Super-Earths difficult to depart from

[lpetrich]

This is something that I have long surmised, and it is nice to see someone get some publicity for calculating that.

Any Aliens on Super-Earths Would Have a Tough Time Flying to Space and No Way Out? Aliens on 'Super-Earth' Planets May Be Trapped by Gravity noting

[1803.11384] Super-Earths in need for Extremly Big Rockets by Michael Hippke, "an independent researcher affiliated with the Sonneberg Observatory in Germany" according to space.com

A typo and some bad grammar. A nicer-looking title might be "Would one need an excessively large rocket to depart from a super-Earth?"

The paper seemed to me rather poorly organized, and it did not survey the various sorts of rocket engines. But its point is a correct one, that departing from a super-Earth is much more difficult than departing from our homeworld.

 

[Cheerful Charlie]

If a super earth was big enough, it would probably have retained so much water from it's earliest days it's seas would be deep enough, there would be no land. No land, no metals, no aliens that could develop civilizations.

 

[lpetrich]

Michael Hippke used  Kepler-20b as an example. [1608.06836] A 1.9 Earth radius rocky planet and the discovery of a non-transiting planet in the Kepler-20 system reports on its radius and mass: 1.868+0.066-0.034 Earth radii and 9.70+1.41-1.44 Earth masses. That planet orbits its star with a period of 3.7 (Earth) days, and its star has a mass of 0.91 solar masses, a radius of 0.94 solar radii, and a surface temperature of 5500 K -- much like the Sun. That planet's equilibrium temperature is about 1200 K. Consulting the planet modeling at Planet Models, I find that it is consistent with being 75% rock and 25% iron by mass (the Earth is 30% iron by mass).

But he is correct that that planet would be difficult to depart from. It would have various other difficulties, due to having a surface gravity about 2.8 that of the Earth. I will consider a habitable-zone version of Kepler-20b with an Earthlike surface and atmosphere.

Its mountains would be only 1/3 as high as Earth mountains, and its atmosphere would fade off 3 times as fast with increasing altitude. Its tallest trees would be only 1/3 as tall as ours, and its largest land animals 1/3 the size of ours. The only way to grow human-sized on such a world would be to be built like an elephant or a sauropod -- and to have a similar lifestyle. To be more humanlike would require being much smaller, like being 60 cm / 2 ft high. That would also mean having a much smaller brain, so sentient organisms may be unlikely on such a world.


For a long-term presence in outer space, the first step is going into a low orbit around one's home planet. It is the first step because it requires the smallest velocity change or delta-V. I find it curious that Michael Hippke did not discuss low orbits.

For the Earth, the low-orbit orbital velocity is about 7.8 km/s, and scaling to Kepler-20b gives 18 km/s, over twice as large.

I will now estimate how much of a mass ratio a rocket will need to get that delta-V. The rocket's initial mass is the sum of its fuel/oxidizer mass, its structural mass, and its payload mass.

Using the Falcon 9 Full Thrust rocket as a comparison, its mass ratio is about 25 to 1, using an initial rocket mass of 550 metric tons, and a payload mass of 23 mt. To get to low orbit from Kepler-20b, one needs a mass ratio of 25^(2.3) or around 1500. A rocket would need more stages to get into orbit, and with the Falcon 9's performance, I estimate that it could only get around 370 kg into orbit. Scaling up to the Saturn V's initial mass of 3000 mt, I find only 2 mt in orbit.

That's just low orbit. Escaping from the planet is even worse. Using the Falcon 9's mass ratio, I find that one goes from 2 mt to 80 kg. Teeny tiny.

So the inhabitants of such a planet would likely consider space travel essentially impossible.

 

[lpetrich]

If a super earth was big enough, it would probably have retained so much water from it's earliest days it's seas would be deep enough, there would be no land. No land, no metals, no aliens that could develop civilizations.

If it had formed with that much water, yes. But that's a big unknown. The Earth's oceans have a mass of 2.3*10^(-4) times the Earth's total mass, and estimates of the water in the Earth's interior are typically some 10 times greater. But it is not very well-understood why the Earth got as much water as it did, and not much more or much less. Did the Earth receive a lot of water by rocky-planet standards? Very little water by such standards? It's hard to tell.

