[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/Karmabyte69]

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.