# If someone built a vacuum tunnel through the atmosphere, could you have an orbit with a sea level perigee?

This is something I've been thinking about for a while now. My initial estimates for the structure were based on people's estimates for an O'Neil cylinder, but assuming you can make the structure a vacuum chamber instead of a pressure vessel, it seemed to my like the buoyancy should be enough to make the whole thing pretty light.

I'm wondering if anyone has any careful analysis that could push this towards or away from plausible.

Edit: what I've learned so far from our answers:

1. Matching an orbit with the Earth's rotation drastically limits orbits
2. Orbit would need to clear the Earth's diameter
3. Keeping a long tube depressurized is hard

Edit 2: I'm having so much fun with this discussion, thanks for humoring my absurd idea:

1. Orbital precision is hard because of gravitational effects from other bodies
2. Unevenly distributed mass causes gravitational turbulence close to Earth's surface
3. Some sort of active elements / electromagnetic assistance to structure and satellite would be greatly beneficial

EDIT 3: fix #5 with clarification I got in the comments

• The density of air at sea level is approximately 1.2 kg/m^3. In order to be buoyant, the structure must have a lower equivalent density. Are there any materials/designs that can satisfy that AND withstand the 101 kN/m^2 of air pressure? Then as you go higher, the structure must be lighter because of the decreasing density. Jul 15 '20 at 3:49
• One fundamental question: What for?!
– SF.
Jul 15 '20 at 10:44
• Wouldn't it be easier simply to remove all the atmosphere? :) Jul 15 '20 at 11:25
• @CarlWitthoft - better get digging... (obligatory xkcd) Jul 15 '20 at 15:54
• For #5 the easiest place to see this would be the moon. Even though it lacks any appreciable amount of atmosphere, orbits near the lunar surface rapidly decay due to discrepancies in gravity. These discrepancies are significant enough that your weight on the moon surface can vary by about 1-3% depending where you are.
– eps
Jul 15 '20 at 16:23

No, unless your structure is located directly on the equator and your satellite follows a perfectly circular orbit, atmospheric "orbits" aren't possible, even in a vacuum tunnel.

Because the Earth is on an axis of ~23 degrees and rotates every day, it is not possible to create an orbit which has no ground track precession except for equatorial orbits. You'd need to cover the entire planet in tunnels to house the sinusoidal path of a non-equatorial satellite. If an equatorial orbit is what you want, that's fine:

If you dug a tunnel around the Earth's circumference along the equator and depressurized it, you could put something in orbit there--underground.

Unfortunately, even an elliptical equatorial orbit isn't possible because the perigee of the orbit would precess, again necessitating ludicrous amounts of tunnel.

As for the actual engineering challenges: simply said it would be very difficult. Since the tunnel would need to be perfectly circular across the entire planet, you'd need to contend with thousands of kilometers of ocean and tunnels through mountains. Furthermore, depressurizing (and keeping it depressurized) would be difficult. If you want to see an example of how difficult it is to depressurize a long tube, just take a look at all the problems hyperloop has with their tubes.

• @tfb Hmm, you might be able to find an equatorial elliptical orbit with a period that is an increment of 24 hours however the orbit would end up with an extreme eccentricity, taking the apogee far beyond GEO and possibly into/past lunar space Jul 15 '20 at 8:19
• are you sure a perfectly circular orbit is even possible? While mascons on earth aren't as drastic as on the moon, mass on the earth still isn't distributed uniformly. Jul 15 '20 at 9:02
• ~~You won't do with one tunnel~~ (actually, even that is false), but it should be mathematically possible to create a 12-hour orbit and make it do with just two tunnels. Jul 15 '20 at 9:42
• Well, just make the tunnel really big so the various precession effects don't bring your satellite in contact with the wall. Jul 15 '20 at 11:24
• If the satellite has a period of one sideral day then I don't think it needs an equatorial orbit. Just any orbit will do, it will retrace the same path relative to Earth every period. (Except that the Moon will probably mess with your orbit). Jul 15 '20 at 21:29

Such a tunnel is not plausible for a number of reasons.

## 1. Problems with orbits

First of all, as other people have said it would only work for equatorial orbits which were either circular (very long tunnel) or had a period which is some rational multiple of the Earth's rotational period. And, again as other people have said, the real Earth is nothing like symmetrical enough that you could get away without ongoing orbital corrections (and there are awkward objects like the Moon and Sun which perturb orbits of course). Any significant error will result in an object travelling at orbital velocity hitting the side of the tunnel and you do not want to be anywhere in the neighbourhood when that happens.

## 2. The tunnel probably can not be built

Secondly it is almost certainly not possible to build such a tunnel at all (if we rule out a tunnel which completely circles the planet's equator, which probably is at least physically possible, although you would have to fight with the particle physicists over it, as they'll see a very different possible use for a huge circular tunnel full of vacuum).