It has been difficult to measure both masses and radii of habitable-zone exoplanets, but it has been done in some cases, notably for the TRAPPIST-1 planets. Some of those planets have overall densities low enough to be consistent with their having oceans a few hundred kilometers deep or thereabouts. That may indicate that the Earth is unusually low on water, but the TRAPPIST-1 star is a low-mass red dwarf, a star much less massive than the Sun, and planets may have formed differently. In particular, there is no evidence of Jovian planets around TRAPPIST-1, while the Solar System has two Jovian planets and two halfway-Jovian ones.

 

[barbos]

Well, high gravity would make intelligent life harder because it would make size of the animals smaller.

 

[Loren Pechtel]

You're not getting off a big planet with chemical rockets. However, that does not mean you can't make it to space. There are three mega-engineering approaches that let you get off no matter what the gravity.

 

[lpetrich]

You're not getting off a big planet with chemical rockets. However, that does not mean you can't make it to space. There are three mega-engineering approaches that let you get off no matter what the gravity.

Like what?

 

[skepticalbip]

Cavorite?

 

[Wiploc]

Cavorite?

Nonsense. You want mix of 87% unobtainium, 13% MacGuffin, and only a trace of cavorite.

 

[Wiploc]

So the inhabitants of such a planet would likely consider space travel essentially impossible.

That's if you launch from the surface, right? But the heavier the planet is, the thicker the atmosphere, and so the easier flight. If you launch from a plane or a balloon, you don't have to carry all the fuel you'd need to escape from the surface.

Moonless planets would have even more atmosphere.

 

[barbos]

So the inhabitants of such a planet would likely consider space travel essentially impossible.

That's if you launch from the surface, right? But the heavier the planet is, the thicker the atmosphere, and so the easier flight. If you launch from a plane or a balloon, you don't have to carry all the fuel you'd need to escape from the surface.

Moonless planets would have even more atmosphere.

Atmosphere would have to have thickness comparable to diameter to planet to have any effect on "surface gravity" That's impossible.

In practice atmosphere would always be a hindrance because of friction.

 

[Loren Pechtel]

You're not getting off a big planet with chemical rockets. However, that does not mean you can't make it to space. There are three mega-engineering approaches that let you get off no matter what the gravity.

Like what?

Launch loops: https://en.wikipedia.org/wiki/Launch_loop

Space fountain: https://en.wikipedia.org/wiki/Space_fountain

And my own approach to this so it doesn't have a name. Far bigger than either of these options and while it still has major moving parts I don't think it's as catastrophically vulnerable if something goes wrong:

Build a ring of towers around the equator. On them build an evacuated tube. In it build a ring that's basically a maglev train, except it's riding on the ceiling. Get it spinning fast, far above orbital velocity. It exerts an upward force. This is matched by extending the towers upward (as you build them up you spin the ring faster.) Build another ring. Continue until you're in space. Engineering analysis: Imagine the towers infinitely close to each other (a wall rather than individual towers.) There are no torque forces. Imagine the rings stacked right on top of each other and infinitely thin. The required strength o the towers goes to zero. Combine these and it's clear that the forces in the overall structure can be made as low needed by simply adding more towers & rings. Your only structural requirements are maintaining a vacuum around the rings--and we can build large vacuum chambers.

Obviously, this will involve some major engineering. The first ring no doubt can't be placed high enough to clear terrain (the Andes)--that means you're going to have to cut through that terrain. Those are some huge tunnels. Some of the towers to support that first ring rest on abyssal plains, they're going to be mighty towers.

The only potential showstopper I see (beyond the fact that this far beyond anything mankind has ever done) is earthquakes--and that applies to all three of these schemes.

 

[Loren Pechtel]

So the inhabitants of such a planet would likely consider space travel essentially impossible.

That's if you launch from the surface, right? But the heavier the planet is, the thicker the atmosphere, and so the easier flight. If you launch from a plane or a balloon, you don't have to carry all the fuel you'd need to escape from the surface.

Moonless planets would have even more atmosphere.

Actually, high g worlds will probably have thinner atmospheres.

How much atmosphere a world has is a function of how much gas of the types it can hold onto is available. Atmospheres consist of whatever gas is available that the planet can hold onto. Big enough and you get a gas giant--while it will have the terrestrial components other than oxygen they'll be small minorities. Something like Earth can't hold the hydrogen and helium, we get what's left.

