Ways of getting to space

How can you get to space and orbit the earth cheaply? Today, it costs $1,500-$3,000 to get 1 kg into low earth orbit (LEO), and more to go further. Is it possible to bring these prices down? The answer is, maybe. Let's have a look at some of the possible technologies and what they might cost; but first, let's talk about where space begins.

Space and Altitudes

There's no clear boundary between earth and space; the atmosphere and gravity don't just end suddenly. The space starting point is usually taken as the so-called Kármán line at 100 km above the earth's surface. Low earth orbit goes from 160 km to about 2,000 km, with the ISS orbiting in the range 400–430 km. For comparison, the distance between London and Paris is 454 km.

Getting to these heights is relatively easy; staying there is much harder. To stay in orbit you need a substantial orbital velocity; for example, at 200 km above the earth, you need to reach 7.7 km/s to stay in orbit. Because of the high cost of entering orbit, the earliest space launches were suborbital, the first being a V-2 on 20 June 1944, which reached 176 km. Achieving orbit takes more fuel, meaning a bigger rocket, so it took longer; the first orbital flight was Sputnik 1 on 4 October 1957, with an orbit of 223–950 km.

Rockets

Although rocketry is proven technology, it has its limitations. Because a rocket has to carry its own fuel, it burns fuel to carry fuel; during the Apollo 11 mission, the Saturn V rocket was 85% fuel by weight.

The fuel fraction needed to get to orbit is expressed by the rocket equation:

$$\Delta v = v_e \ln \frac{m_0}{m_f} = I_{sp}\, g_0 \ln \frac{m_0}{m_f}$$

Where:

• \(\Delta v\) is the change in velocity
• \(v_e\) is the exhaust velocity, given by:
  • \(I_{sp}\) — the specific impulse
  • \(g_0\) — gravitational acceleration
• \(m_0\) is the mass of the entire rocket, including propellant
• \(m_f\) is the mass of the rocket without propellant

This equation is a simplification that applies in this form to single-stage-to-orbit (SSTO) rockets, but it's enough to show the problem. Wikipedia's example calculation shows that an SSTO rocket must be 88.8% fuel. This percentage drops for a two-stage rocket, but the cost is added complexity.

The rocket equation tells you how much fuel you need to carry a payload to orbit. The bigger the mass, the more fuel, and hence the bigger the engineering challenge which is the so-called tyranny of the rocket equation.

(Copilot's retro rocket.)

To put rocket costs into perspective, let's look at something simple. A cup of coffee weighs about 240 g, or 82 g just for the coffee. The cost to orbit for this mass is $360–$720 for the cup, or $123–$246 for the coffee itself. These costs are coming down, but they're still high enough that rocket space travel is restricted to governments and billionaires.

Fuel costs aren't the only costs. There's obviously R&D which is extremely high. By using mass-production techniques and riding the experience curve, we can cut costs to orbit, but the rocket equation puts a floor on costs; rockets are always going to be expensive.

Planes

Normal jet engines require oxygen to burn fuel and sufficient atmosphere for their wings to provide lift. Both fall off with altitude, preventing jets from reaching space. However, a high-flying jet can reach the Kármán line by carrying momentum built up from acceleration at lower altitudes.

In the 1960s, the US X-15 experimental plane was flown above the Kármán line twice, and in 2004 SpaceShipOne did it three times. These are suborbital flights; the craft only briefly touched the highest altitudes. Reaching orbit by plane would require a rocket at some point, and might require three types of propulsion: a jet, a scramjet, and a rocket.

Commercial planes typically fly at about 9–12 km; much, much lower than the Kármán line.

Guns

The idea is simple: build a large gun and fire a payload into space. It's an old concept, famously appearing in Jules Verne's 1865 novel From the Earth to the Moon. In practice, it's much harder than it seems.

The acceleration in a space gun is enormous, over 1,000 g, which would kill a person almost instantly. This limits space guns to launching satellites, though a cheap satellite launch is still hugely valuable.