### 2a. Atmospheric pressure problems

So, ruling out those sorts of tunnels, consider an open tunnel (so not one that goes all around the Earth) and consider the pressure at the open end of the tunnel. At whatever height it is, there will be some atmospheric pressure. If the tunnel is initially evacuated, then that atmosphere will obviously start to fill the tunnel, until the pressure at the top of the tunnel equilibriates with the atmosphere. At that point the bottom of the tunnel will be at something close to atmospheric pressure on the surface, if we assume it is at the surface. To deal with this the tunnel will have to be continuously pumped, and the top of it will need to be high enough that the amount of atmosphere leaking into it is small enough that it can be pumped.

Well, let's say that this means that the top of the tunnel needs to be somewhere around the Kármán line, which I will take to be 100km up.

### 2b. Other pressure problems

This means that the top of the tunnel needs to be supported by some structure about 100km tall. What would such a structure be like? Well, first of all let's consider the acceleration due to gravity, $$g$$, to be constant over the height of the structure: this is true to about 3% for the Earth, so it's a reasonable approximation. Whatever tower supports the top of the tunnel has radius, $$r$$ which is a function of height. And it turns out that:

$$r = r_0 e^{-\frac{g\rho}{2 P}h}$$

where:

• $$h$$ is height up the tower;
• $$r_0$$ is the radius at ground level;
• $$g$$ is the acceleration due to gravity (assumed constant with $$h$$);
• $$\rho$$ is the density of the material from which the tower is made;
• $$P$$ is the pressure at which the material from which the tower is made flows.

Further, the mass that the tower can support at a height $$h$$ is:

$$m = \kappa r_0 \frac{P}{g}e^{-\frac{g\rho}{P}h}$$

Here everything is as before except for $$\kappa$$ which is a fudge factor determined by the cross-sectional shape of the tower, with $$\kappa\ge\pi$$ and the equality only for a circular tower.

So this tower becomes exponentially large at the bottom, and depending on the material used it may be absolutely vast. If you consider $$g$$ properly, allowing it to decrease with height as it really does, then things get a bit better, but the change in $$g$$ over this height is too small to help significantly.

But it gets worse: the tower has to sit on something. So however super the material you use to make the tower, if $$P$$ at the base of the tower is greater than the pressure at which rock flows, it will just sink into the Earth. Well, there's a reason planets don't have arbitrarily tall mountains and it is basically this.

So even if you could find some amazing material with a very high $$P$$ and a very low $$\rho$$ you probably can't build this thing. I have not looked up what the best such materials are.

## 3. If you could build it, you wouldn't

So let's assume we've solved the problem of the 100km tall towers to support the top of the tunnel. OK, wait: we now have a 100km tall tower up which we can lift a spacecraft and then launch it from the top, avoiding the whole tedious atmospheric-drag thing (obviously you still need the very significant $$\Delta v$$ to achieve orbit, but you don't have to worry about all of the complexities involved in getting a rocket up through the atmosphere). So, forget the tunnel, just use the tower to lift spacecraft and launch them from the top!

Disclaimer: I've checked the above for dimensional sanity, but I wrote it all down rather quickly. Certainly the radius is exponential but I may have factors wrong.

• This is incredibly well written, and I agree that pressure structural challenges are tremendous, however, your structural calculations assume a rigid structure all the way down, when under the influence of air pressure, the structure could be supported (maybe not stabilized) with buoyancy. The buoyancy decreases as you approach the carmen line, but so do pressure requirements. Jul 15 '20 at 15:18
• Great answer. I think no one has pointed out yet, that the earth slowly precesses ("tumbles") in its rotation, which is another thing that will sink this project, even at the equator. Also, I think the largest perturbations will be different densities of the surrounding terrain (depending on the apogee, of course). Jul 16 '20 at 0:02
• I just love the idea of a "tunnel full of vacuum" ;) Jul 29 '20 at 15:07

This would be a tunnel a couple thousand kilometers long, that extends from the surface of the Earth to approximately low earth orbit altitude at both ends, strong enough to keep vacuum inside and the atmosphere out at sea level, such that its openings are in place for a space station in a highly-elliptical geosynchronous orbit comes flying through at about 10.7 km/s, once a day.

And the orbit's period must be an integer multiple of the Earth's sidereal rotation period. If it's not, you're going to have to build more than one of these, because the first one won't be in position when the satellite comes back towards perigee again.

I don't think this is feasible for a civilization except as planetary-scale art.

