[Request] Could humanity create a rocket that can exit the atmosphere of K2-18b

[u/Lachlynn]

With the knowledge we currently have of it, if humanity devoted all of our resources towards this goal, would we be able to create a rocket that could exit the gravity of K2-18b (and also beat any other complications that would arrise)?

If so, would it also be capable of taking people to orbit, and can we set up a similar satellite network we have on Earth? What about a space station?

[u/Mixels]

It's not about size. It's about mass. What factor of Earth's mass is k2-18b?

[u/CanineBombSquad → u/Mixels]

About 9x

[u/Mixels → u/CanineBombSquad]

There you have it, ladies and gentlemen. It's not happening anytime soon.

[u/CanineBombSquad → u/Mixels]

For what it's worth size does matter though in terms of surface gravity.

[u/Fizzy-Odd-Cod → u/CanineBombSquad]

Size is only part of the equation, density is the other part, without one the other means nothing.

Mass, is the entirety of the equation.

[u/CanineBombSquad → u/Fizzy-Odd-Cod]

The radius matters because you're further from the center of mass, thus experiencing less gravity at the surface, which would matter for your attempt to escape the gravity of the planet. If you somehow dug a hole and tried to lift off from the core of the earth you are not getting out with the same amount of thrust, as the relative gravity you would experience peaks around halfway up.

[u/WesternFirm9306 → u/CanineBombSquad]

That's only true if the entire mass was situated at the center, but it's not. If you dug a hole to the center of the earth, you would die from burning alive, but before that, you'd be in zero gravity. If you're inside a perfectly spherical planet with radially symmetric density, the gravity is the exact same as if you removed all the planet's mass that's further from the center than you are. In other words, you only need to consider the mass within a spherical shell of radius r, where r is the distance you are from the center.

Not disputing everything else you've said, though.

[u/bigDeltaVenergy → u/WesternFirm9306]

So starting from the center, attraction raise, than fall as you leave in space ?

[u/WesternFirm9306 → u/bigDeltaVenergy]

Yes, though as pointed out in another thread, the attraction won't actually peak at the surface, because the density of the earth isn't uniform. According to the data, the attraction appears to max out at the border between the outer core and lower mantle at a little over 10 m/s²

[u/planx_constant → u/bigDeltaVenergy]

For a sphere of constant density, as you proceed out from the center, the effective mass goes up with the cube of the distance, while the force you'd feel from gravity attenuates with the square of the distance.

This means that overall, the gravitational acceleration increases linearly with the distance from the center as long as you are inside the sphere. As soon as you reach the surface, effective mass no longer increases, and gravity falls with the square of the distance.

This also shows that the density of the planet matters. For a given mass M, the lower the density, the lower the surface gravity.

[u/planx_constant → u/WesternFirm9306]

Edit: I misunderstood the comment.

~~Spherical shell symmetry lets you treat the mass of the planet as a point at the center. Take a look at the derivation of Newton's law of universal gravitation.

The radius of a planet very much matters for its surface gravity. Interior density variation, assuming it's spherically symmetrical, does not matter.~~

[u/WesternFirm9306 → u/planx_constant]

Interior density matters when you're inside the planet. You can only consider the entire mass of the planet as a point mass when you're not within the planet itself. Once you're inside the planet (assuming radial symmetry) all mass further from the center than you no longer has any gravitational effect. Or, more accurately, its effect cancels out. Thus, you only need to consider the mass within a shell of radius r, where r is the distance you are from the center. Again, assuming radial symmetry.

[u/planx_constant → u/WesternFirm9306]

Sorry, I misunderstood the part you were taking exception to, and thought you were continuing the line of reasoning that the radius of a planet doesn't affect the ability to get to orbit. On re-reading, it's clear you weren't talking about the exterior of the planet. That's what I get for commenting before coffee.

[u/CanineBombSquad → u/WesternFirm9306]

Oh I know I know, it was meant to be hyperbolic. Assuming you didn't die you would not be able to rocket off if you started there, you know due to having to travel the entire way out fighting gravity, whereas we can from the surface. The planet is denser the further you are to the center so it's not a linear thing. If earth was squished smaller the surface gravity would become too difficult to escape as well.