The most notable real-world space gun attempt was the HARP project in the 1960s, which managed to send a projectile to 179 km, comfortably above the Kármán line, at a cost of only $300–$500 a firing. The project ended in 1967, apparently from funding pressure and politics.

Chemical space guns run into pressure problems that limit acceleration and the height the projectile can reach, so electromagnetic rail guns have been suggested as alternatives. The StarTram concept uses this idea with some additional twists, but remains only theoretical.

The HARP project was the high-water mark of the space gun approach. Its architect, Dr. Gerard Bull, subsequently tried to get more space guns built but struggled for funding. Eventually he persuaded Saddam Hussein to fund "Project Babylon," a supergun capable of firing projectiles 750 km. The project ended when Bull was assassinated, most likely by Mossad,  in a Brussels hotel in 1990. No one has seriously attempted a space gun since.

Centrifugal Launches

Taking inspiration from a bolas, what if you accelerate an object in a circle and, once it reaches a high enough velocity, release it? If you accelerated a payload in a vacuum, you could hit 10,000 g and reach a tremendous exit velocity, enough to fling your payload high into the atmosphere. Even if you couldn't reach orbit, by sending a rocket far into the upper atmosphere, you would dramatically reduce its fuel needs (and hence cost). Of course, a person would be squished by this acceleration, but once again, a satellite or cargo launch would be good enough.

A company called SpinLaunch built a prototype in New Mexico to investigate the idea. Unfortunately the engineering challenges proved too much and they've since pivoted to more traditional rockets.

The Space Elevator

Space elevators are beloved by science fiction authors. The idea was popularized by Arthur C. Clarke's novel The Fountains of Paradise and it's appeared in several other novels since.

Here's the concept: move an asteroid into geostationary orbit as a counterweight, deploy a cable down to earth, anchor it to the ground, and ride an elevator up the cable into space. Simple in principle, but the forces on the cable would be extraordinary, requiring entirely new super-strong materials. Clarke suggested threads of buckyball-type nanoparticles, which didn't exist when he wrote the book.

(Gemini's view of a space elevator.)

The engineering challenges are immense: capturing an asteroid, developing the cable material, surviving lightning strikes and weather, and so on  It's not likely to happen any time soon.

A baby step towards a space elevator was attempted in 1996 ,when the space shuttle crew tried to deploy a satellite on a 20 km tether; unfortunately it snapped before being fully deployed, illustrating the difficulties.

Skyhooks

Imagine a satellite with two huge rotating arms long enough to reach into the upper atmosphere. As the satellite rotates, one arm dips into the atmosphere. A plane flies up, the arm catches it and flings the plane into orbit. Conversely, you could de-orbit spacecraft without dangerous re-entry.

(Claude's view of the skyhook)

To use this system, a plane only needs to reach Mach 10+ at high altitude, far cheaper than reaching orbit unaided. Although it sounds outlandish, it appears more feasible than the space elevator. Still, it's likely decades away from development.

Space Fountain

Imagine a water fountain pushing a ball aloft, now scale that up to lifting a platform to space. Instead of water, a space fountain would use a stream of metal pellets fired electromagnetically upwards to lift a platform high into space. Like the space elevator, the platform transports people and cargo into space and back again.

The key idea is that the pellets never physically contact the platform. Instead, a magnetic deflector captures each pellet and an electromagnetic accelerator fires it back down; the ground station catches and re-fires them upward. The pellets are continuously recycled.

(Perplexity's view of a space fountain. It looks a lot like a rocket to me, but then, there's never been a real space fountain...)

It's an elegant concept, but the engineering challenges are immense, and the electricity bill to run the electromagnets would be enormous.

Balloons and Rockets (Rockoons)

A balloon can carry a rocket high into the atmosphere, the combination is called a rockoon. One of the early pioneers was James A. Van Allen, whose rockoon experiments provided the first evidence of the radiation belts now named after him.