• I didn't think about matching up the orbital period with Earth's rotation, that does complicate things a bit. Jul 14 '20 at 22:24
• Don't you think assuming we could get the material to build it and automate construction in an exponential fashion it would make reaching orbit much easier? Jul 14 '20 at 22:28
• @brysgo If a civilization has the materials that can build something like this tunnel, the civilization would probably find it far less hassle to build a traditional space elevator. Jul 14 '20 at 23:02
• I would also think that even if you could solve the engineering issues (and choose an equatorial position) the fact that the planet's mass is not evenly distributed would be greatly magnified by such a set-up (because the distance factor would be very much shortened). Jul 15 '20 at 6:30
• @brysgo: Matter is not distributed perfectly evenly throughout the Earth, maintaining an orbit within a tunnel would obviously require that the object not touch the walls but that uneven mass distribution would tend to draw your satellite off-course from the tunnel's center-line. Jul 15 '20 at 16:08

There is no stable orbit around the Earth. Earth is not homogenous, there are tides from the Moon, the Sun, etc, ... well, sun-synchronous orbits sound promising, but one can never create an orbit that is both sun-synchronous and moon-synchronous.

Even the geostationary orbits require station-keeping or the satellite starts swinging north/south.

In space, a kilometer or two left or right is rarely an issue, in your tunnel you will need quite a precise orbit control in a way not compromising the vacuum inside. Probably electromagnetic? Larger satellites will also need a precise attitude control in order to orient to the cylinder axis and keep a sufficient annulus.

Yes, if you could build the vacuum tunnel.

For example, the Sentinel 1A satellite (which currently orbits the earth every hour or so) is designed to maintain its orbit within a 100m diameter virtual tube, fixed with respect to the surface of the earth, for a decade. (Like many other remote sensing DInSAR satellites, the quality and usefulness of the data it collects is entirely dependant on how exactly this orbit revisits its own track.)

So if your tube is at least 100m in diameter, it is possible to maintain an orbit within it for years. Generally an orbit is selected that takes advantage of the oblateness of the earth, so that it will naturally precess in synchrony with the daily rotation of the surface. Longer term, the precise control is usually limited by how much thruster propellant the satellite carries (for adjustment manoeuvres), but if it travelled through a built structure then you could externally make adjustments to the orbit perpetually. Launching the satellite with such a precise initial trajectory might also be unprecedented, but could probably be accomplished by using a section of the tube itself as an electromagnetic coil gun.

Furthermore, there is no reason the perigree (or even the entire orbit) couldn't be underground, if you could construct the vacuum tunnel. (The orbital math is only slightly more complicated, since the net gravitational pull reduces at depths below the surface.)

Obviously, constructing the tunnel would be the biggest challenge. The vacuum itself is probably a minor detail; compare existing laser interferometer gravitational wave detectors (such as LIGO, which evacuates about 10km of >1m diameter tube, maintained for years at a vacuum pressure that is about a million times more extreme than what satellites orbit in). A more practical (and useful) space-themed engineering challenge might be something like a lunar space elevator ribbon.

• I love the examples cited here, I think the devil's advocate questions here would be around whether the structures could handle increased perturbations from the lower orbit. Jul 30 '20 at 11:51

This is intended as an addition to other answers. It's more than a comment as it is (hopefully) worth maintaining:

You could 'steer' the vehicle electromagnetically while within the 'tunnel' and by whatsoever means are appropriate when out of the tunnel.

If the structure broadened at entry and exit you could apply precession correction on exit and approach.

This would be immensely hard and expensive - so quite possibly no harder than the rest of the task :-).

• Yes, this is how I imagined getting over the problem of wind blowing the tunnel around too. Jul 15 '20 at 10:53
• Also worth mentioning that the satellite would be going faster than 7.9 km/s while in the tunnel, so a 1° change of direction would require at least 138 m/s (497 km/h) of delta-v. While it should be possible to change the overall orbit, I very much doubt you can steer your way out of a spectacular failure if the tunnel does deform.
– Fax
Jul 15 '20 at 14:52
• What I'm struggling with is the apparently stability that comes from such a speed juxtaposed with the unpredictability due to gravitational turbulence, if the forces are that extreme would they just tear the satellite apart, and if they are not so extreme, couldn't you just compensate with equally not so extreme application of force? Jul 15 '20 at 18:02
• I switched my brain to picturing it as brownian and I'm starting to understand how the orbit could drift quite drastically, but intuitively I can't imagine the instantaneous delta in force applied would be enough that a small continuous guiding force wouldn't do to correct it. Jul 15 '20 at 20:13

Maybe I'm not understanding the question correctly, but it sounds like to me that you are describing "Orbital Ring". You can find more about them at Orbital Rings on Wikipedia.

There is a great video about it on Orbital Rings by Isaac Arthur on YouTube. He does a good job of describing physical limitations vs engineering limitations.

Sorry for the short answer, but I really feel like those links describe the answer far better than I could. It really seems like knowing the term "Orbital Ring" should give you information you are seeking.