Super Earths and space travel

[Moontanman]

I was reading about the fact that many of the planets so far discovered in the rocky planet category are know as super earths, some are estimated to have gravity 4X earths surface gravity or more.

 

If we had been dealing with 4 g surface gravity how much harder would the apollo missions have been? Would it as been as straightforward as 4 X as big a rocket or is the difference more likely 8 X?

[imatfaal]

Assuming a planet with 4 times the mass rather than 4 times the gravity.

 

Escape velocity varies with the root of the mass (so that would be a factor of two) and inversely with the root of the radius (assuming constant density the radius will go up with the cuberoot of the mass - giving the sqrt of the cube root of 4 - which is cube root of two). A bit of algebra will bring this total change to 4^1/3 - this is about 1.58 times the escape velocity of an earth size planet.

 

The atmosphere will also be very different - denser at sealevel and of greater extent; this might make more difference than the escape velocity. Not sure where to start estimating this.

 

It is possible with a much thicker atmosphere that other methods of propulsion might provide more bang for your buck - ie something more like a jet that throws atmosphere back out the back at high speed. I am sure some of the aeronautics guys could set me straight on this very quickly

[MigL]

I don't know much about these 'super earths', but I'll assume that they are in an orbit close to 1 Au so as to have the possibility of liquid water ( if orbiting a star similar to the sun ).

Something I've always wondered about though, would a higher gravity ( 4x ) retain more of the light elements like Hydrogen and Helium in the atmosphere ? As Imatfaal has stated, these planets would retain gases where the mean speed of molecules is 60 % higher than on Earth, i.e. higher percentage of light elements in the atmosphere.

 

Or am I thinking about it the wrong way ?

Could the lighter gases be expelled by the star/sun's radiation from a certain radius, as the solar system/planets are forming, such that inner rocky planets don't have much Hydrogen/Helium to begin with.

 

Or is this even on topic ?

[Enthalpy]

At identical density, mass *4 and radius *cuberoot(4) imply a gravitation energy per mass unit *2.52 and the escape velocity *1.59 as compared with the Earth, agreed.

 

Escaping the Earth takes mean 11186m/s plus some 1300m/s due to the limited acceleration at the beginning. 7367m/s more are a hard penalty: with hydrogen and oxygen ejected at 4500m/s, it takes two stages more and - depending on the stages' inert mass - 6.0* more lift-off mass. That wouldn't stop Mankind but is a big difficulty.

 

The atmosphere brakes a rocket very little, a big one far less. Its real drawback are the potential bending moments and vibrations that let build the rocket and payload heavier and let go too slowly through the lower atmosphere, giving gravitation more time to waste some propulsive force.

 

Up to now, our atmosphere brings nothing useful to reach orbit. Many launcher attempts wanted to use it (Skylon presently) but basically, getting a push by an aerobic combustion at 2km/s (M6) is quite difficult; this may be 1.5km/s more efficient than tranporting the equivalent liquid oxygen, good and fine - but the added complexity saves only 1.5km/s over the 9.5km/s to the low orbit. For that, I wouldn't afford exotic engines, wings, a landing gear, the extra mass, the conflicting requirements of plane and rocket, and so on.

 

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Bigger planets retaining light elements: from popular science papers, this knowledge isn't really established. The magnetic field seems important to avoid the dissociation of vapour by ionizing particles, followed by the loss of hydrogen.

 

Before extrasolar planets were discovered, our solar system let believe that big planets are gaseous and far from the star, small ones rocky and near. This has changed, and the explanation by the star ripping the light elements away has weakened.

 

One should also remember that the composition of our "gaseous" planets at depth is much unknown. And up to now, models for protoplanetary systems ignore the segregation of elements and isotopes by gravitation.

[Moontanman]

Actually I was thinking of 4 times the surface gravity but I may have been reading it wrong, I know many of them have twice the diameter of the earth or more yet with similar density.