The idea is cheap and effective for experiments, but suffers from a fundamental problem: balloons are nearly impossible to steer. Payload capacity is also limited by the balloon's lifting power. Rockoons may work for small scientific payloads, but won't get large amounts of material into orbit.

There have been a lot of pictures in the press showing the curvature of the earth taken from balloons, giving the impression a balloon can get you to space, but that's not so. Balloons typically reach about 30 km where 99% of the atmosphere is below them and the sky above is dark black. It looks like space, but it isn't. The highest a balloon has ever reached is 53.7 km.

Atomic Bombs

There's an urban myth that the first object into space was a manhole cover launched by the first atomic bomb test. In reality, it was during the 1957 Plumbob test, not the original Trinity test; and it was a steel bore cap, not a manhole cover. In any case, the "manhole cover" was almost certainly vaporized in the explosion and never made it to space.

In the 1950s–60s, Project Orion envisaged using miniature nuclear bombs to push a vehicle into orbit, requiring around 800 detonations per launch for a crewed mission. Thankfully, the project never progressed beyond simple chemical explosive tests.

Nazi Super-Science

While researching this post I came across a demented conspiracy theory claiming the Nazis developed an anti-gravity device called Die Glocke (the Bell), supposedly capable of time travel, anti-gravity, and spatial distortion. It's plainly nonsense, but it does have believers.

So It's Rockets for the Foreseeable Future?

Unless there's some extraordinary breakthrough, it really is just rockets for now. 

AI statement

This is all my own writing. I used AI  to generate images and to help with some research, but not for any piece of the writing itself.

Rotating space habs!

I was on a boring train journey the other day (yes, some trains still exist in the US) and my mind started to wander. I thought about the novel Rendezvous with Rama and rotating space habitats. I wondered about simulating gravity and some of the consequences. Here's are the results of my musings. I hope you like them.

(NASA/Rick Guidice, Public domain, via Wikimedia Commons)

Some basic physics of rotating bodies

To understand what a resident of a rotating habitat might experience, we need to understand two important ideas. Unfortunately, they're both a little complex. I'm going to try and explain them simply.

Centrifugal and centripetal forces

Imagine a rock on the end of a string and you're whirring the rock in a circle above your head. If you cut the string, the rock would go flying off on a tangent to the circle.

To keep going round, the rock must experience a force towards the center of the circle; a centripetal force (where -petal means towards the center). This force comes from the tension in the string.

The centrifugal force is the outward force the rock feels (-fugal meaning fleeting the center). It's sometimes said that the centrifugal force isn't real, but it is. If you've ever been on a fairground ride that spins you in a circle, you've experienced the centrifugal force for yourself and you know how real it is. The misunderstanding comes from the fact you need to use a non-inertial frame of reference to do the math. 

For a rotating space habitat the centrifugal force is what someone on the inside rim of the habitat would feel as 'gravity'.

Size and rotation speed

Textbooks usually show a diagram like this to explain what's going on with the rock on a string.

The string travels round the circumference of the circle in a given time and we can express this as a linear or tangential velocity and an angular velocity. The angular velocity is usually written in terms of radians per second. The tangential velocity is the length of the circumference in \(m\) divided by the time it takes to go round in \(s\). 

It's worth noting something important here; at any point along the string, the angular velocity is always the same, but the tangential velocity increases as you move away from the center of rotation.

Through math I'm not going to show here, we can calculate the angular and linear accelerations. The centrifugal force the rock on the string experiences is:

\[F = ma = m \omega^2 r\]

where:

• \(F\) is the centrifugal force
• \(r\) is the radius of the circle
• \(\omega\) is the angular velocity in radians/s
• \(m\) is the mass.
• \(a\) is the acceleration away from the center.

