. If the propellant was krypton (which SpaceX used for its first Starlink satellites) at 290 USD/kg, that would cost $13 per kg launched. If the propellant was argon at 0.931 USD/kg, that would cost 0.043 USD per kg launched.

Skyhooks might not be a good idea around Earth because of space debris, and they might not have the send-payloads-anywhere-you-want flexibility of a rocket, but they certainly have a very high theoretical energy efficiency.

Starship

The true cost of Starship is a far more interesting question. In truth, it’s probably going to be just a little bit cheaper than the next best alternative, since Elon Musk will want to make as much money as possible - both because he has a duty to his shareholders and because he wants to build a city on Mars.

To arrive at a customer cost-per-kg in a more analytical way, we can compare the Starship launch system to the most similar kind of system that we do have accurate cost data for, and then adjust the cost by identifying and accounting for the all the major differences. To find the most similar operational system, let's consider the characteristics of the Starship system first.

Starship’s first stage, Superheavy:

• Launches,
• Boosts back to the landing pad, and
• Lands propulsively with a tower catch.

Starship’s second stage:

• Does a long burn to achieve an elliptical orbit.
• Does not jettison fairings
• Does a circularization burn
• Does not jettison any engines or propellant tanks
• Delivers its payload
• Does a de-circularization burn
• Reenters the atmosphere
• Lands propulsively with a tower catch.

All components are refurbished, re-flight-qualified (at least occasionally), and reused.

The operational system most similar to Starship is Falcon9 plus Crew Dragon 2. Typically Falcon 9’s booster:

• Launches,
• Continues down range,
• Does a reentry burn, and
• Lands propulsively on a drone ship with landing legs.

Falcon 9’s second stage plus Crew Dragon:

• Does a long burn to achieve an elliptical orbit.
• Does not jettison fairings
• Does a circularization burn
• Does jettison its engines and propellant tanks
• Delivers its payload
• Does jettison its trunk
• Does a de-circularization burn
• Reenters the atmosphere
• Lands in the ocean with parachutes and is recovered.

All components are refurbished, re-flight-qualified, and reused except for the second stage engine, propellant tanks, and the trunk.

We can make a list of the major differences between the two systems…

1. Superheavy returns to the launch pad instead of landing down range,
2. Starship is made with stainless steel whereas Falcon 9 uses aero-grade aluminum,
3. Starship reuses its entire second stage, Falcon 9 jettisons an engine, tanks, and trunk.
4. Superheavy doesn’t need landing legs whereas Falcon 9’s booster does,
5. Starship carries extra propellant for its propulsive landing whereas Crew Dragon carries parachutes,
6. Starship needs Mechzilla where as Falcon 9 needs a drone ship and the Crew Dragon recovery vessel,
7. Starships engines burn liquid methane whereas Falcon 9 burns RP1,
8. Starship is larger.

Difference 1 - Return to Launch Site We can estimate the performance impact of returning to the launch site versus landing downrange by doing a performance query on a NASA website to compare Falcon 9 Return to Launch Site (RTLS) to Falcon 9 Automated Spaceport Drone Ship (ASDS).

NASA Launch Services Program Launch Vehicle Performance Website

For the 400 km orbit (lowest the tool supports for Falcon 9) the payload supported drops by a factor of

$$RTLS/ASDS = 11700/15500 ~= 0.75$$

Difference 2 - Stainless Steel Stainless steel's specific strength is 63 kNm/kg. Aerograde aluminum's specific strength is 204 kNm/kg. So, Starship structure will be 204/63=3.24 times heavier, everything else being equal.

Difference 3 - Fully reusable The Falcon 9 system requires a new second stage and trunk to be manufactured for each mission. These components cost, according to some estimates, around \$20M, which is around \$6000 per kg, given that the upmass capability of Falcon 9 plus Crew Dragon 2 is 3307 kg.

Difference 4 - Landing Legs This is likely to be a small performance improvement in Starship's favor.

Difference 5 - Propellant for landing Starship At the Raptor's mass flow rate of 650 kg/s, and assuming a 17 second burn with 2 engines, this propellant will mass

$$m=(650)(17)(2) = 22,100 kg$$

This value does not include any margin. The landing procedure will likely improve over time. But its clear that the fuel mass is not insignificant. It is probably also much heavier than the mass of a set of parachutes.