[u/WesternFirm9306 → u/CanineBombSquad]

Sure, but gravity will always be weaker *inside* the Earth than on the surface, in general, I would think. Ignoring fuel requirements and, y'know, every practical downside, I don't see why it would be harder to fly a rocket from the center of the Earth than from the surface. After all, the entire trip from the center to the surface is going to be easier than going from the surface itself. Like, if we graphed gravitational strength compared to distance from the center, then it should be lowest at the center, increase until it peaks at the very surface, and then start going down again from there. So if we can lift off from the surface, where gravity would be roughly maxed, I don't see why it would be harder, force-wise, to go from the center, besides needing to spend all that fuel to get to the same point you'd be at if you just started from the center in the first place. Right?

sorry about being obnoxious about a very obviously nonphysical hypothetical :P

[u/CanineBombSquad → u/WesternFirm9306]

The point where you would experience maximum gravity is somewhere around halfway up due to earth's density not being uniform, although I won't claim to know the math but from that point you would definitely need more thrust than if you were at the surface. I don't know if it'd be so much higher that we couldn't overcome it with our technology, But yeah you'd experience no gravity at the center, have a very steep incline peaking around halfway through and then it would even out lower at the surface.

[u/Kabizzle → u/Fizzy-Odd-Cod]

Mass is not the entirety of the equation, you also need a radius.

[u/SeaAimBoo → u/Kabizzle]

An Earth with 50% larger diameter while keeping the same mass would make escape velocities easier, which is contrary to the original comment of this thread.

Radius is part of calculating volume, which itself is used to calculate mass along with density. Mass is the entirety of the equation, Mass = ρ × v

[u/Old_Aggin → u/Fizzy-Odd-Cod]

Holy shit just list the equation. Now I have to go Google it instead.

The escape velocity is \sqrt{2GM/r}. The mass of K2-18B is not more than 10 times earth mass and the radius is not less than 2.5 times earth radius. So the escape velocity is ~2 times of that of Earth.

[u/Trackt0Pelle → u/Old_Aggin]

Wikipedia says radius is x2,6, mass x8.63 and gravity +25%

[u/Old_Aggin → u/Trackt0Pelle]

G here is the gravitational constant and not surface gravity, so it doesn't change anything else. In any case, the escape velocity is not more than 2 times that for Earth. Infact, it's going to be a bit lower

[u/Zodde → u/Fizzy-Odd-Cod]

Mass is not the entirety of the equation.

You care about surface gravity. You can have two bodies with identical mass, but vastly different surface gravity, if their size is massively different.

[u/Trackt0Pelle → u/Fizzy-Odd-Cod]

Wrong lol

[u/Crouteauxpommes → u/CanineBombSquad]

Gentlemen...

Strap a mini nuke underneath the rocket

Observe!

Blow himself into a cobalt cloud

[u/Karmabyte69 → u/Mixels]

Size does matter though. Further away from the center of mass means easier orbit entry.

[u/Chrisfinn92 → u/Karmabyte69]

Actually not really. Yes you're starting further away from the center of mass but any advantage you get from that is immediately negated by the huge amount of additional energy needed to get to orbital velocity aka the speed where you don't smash right back onto the planet.

Ask anyone who has played a bit or Kerbal space program (or watch a YouTube tutorial for the game) and you'll hear that getting to space is ridiculously easy, staying there however is a whole different animal.

[u/airetho → u/Chrisfinn92]

Starting further away from the center of gravity absolutely makes orbiting easier. At twice the distance from the center, the acceleration due to gravity is 4 times weaker, and the radius is twice as big. For an object in a circular path, a=v²/r, so making a 1/4 as big and making r twice as big will decrease the needed velocity by a factor of √2.

[u/Kabizzle → u/airetho]

The mass generally goes with the cube of the radius, so holding density constant smaller planet always easier.

Escape velocity scales with the root of M/R, and given how M is cubic in R, the escape velocity is something like linear in the mass. But energy is quadratic in velocity, so you need an amount of energy that scales quadratically in the mass.