This means that:

\[a = \omega^2 r\]

Let's re-cast this equation into something more relevant to our rotating space habitat. It's more usual for people to think of rotation in terms of revolutions per minute instead of radians per second, so we'll make that change. We want the habitat to feel like earth, and on earth, the acceleration due to gravity is close to 9.81\(ms^{-2}\) (I'll call this 1\(g\)). Using this value of \(a\), we can rewrite the previous equation as:

\[9.81 ms^{-2} \approx \left(\frac{2\pi \text{RPM}}{60}\right)^2 r\]

which gives us the relationship between rotational speed and radius. I've plotted out this relationship below.

Note that the relationship isn't linear and as the radius gets bigger, the revolutions per minute get less. This has some important implications for our space hab.

A small habitat with a radius of 5\(m\) would have to rotate at a speed of about 13.4\(rpm\) to give a centrifugal equivalent of 9.81\(ms^{-2}\). As we'll see, that causes problems with the Coriolis effect, but there's another problem. An astronaut in such a 'narrow' habitat would face a serious problem, the "gravity" at their feet would be different from the "gravity" at their head. For a 1.8\(m\) tall astronaut, this would mean 9.81\(ms^{-2}\) at their feet and 6.28\(ms^{-2}\) at their head, which would be very disorienting to say the least.

What about a much larger habitat, say one with a radius of 10\(km\)? This habitat would spin at a rate of 0.299\(rpm\). Here a 1.8\(m\) astronaut would experience 9.81\(ms^{-2}\) at their feet and 9.8082\(ms^{-2}\) at their head. This is a really small difference and they wouldn't notice it.

For comfort then, a bigger habitat is better.

(As a side note for later, I'm going to point out that the tangential velocity for our 5\(m\) habitat is 7\(ms^{-1}\), and for our 10\(km\) habitat it's 313.2\(ms^{-1}\).)

The Coriolis effect

This is another tough one to explain. Let's start with a couple of examples and I'll explain how it works on a rotating habitat.

The earth rotates on its axis. If you're at the equator, you travel the full circumference of the earth in 24 hours. If you're at a pole, the circumference is zero. If you're halfway in-between, you travel the circumference of the earth at that point in 24 hours. Let's write down some number in a table.

Location	Latitude	Effective radius (m)	Tangential Velocity (m/s)
Equator	0°	6,378,000	463.8
45° latitude	45°	4,509,900	328.0
Pole	90°	0	0

Let's imagine I'm at the equator and I fire a cannonball due north to the halfway 45° point. The cannonball starts with the same tangential velocity (464\(ms^{-1}\)), but the tangential velocity at the halfway 45° point is less (328\(ms^{-1}\)). Relative to an observer at the halfway point, the cannonball has north velocity and an east velocity. This means, the cannonball will go east as well as north, even though it's fired in a true straight line. Here's a diagram of the flight of the cannonball.

The cannonball will travel north 5,004\(km\) but it will also travel east 563\(km\).

The Coriolis effect was first observed in artillery firing and modern day artillery calculation take it into account. Similarly, long-range snipers have to calculate its effect to hit their targets. It's not just a war thing; the Coriolis effect is present in the movement of air in the atmosphere and the currents in the ocean, it also affects the routes planes take.

The physics of the Coriolis effect are complicated. It's governed by this equation:

\[\textbf{F}_c = -2m( \mathbf{ \Omega} \times \textbf{v})\]

where:

• \(F_c\) is the Coriolis force vector
• \(m\) is the mass of the object
• \(\Omega\) is the angular velocity of the rotating frame
• \(v\) is the velocity of the object as seen by the rotating frame.

I'm not going to go too deeply into the math here, but you should know it's possible to work out the Coriolis effect if you have all the data.