 

A NASA podcast I saw a year or so ago indicated the current thought was a super earth could maintain earth like temps out to 3 or 4 AU via retaining a deep high pressure hydrogen atmosphere but still contain things like nitrogen and CO2 and be clear enough to sustain photosynthesis on the surface, possibly a sun powered Hydrogen cycle instead of Oxygen as suggested by Isaac Asimov. Or closer in have a high pressure conventional atmosphere and maintain Earth like temps at 2 or 3 AU, one of these super earths at one AU around a Sun like star would be more likely to be Venus on steroids than Earth.

 

Ok I checked the figures it looks like such a planet would have a surface gravity of 19.66 Meters per sec, 22.38 Kps escape velocity, and 8 times Earth's mass and volume...

[Danijel Gorupec]

...it takes two stages more and...

How did you conclude/estimate this? (I am asking to learn).

[pavelcherepan]

How did you conclude/estimate this? (I am asking to learn).

 

Even starting from the Earth we generally use two- or three-staged designs, which is simply due to the fact that it's very inefficient to carry around empty fuel/oxidizer tanks and would be even more inefficient on a planet with higher gravity and denser atmosphere.

[Moontanman]

At identical density, mass *4 and radius *cuberoot(4) imply a gravitation energy per mass unit *2.52 and the escape velocity *1.59 as compared with the Earth, agreed.

 

Escaping the Earth takes mean 11186m/s plus some 1300m/s due to the limited acceleration at the beginning. 7367m/s more are a hard penalty: with hydrogen and oxygen ejected at 4500m/s, it takes two stages more and - depending on the stages' inert mass - 6.0* more lift-off mass. That wouldn't stop Mankind but is a big difficulty.

 

The atmosphere brakes a rocket very little, a big one far less. Its real drawback are the potential bending moments and vibrations that let build the rocket and payload heavier and let go too slowly through the lower atmosphere, giving gravitation more time to waste some propulsive force.

 

Up to now, our atmosphere brings nothing useful to reach orbit. Many launcher attempts wanted to use it (Skylon presently) but basically, getting a push by an aerobic combustion at 2km/s (M6) is quite difficult; this may be 1.5km/s more efficient than tranporting the equivalent liquid oxygen, good and fine - but the added complexity saves only 1.5km/s over the 9.5km/s to the low orbit. For that, I wouldn't afford exotic engines, wings, a landing gear, the extra mass, the conflicting requirements of plane and rocket, and so on.

 

----------

 

Bigger planets retaining light elements: from popular science papers, this knowledge isn't really established. The magnetic field seems important to avoid the dissociation of vapour by ionizing particles, followed by the loss of hydrogen.

 

Before extrasolar planets were discovered, our solar system let believe that big planets are gaseous and far from the star, small ones rocky and near. This has changed, and the explanation by the star ripping the light elements away has weakened.

 

One should also remember that the composition of our "gaseous" planets at depth is much unknown. And up to now, models for protoplanetary systems ignore the segregation of elements and isotopes by gravitation.

 

Ok I checked the figures it looks like such a planet would have a surface gravity of 19.66 Meters per sec, 22.38 Kps escape velocity, 4 times Earth's surface area, 8 times Earth's mass and volume...

 

Considering the new numbers I obtained are your figures still accurate or would it be a bit harder?

Edited March 29, 2015 by Moontanman

[Enthalpy]

Oops, I had drifted towards Imatfaal's figures of mass*4.

Back to Moontanman's original 4g, admitting the same density as Earth (despite pressure compresses stones and metals in planets):

 

Radius *4, mass *64, gravitation energy *16 at the surface, escape speed *4. Scaling Earth's 9500m/s to low-orbit, that's now 38,000m/s, horribly much. It exceeds Earth's orbital speed, something that humans have never made with their engines.

 

Even if all stages expel gas at 4500m/s and have zero dry mass, the ratio of initial/final masses is exp(38,000/4,500)=4649 - bad start, which the dry mass can only make worse.

 

With dry masses: let's take 7 stages bringing 5429m/s each, with 4560m/s exhaust speed (even for the first one) and 100kg dry mass per ton of propellants. Then each stage is 3.97 times heavier than the next one, and the rocket starts 15,500 times heavier than its paylod only to reach the low orbit. At Earth, existing rockets are ~300 times heavier than their Leo payload. That's 52 times worse, not 4 nor 8, because Tsiolkovski's equation contains an exponential.