Difference 6 - Mechzilla versus Drone Ship, etc. Perhaps this difference is a wash from a performance perspective. But if Starship operations move off-shore to mitigate the noise problem, then Starship's marine assets may be more expensive to operate that those used for Falcon 9 and Crew Dragon 2.

Difference 7 - Raptor versus Merlin Merlin's exhaust velocity is 3000/3414 m/s (sea-level/vacuum). Raptor's exhaust velocity is 3208/3433 m/s. The difference is 1.07/1.006. So, this very slightly favors Starship, but it should be noted that Raptor's performance in an operational system might be lowered in the interests of rapid re-usabilty.

Difference 8 - Starship is Larger The square-cube law comes into partial effect. It doesn't come into full effect, however, because the tanks are still pressurized to ensure rigidity, even though they hold cryogenic propellants. So the wall thickness does need to increase with diameter. But Starship is 2.4x wider than Falcon 9, so the square-cube law, if it was in full force, would mean that Starship's propellant tanks would require 1/2.4 as much material. In practice, the savings will be less than this because the square-cube law is not in full force. (Learn more from this question)

Summarizing...

In the end we have a number of differences that will impact performance. Differences 1, 2, and 5 clearly favor the Falcon 9 architecture. Differences 3, 4, and 8 favor the Starship architecture. Differences 6 and 7 have more of a neutral performance impact.

What we can say is that we have not identified a good technical or logistical reason why Starship will have, for example, 50% better cost-per-kg performance than Falcon 9 plus Crew Dragon.

According to an Audit Of Commercial Resupply Services To The International Space Station by the Office of the Inspector General (OIG) ("Dragon 2 Upmass Per Mission ... 3307 kg", Table 1, page 12) Falcon 9 plus Crew Dragon can deliver 3307 kg of payload to the ISS. It might be able to deliver a little more to a lower orbit.

In a NASA Press Release, NASA says that Crew-10, Crew-11, Crew-12, Crew-13, and Crew-14 flights will cost USD 1,436,438,446, which works out to roughly USD 287,287,689 per flight, or USD 86,873 per kg if you assume the maximum payload of 3307 kg from the OIG report above.

It's probably worth noting that in a big-picture sense, NASA (and taxpayers) pay more per kg because NASA also awards contracts to other launch providers, such as Boeing and Sierra Nevada. As of Jan 2024, these other providers' launch systems are not in service the way SpaceX's system is.

When Elon said that the fully considered cost to a useful orbit will be $100 per kg in 2024-2025 timeframe with Starship, he was stating a value that is 869 times cheaper than what he is charging NASA in the same time frame. One has to work really, really hard to come up with a technical or logistical reason that can explain how he was able to arrive at this number analytically (as opposed to aspirationally).

Still, many people believe that Starship is going to lower the cost to orbit by multiple orders of magnitude. Why is this? Well, it is in a large part due to psychology. There's quite a good video on the effect here, but the main point is...

When something happens, and in that moment people perceive that it aligns with their personally relevant goals (i.e. it's what they want) they judge that something as good and project that judgment into reality. And almost as soon as they do this, they kind of wipe their own memory of that projection. It's like a self-imposed amnestic disorder. And since they forget, or willfully suppress, that awareness that they projected that judgment into reality, they then experience reality as if their judgments inhere in reality itself.

Another reason is that optimistic people put a lot of faith in Experience Curve Effects and economies of scale. The "airplanes wouldn't be nearly as cheap if they weren't reusable" argument is also compelling. Finally there is a lot of Circular Reporting that helps to reinforce the belief. Also, it has been suggested that NASA adds a lot of cost by imposing its safety culture on suppliers. It probably is true that more mass could be launched by simply reducing safety margins, but then more accidents might happen, which could increase costs and downtime.

But we're not finished. We want to go to GEO!

Starship will still need be refilled so that it can get from LEO to GEO, circularize, drop of its payload, and de-circularize, and re-enter. To be able to do these burns, if each refilling mission can deliver 100 metric tones to LEO, Starship will need roughly 5 refilling missions (according to my estimate - please feel free to check these numbers yourself). So, if true, then the cost to GEO could be around 6 x 86,873 = 521,238 USD/kg.