Let me give another example of the effect before we get to the habitat. Imagine I'm on the equator of the earth standing over a very deep mine shaft. The mine shaft goes straight down deep into the earth. I drop a rock down the mine shaft. Surely, the rock will drop all the way to the bottom without hitting the sides? The Coriolis force says no. As the rock falls, the circumference at of the earth it "sees" gets less and less. If the mine shaft went to the center of the earth, the circumference of the earth would be zero. See the diagram below to get the idea.

Remember the tangential velocity at the equator is 464\(ms^{-1}\) and at the poles (or at the center) it's 0\(ms^{-1}\). This means, our falling rock would be subject to the Coriolis effect. After a fall of 3.7\(km,\) it would move 5\(m\) off center. So even if we drop the rock straight down, it may hit the sides of the shaft before it's fallen very far.

Life in a rotating hab

Now we know about “gravity” and the Coriolis force, let’s think about what that means for life in a rotating habitat.

Running and walking

If I run in the direction of spin my angular velocity increases, so I feel a greater centrifugal force. In other words, the faster I run, the heavier I feel. Of course, the opposite is also true if I run against the direction of spin. In a large hab (10\(km\) radius) this isn’t really noticeable, but in a smaller hab, it can be.

A good runner can sprint 7\(ms^{-1}\), which is the same as the tangential velocity in a 5\(m\) hab. If our runner ran in the direction of rotation, they would feel a "gravitational" acceleration of 4g, which would be punishing to say the least. If they ran against the direction of rotation, they would become weightless!

In a 5\(m\) radius hab, a person walking 1.4\(ms^{-1}\) would experience a Coriolis acceleration of 3.9\(ms^{-2}\), or 0.4\(g\). That's a lot. It would feel that you were being pushed sideways as you walked. If you dropped an object, it would curve before hitting the floor (see the mineshaft example above). It would also be very disorienting because the fluids in your inner ear would be affected. Bottom line is, life would be very unpleasant, it would feel like you were in a never-ending fairground ride.

Life in a 10\(km\) hab would be much more pleasant. The Coriolis force a person walking at 1.4\(ms^{-1}\) would be about 0.09\(ms^{-2}\) or about 0.009\(g\). Under normal circumstances, you wouldn't feel it.

Plants

Once again, everything would be 'normal' in a 10\(km\) hab.

Things would get weird in a 5\(m\) hab. A tall plant or tree might actually reach 5\(m\) which is the zero "gravity" area and I have no idea what might happen! Plants rely on gravity for internal fluid flow, but we know some plants can grow in space. In a 5\(m\) hab, a tall plant would end up weirdly distorted or die. Of course, the Coriolis effect comes into play too. Plants would probably end up growing at an angle.

Weather

On earth, the atmosphere is affected by the Coriolis effect and it would be the same but worse on a hab. Air would likely flow in spiral patterns. In a 10\(km\) hab, things might get strange, but in a 5\(m\) hab of any size, things could get really strange; an astronaut might feel different wind speeds on different parts of their body.

It's not clear to me how chaotic the atmosphere would be. It's possible it would be strange (meaning different from earth), but entirely predictable. Would it rain, and if so, what would that look like?

Sports

Plainly, sports would be downright weird at 5\(m\). So weird, I wonder if you could invent new games, like some kind of zany squash for physicists. 

At 10\(km\), things get saner, but there could still be some noticeable effects.

Golf could end up being very different. The trajectory of the ball will be dependent on its direction relative to the spin of the hab (Coriolis again). Of course, the higher the ball goes, the less "gravity" it sees, so a ball may travel further if it travels higher.

Other sports, like football and baseball or cricket, might see some weirdness at the elite level when balls are kicked or hit long distances.

If you're building a football pitch or any kind of athletic track, you'd have to think about how it's oriented. You would probably want the long axis to be perpendicular to the direction of rotation. Of course, the ground on the rim would curve upwards and you'd have to correct for that, or maybe you'd just leave it as a feature of hab sports.