Now, enter scale height. The scale height of an atmosphere is the distance in which the pressure drops to 1/e of what it was. On Earth that is about 8km. Note that gravity appears in the denominator of this calculation. Now, it's impossible to truly define the edge of the atmosphere but the lowest practical orbit is 160km so I'll use that as the edge. That's 20 scale heights.

Consider a 2g world with an atmosphere like ours. Lets take the same "edge" to the atmosphere and see what happens: It's 20 more scale heights. A simplistic calculation says the surface pressure is enough to compress the atmosphere to white dwarf densities--obviously, in reality it has ceased to be a gas by then.

Thus a 2g world can't really have an atmosphere as thick as ours even if it's much denser.

 

[Jokodo]

Now, enter scale height. The scale height of an atmosphere is the distance in which the pressure drops to 1/e of what it was. On Earth that is about 8km.

5.5 km I believe. Maybe you had the correct figure in head and thought it was in miles, so you translated it when it actually was in km already?

You guys should just stop using miles and stuff. I believe you actually crashed a spacecraft because of them, right?

 

[skepticalbip]

Now, enter scale height. The scale height of an atmosphere is the distance in which the pressure drops to 1/e of what it was. On Earth that is about 8km.

5.5 km I believe. Maybe you had the correct figure in head and thought it was in miles, so you translated it when it actually was in km already?

You guys should just stop using miles and stuff. I believe you actually crashed a spacecraft because of them, right?

Not exactly. The crash was due to some using Metric units and some using US Customary units (and someone not converting). If all had used the same system, either one, then everything would have been fine.

 

[bilby]

Now, enter scale height. The scale height of an atmosphere is the distance in which the pressure drops to 1/e of what it was. On Earth that is about 8km.

5.5 km I believe. Maybe you had the correct figure in head and thought it was in miles, so you translated it when it actually was in km already?

You guys should just stop using miles and stuff. I believe you actually crashed a spacecraft because of them, right?

Not exactly. The crash was due to some using Metric units and some using US Customary units (and someone not converting). If all had used the same system, either one, then everything would have been fine.

Yup. If only the other 95% of the world had conformed to the idiosyncrasies of your 5%, everything would have been fine.

Seriously, if the problem is that people needed to all use the same units, and that didn't happen, the blame is NOT equally shared. It falls squarely on the shoulders of the 5% of people who cling to an outdated and obsolete system.

 

[Loren Pechtel]

Now, enter scale height. The scale height of an atmosphere is the distance in which the pressure drops to 1/e of what it was. On Earth that is about 8km.

5.5 km I believe. Maybe you had the correct figure in head and thought it was in miles, so you translated it when it actually was in km already?

You guys should just stop using miles and stuff. I believe you actually crashed a spacecraft because of them, right?

8km: http://lasp.colorado.edu/~bagenal/3720/CLASS2/2BaratropicLaw.html

 

[Jokodo]

Now, enter scale height. The scale height of an atmosphere is the distance in which the pressure drops to 1/e of what it was. On Earth that is about 8km.

5.5 km I believe. Maybe you had the correct figure in head and thought it was in miles, so you translated it when it actually was in km already?

You guys should just stop using miles and stuff. I believe you actually crashed a spacecraft because of them, right?

8km: http://lasp.colorado.edu/~bagenal/3720/CLASS2/2BaratropicLaw.html

"Level of 500 hPa is roughly dividing the mass of the atmosphere in two. It lies near 5 km, and it's height is typically analysed at intervals of 40 or 80 m, corresponding to MSLP isobars at intervals of 5 or 10 hPa." http://weatherfaqs.org.uk/node/142

 

[Peez]

Mission of Gravity

 

[Loren Pechtel]

8km: http://lasp.colorado.edu/~bagenal/3720/CLASS2/2BaratropicLaw.html

"Level of 500 hPa is roughly dividing the mass of the atmosphere in two. It lies near 5 km, and it's height is typically analysed at intervals of 40 or 80 m, corresponding to MSLP isobars at intervals of 5 or 10 hPa." http://weatherfaqs.org.uk/node/142

Aha!

Scale height is 1/e, not 50%.