A skyhook, on the other hand, if it were possible to build one, could reduce costs to below $10 per kg. The technical argument is sound and compelling. What's not compelling about the approach is the space debris problem.

Yes, if we find reasons to launch way more mass into space, the costs would come down - but this would be true for any launch system. The Starship architecture does not put the chicken before the egg. A skyhook, on the other hand ... might.

Answer 2

Yes, it could. For some cases at least. Would it? It is impossible to say without any Skyhook project of comparable technological readiness level to Starship. (also see the question comments as to why question is too widely phrased to give simple answer).

One example (note that you could probably pick another example use case which might favor other solution):

• Requirement: 20 launches in a year, each worth 100 tons of satellites, in one year to specific LEO orbits (different one for each launch), without requiring satellites to expend their own propellant to reach orbits (but reserve it for their operational life)

• SpaceX Starship:

  • cost of launch facility, superheavy/starship production line and dozen or so ships and superheavies - about $3B current costs + $1B estimate to full operational level = $4B.
  • Starship capacity: 100 tons fully reusable. Aspirational cost per launch after ramping up period of few years - about $10M per launch. (although some optimistic Elon gueestimates go as low as $2M per launch, half of that being being fuel and other half other operational costs). Estimated to be capable of frequent launches. But even if it were order of magnitude costlier at about $100M, it would change the result much.
  • positioning to wanted orbit: included in Starship launch.
  • So; total cost of project, reasonable case estimate (as the question was whether is it is possible, not whether it is guaranteed), about $4B + 20 * $10M = ~ $4.2 billion.
  • cost of failure (aspirational) - about $10M+$4M=$14M for new Superheavy + Starship, no delays due to waiting for replacement.

• Skyhook:

  • cost of building and launching one fully operational skyhook: unknown due to low TRL, so let's go with totally random $2 B estimate for first one, and half that price for subsequent ones. ([better estimates needed, help]!)
  • positioning to wanted orbit after leaving skyhook: kick stage of some kind required (or increasing the payload mass/capacity). Cost: unknown. Estimated order of magnitude $300k for Rocketlab photon. Launch mass of photon 50kg for 170kg payload. This increases skyhook initial mass of 20*100*1000kg by about 30%, so 2600 tons.
  • capacity (as per @phil1008 answer) - 8760 kg per year of expelled propellant needed in ideal case (and 0.046 kg of propellant needed for 1kg of payload). That makes skyhook capable of lifting about 190 tons of payload per year in ideal case. Thus, required skyhooks to accomplish selected mission: at least 14. That will however help (but not completely) with orbit costs. Let's assume the second ones are half the price, so total infrastructure cost $2B+13*$1B = $15B.
  • cost of getting payload to skyhook: unknown. I don't know the maximum capacity that can be sling per load, but lets assume it can somehow throw up to 500kg (which would require mass of skyhook double of that of ISS, which would likely make skyhook cost much more than mere $2B !), that is still 7200 slingshots per year, so about 2 photons per sling. Electron launch (cheapest?) is about $7.5M per launch, so that would be $54B just to get that amount of payload to skyhook! But let's say you get volume discount of 50%, so it is half price, at mere $27B. Still not economical at all! You'll need to invent some other tech like more economical parabolic suborbital rockets or transfer for airplane or something to even have a fighting chance - but note that those techs still have to be invented, tested and deployed, and that has both capital and operational costs associated with it.
  • aspirational Skyhook cost per launch: $10/kg. For mass of all launches, that is about $200M. (although that seems unrealistically low if it is meant to include maintenance / operations for whole year of daily operations of 12 skyhooks!!)
  • thus, total cost of accomplishing that specific mission would likely be not less than $15B+ $27B+$200M = $42.2B
  • cost of failure (aspirational) - about $1B for new Skyhook, years longs delays for building a new one in case of a failure, with reduced rate of launches in that time.

---

TL;DR (for this random project, with totally random estimates all over the place):

• Starship total project cost estimate: $6.0B. Risk per failure $14M.
• Skyhook total project cost estimate: $42.2B. Risk per failure $1000M.

So, yes, if those estimates hold (which is totally questionable for both sides), for that specific project (unless I miscalculated somewhere), SpaceX Starship would be significantly cheaper.