Aerial recreations

Hang gliding and related recreations like paragliding would be deeply weird and probably immense fun. In a 10\(km\) hab, the winds would be pretty weird giving some interesting thermals to ride. Of course, the higher you go, the less "gravity" would be (and the lower the atmospheric pressure, so you'd have to have breathing equipment). The view would be stupendous as you got closer to the center of rotation. It might even be possible to cross to a point diametrically opposite to where you started.

Thinking of aerial things, it worth pointing out that humans probably wouldn't be the only species on the hab. How would birds live in a place like this? How would they behave?

Rendezvous with Rama

This is a 1973 novel by Arthur C. Clarke about humanity's encounter with an alien space habitat with a radius of 10\(km\) and a length of 50\(km\). As we've seen, if the habitat were rotating at 0.299\(rpm\), a habitat this size could be pretty comfortable for its residents at the rim. They wouldn't feel much of a gravity gradient between their heads and their feet, and the Coriolis effect wouldn't be very much. In the book, the astronauts entered from a central point at one end (starting from 0\(g\)) and descended to the rim via ladders.

(Gemini's rendering of Rama.)

Rendezvous with Mike

The Rama habitat was the starting point for my train musings, but I ended up imagining something a bit different which is a twist on the ideas here. I imagined a habitat with tapered ends instead of a cylinder, so it would look something like this in cross section.

Here's Gemini's rendering of the same thing.

What would it be like to walk up the taper towards the 0\(g\) center point?

In my diagram, the taper is about 27°, which would be like climbing a staircase that went on for a long way. You'd probably have to take frequent breaks as you started off and fewer as you reached the center. Of course, breaks would give you an opportunity to admire the view, which would get better and better as you climbed.

As you ascended, "gravity" would decrease, but you'd feel a component of gravity pushing you back down the slope (there's nothing like it on earth).

The Coriolis effect would increase as you got closer to the center, to the extent that you you'd have to lean to compensate.

Plants and trees would start off "normal" on the rim, but get weirder as you got further up the taper and they'd disappear entirely once you got closer to the center. Bear in mind, the forces on the soil would push it towards the rim, so "erosion" could be severe, however, let's ignore that for now. The Coriolis effect and "gravity" would cause plants to lean towards the cylindrical section and in the direction of spin. As gravity decreased, tree growth would become weird and chaotic.

Atmospheric pressure would also fall off as you ascended. At about 5\(km\) radius, you'd probably have to have breathing apparatus. At the center, the pressure could be close to zero. That would mean less and less plant and animal life as you climbed, regardless of other effects.

Once you got to the center, you'd be weightless, so you could play around with floating for a while. Of course, you'd have to be careful you didn't stray too far from the tapered end. A small deviation from the axis of rotation would mean you'd feel "gravity" again and fall. That wouldn't be so bad if you were at the end of the taper, but it would be very bad indeed if you were in the main body of the cylinder.

Diminished gravity might be a good thing for the old and infirm, so maybe there would be hospitals or retirement homes on the slopes.

Some history

Of course, I'm not the only person to have thought of this. There's a very long history of theorizing about space habitats, see this Wikipedia page for some of it: https://en.wikipedia.org/wiki/O%27Neill_cylinder. In fiction, it's not just Arthur C. Clarke's Rendezvous with Rama, there have been many novels set in rotating habs. These habs have even been in movies, including some recent ones.

The "objection" I've heard to these sorts of ideas is, why don't we fix the planet we have rather than spending money on building paradise for a few? I agree, but it's nice to dream a little. 

What have I missed or got wrong?

I'm sure the weather in a large hab would be more complex that I've described. Maybe there would be permanent clouds along the axis of rotation? Where would lighting come from?

A central sea (as in Rama) would be weird. I wonder how it would behave? Maybe it would be an attraction for surfers - could you imagine surfing a wave for many kilometers?

I'm sure the experience of walking up the taper would be quite something and I'm sure it would be weirder than I described here.

I'd love to hear your views of this post, What have I got wrong? What did I miss?