I encountered sci-fi stories about planets of the twice the mass of Earth, and the characters were able to leave them in spaceships.
I wonder, whether it is possible at all?
I encountered sci-fi stories about planets of the twice the mass of Earth, and the characters were able to leave them in spaceships.
I wonder, whether it is possible at all?
On Space Exploration Stack Exchange, Russell Borogove addressed a very similar question and made some reasonable estimates about the required mass of a Saturn V-like rocket (arguing it's impractical to consider all possible rocket designs, given the variation in performance) to escape a planet of various surface gravities (see also Hippke 2018). Above $10g$, the rocket is effectively the same mass as the planet. At this point, we would need literally quadrillions of Saturn Vs. Even escaping a planet with a surface gravity of $6g$ would require millions of them. On the other hand, that assembly would weigh 38 billion tons, which is tiny compared to Earth's mass. $10g$ is a somewhat generous limit, but beyond that, we do know it's fairly absurd. This corresponds to an escape velocity of $35.4\text{ km s}^{-1}$.
From an astronomical point of view, is it even possible to have a terrestrial planet with that sort of escape velocity? Looking at the mass-radius curves by Seager et al. 2007, it seems like a super-Earth composed predominantly of silicates and iron could achieve that surface gravity with a mass of $M\sim30M_{\oplus}$ and $R\sim2.5R_{\oplus}$. From a compositional perspective, this is certainly reasonable, according to their numerical work.
What if we consider non-silicate compositions? Perhaps we could make the planet less dense, ensuring that the same mass yields a higher radius and therefore raises the mass limit. Say we have a planet made mostly of water. To achieve that same velocity, it appears that we may be able to reach $\sim40M_{\oplus}$.
On the other hand, super-Earths larger than $2R_{\oplus}$ aren't expected to exist. At masses above this (corresponding to $20M_{\oplus}$ for a mainly silicate planet, and larger for an iron planet), the body would accrete a thick atmosphere, beginning to bridge the gap between terrestrial and gas planets (see Lopez & Fortney 2013 for an even more conservative limit!). (Coincidentally, this ends up yielding, actually, a similar escape velocity for the silicate case.)
In the particular scenario you describe, a $2M_{\oplus}$ planet would have a radius of perhaps $1.4R_{\oplus}$, according to Seager et al.'s models, and thus a surface gravity (and escape velocity) barely greater than Earth's. This is obviously quite easy to escape with a chemical rocket.
Rockoon!
https://en.wikipedia.org/wiki/Rockoon
Gravity drags hard on rockets. But a balloon cares nothing for gravity. The lift conferred by a hydrogen balloon will depend on the composition of your atmosphere, but will be the same regardless of the gravity of your planet.
Using balloons to get rockets above the atmosphere and (partly) out of the gravity well is a real thing.
https://www.universetoday.com/tag/rockoon/
Is there a better way to get to space? Current traditional methods using expendable rockets launching from the surface of the Earth are terribly inefficient. About 90% of the bulk and mass of what you see on the launch pad is expended in the first few minutes of the mission, just getting the tiny payload above the murk of Earth’s atmosphere and out of the planet’s gravity well.
Recently, on May 20th, 2016, Zero2infinity lofted Aistech’s first satellite into the upper atmosphere, aboard its Sub-Orbital Platform in Near Space balloon system. Zero2infinity uses these Near Space balloons to carry client payloads up above 99% of the Earth’s atmosphere. This is a cheap and effective way to get payloads into a very space-like environment.
I here assert that one could use this method with a high gravity planet and avoid the need for a prohibitively large and powerful rocket. But you cannot leave the planet in a balloon - you still need the rocket to get away, and so this meets the OP's request for "a chemical rocket to leave it".
The escape-speed of a planet is given as
$v_2=\sqrt{{2GM}\over{r}}$
r = radius of the planet
G = gravitational constant
M = mass of the planet
As long as the spaceship is able to reach this speed, it can leave the planet. Twice the mass of earth and the same radius would result in $v_2$ = 15.7 km/s, that's absolutely possible.
I suggest that a deltaV of 13.5km/s is about the most that might be expected for a chemical rocket.
This is calculated from the rocket equation and assumes a high (hydrogen-oxygen based) exhaust velocity and a high mass ratio (20:1) giving a deltaV of 4500*In(20) = 13.5km/sec but is probably optimistic. Although using hydrogen provides a good exhaust velocity, it is very low density and so needs a very big tank which in turn makes a mass ration of 20:1 very difficult.
But taking this as a best case, it is possible to put this number into the escape velocity equation holding either the radius constant or the mass constant to see what we get.
Keeping the radius constant whilst increasing the mass: A mass of 1.4 x Earth mass would produce an escape velocity of 13.2km/s
Keeping the mass constant whilst decreasing the radius: A radius 0.7 x earths would have an escape velocity of 13.4km/s
Alternatively the mass can be increased whilst the radius is also increased. Case in point as suggested by HDE where mass = 2 x Earths mass and radius = 1.4 x Earths mass: In this case the escape velocity would be 13.4km/s
In each of these cases it may be just barely possible to escape from the planet using chemical rockets alone. But I would stress only with the greatest of difficulty.
It should also be noted that it might be possible to escape from a planet using an orbital rather than an escape velocity. This might be achieved by using gravitational assists from moons and planets.
Alternatively this might be achieved by retanking the rocket in orbit. Refilling the propellant tanks in orbit provides a practical method for effectively increasing the mass ratio.
Minimum DeltaV for low Earth orbit is 7.8km/s (9.4km/s allowing for air resistance and gravitational losses), whereas Earth escape velocity is 11.2 km/s so there is a bit of wriggle room here.
There is a limit to the size of a planet, above which it is a star. Jupiter is nudging that. Jupiter doesn't exactly have a surface, but at the cloudtops it has a little over 2.5g, which is I think escapable with a suitable chemical rocket.
The problems of assembling a suitable rocket and suitable chemistry are left as exercises ;)
Hal Clement wrote about a solid and dense planet, Mesklin, with a high surface gravity, but with a very high rate of rotation. Launching from near Earth's equator reduces the delta-V for escape by a 25th - for orbit by an 18th. Spin your planet fast enough, and you should be able to jump off the equator. It may be a bit windy.