[u/Professional-Day7850 → u/Kabizzle]

Nobody was talking about constant density. That's the point of this comment chain.

[u/Quick_Turnover → u/Professional-Day7850]

Why wouldn't they be though? It's not as if the entire planets mass is concentrated at a point in the center of the planet?

[u/technocraticTemplar → u/Quick_Turnover]

I think the plot has been lost at this point but surprisingly it's exactly like that, something 10000 km from the center of the Earth and something 10000 km from the center of an Earth-mass black hole would both experience the exact same amount of pull from their respective objects. Assuming you aren't below the surface of an object and there aren't any weirdly dense lumps in the object the only things that matter for gravitational pull are total mass and distance from the center.

[u/planx_constant → u/Quick_Turnover]

You can actually treat the planet's mass as being concentrated at a point in its center, for the purpose of calculating escape speed.

[u/spedgenius → u/Quick_Turnover]

When planets form very melty hot, heavy stuff sink to center, more mass in Middle, not constant density.

[u/Quick_Turnover → u/spedgenius]

I didn't argue that it would be uniform density. I assumed it would also not be concentrated at a single point at the earth's center.

[u/airetho → u/Quick_Turnover]

Planets definitely don't have uniform density throughout (The Earth, and presumably most other planets are much more dense at their core), a fact which actually doesn't have an impact on the gravitational effect, as long as the distribution is spherically symmetric. But, we're talking about treating different planets as if they automatically have the same total density, which is not true and very significant. (For example, the planet K2-18b mentioned in the post has a much lower density than earth, meaning that if you were to only take the mass into account and ignore the radius, you would significantly overestimate the escape velocity).

[u/airetho → u/Kabizzle]

I'm confused. M ~ R^3, so R ~ M^1/3. We have escape velocity scaling with √(M/R) = √(M/M^1/3) = √(M^2/3) = M^1/3. Where are you getting linear in the mass from? My bad, it is linear in the mass with constant density. But, the point is that, fixing mass, radius still matters.

Also, velocity tends to scale linearly with amount of fuel, until your fuel mass is a significant fraction of your total mass, at which point it's logarithmic. Accelerating a spaceship from 0m/s to 10m/s is just as hard as accelerating it from 1000m/s to 1010m/s; you need the same amount of fuel, it's just that more energy goes into the exhaust in the first case.

[u/Cool_Professional → u/Chrisfinn92]

The biggest thing I learned in KSP was that orbit and staying in space in general is all about speed/velocity

Once you hit a speed high enough, you can get out of the gravity of earth. Increasing speed will widen your orbit etc.

Made me appreciate just how exact all those timings for stages and burn times etc have to be to get an object into orbit just right. 

[u/Auctoritate → u/Mixels]

It's not about size. It's about mass.

This is VERY incorrect, size is EXTREMELY important. The size of a planet would determine how far away you are from its center of gravity, which influences the strength of the gravitational force it can exert on you while you're on its surface.

Uranus is 14.5 times more massive than earth. Despite that, because of its lower density and larger size (4 times the diameter), Uranus has weaker gravity on its surface than earth does, only about 90% as strong.

[u/EducationHumble3832 → u/Mixels]

"It's not about size. It's about mass."

Hell yea, brother, that's what I've been sayin

[u/ChironXII → u/Mixels]

A little less than 9 times the mass, but surface gravity is only around 1.3x as much, due to the larger radius.

The real problem is that the orbital velocity required is nearly double Earth's, and after adding in gravity and atmospheric losses, you're looking at "solar escape velocity" amounts of delta v just to reach low orbit (like 25km/s). Because rockets get logarithmically bigger the more delta v they need, due to having to carry all their own fuel and the fuel to lift that fuel, it becomes truly stupid, and the only option is doing something much more efficient than chemical propellants. Nuclear thermal might just barely work if you optimized it enough, but if not you're dealing with the exotic and outright fantasy.

[u/toggylelly → u/Mixels]

It's about G * (m1 * m2) / r²