 

My unverifiable bet is that humans would have made it nevertheless.

[Moontanman]

Oops, I had drifted towards Imatfaal's figures of mass*4.

Back to Moontanman's original 4g, admitting the same density as Earth (despite pressure compresses stones and metals in planets):

 

Radius *4, mass *64, gravitation energy *16 at the surface, escape speed *4. Scaling Earth's 9500m/s to low-orbit, that's now 38,000m/s, horribly much. It exceeds Earth's orbital speed, something that humans have never made with their engines.

 

Even if all stages expel gas at 4500m/s and have zero dry mass, the ratio of initial/final masses is exp(38,000/4,500)=4649 - bad start, which the dry mass can only make worse.

 

With dry masses: let's take 7 stages bringing 5429m/s each, with 4560m/s exhaust speed (even for the first one) and 100kg dry mass per ton of propellants. Then each stage is 3.97 times heavier than the next one, and the rocket starts 15,500 times heavier than its paylod only to reach the low orbit. At Earth, existing rockets are ~300 times heavier than their Leo payload. That's 52 times worse, not 4 nor 8, because Tsiolkovski's equation contains an exponential.

 

My unverifiable bet is that humans would have made it nevertheless.

 

Thanks Enthalpy, 4g was my mistake, again I did not state myself clearly, I was thinking of the planets so far found, as far as I can see none of them are thought to be 4g at the surface, I was thinking of twice the diameter and the same density as earth, for reason i had assumed it would be 4g but as it turns out it would be 2g, twice the diameter, 4 times the surface area, and 8 times the mass and or volume assuming the same density which may or may not be a valid assumption for a rocky world.

 

Possibly some form of very energetic nuclear power would be necessary...

[Enthalpy]

How did you conclude/estimate this? [Enthalpy's "two stages more"]

 

There is no fixed rule, and designs vary a lot, accordingly. If each stage adds a bit more speed than its own exhaust speed, that's a good start - but only a start.

 

The idea of stages is to throw away masses becoming useless, especially empty tanks - and also engines too powerful for the remaining mass. Keeping a stage for too long is a waste; if exaggerating, its empty mass can be all the mass it can accelerate to the excessive speed objective, and then the stage carries zero payload, zero next stage. Throwing a stage too early means carrying dry mass too many times - this limit is never approached in existing designs - and, above all, designing too many stages.

 

The heavy tendency is to have fewer stages and accept a heavier mass at lift-off, because development is the main cost of a launcher, not mass. The recent Zenit and Falcon go to Gto (geosynchronous transfer orbit) with only two kerosene stages; that's 12,000m/s performance with some 3,300m/s exhaust speed - a serious stretch, but is saves a third stage.

 

Lighter dry masses improve that, to the point that we could go to Leo in one stage if we wanted it. This is one point that has progressed more than the engines and has still potential for improvement.

 

It is also an arguments against solid first stages. As solids provide only 3500m/s at best, one single next stage reaches only Leo and uncomfortably, Gto never, Gso even less. That is, whether you add a solid first stage or not, you need two liquid stages over it, so you better avoid the solid altogether.

 

It's an even stronger argument against air-breathing first stages, which stop at 2,000m/s.

[...] twice the diameter and the same density as Earth [...]

 

So this time mass *8, acceleration at the surface *2, gravitation energy at the surface *4, escape speed *2.

 

19,000m/s to reach a low orbit including losses.

3 hydrogen stages provide each 5100m/s with 100kg/t dry mass and 4400m/s exhaust speed: each m*3.80

1 kerosene stage provides 3700m/s with 100kg/t dry mass and mean 3200m/s exhaust speed: m*3.78

The lift-off mass is 207 times the payload in low orbit. 7 times worse than Saturn V with better tech.

 

It's only 4 times more than Vulkan

http://www.buran-energia.com/energia/vulcain-vulkan-desc.php

http://www.buran-energia.com/energia/vulcain-vulkan-carac.php

[pavelcherepan]

Wow! Thanks for that, Enthalpy! That was an amazing explanation!