Space Travel from Red-Dwarf Planets?

[lpetrich]

Escape from Proxima b - Scientific American Blog Network -- "A civilization in the habitable zone of a dwarf star like Proxima Centauri might find it hard to get into interstellar space with conventional rockets"

Author Abraham Loeb worked out the numbers, and found it very difficult. Some of his numbers are not the "right" numbers to use, so I'll have to find the correct ones.

First, our Solar System.

The first step in getting off our planet is getting into low Earth orbit. One can go directly into an escape orbit if one can do enough velocity change or delta-V, but low Earth orbit is a minimum for getting into outer space and staying there. For a 300-km altitude, one's orbit velocity is 7.73 km/s and one's orbit period 1.5 hours. One needs about 1 or 2 km/s delta-V more than that to get into orbit, since one must fight our planet's atmosphere and gravity. So one needs 10 km/s delta-V with a high-thrust engine.

Over a century ago, Konstantin Tsiolkovsky worked out from Newtonian mechanics a simple equation that relates rocket initial mass (mi), final mass (mf), exhaust velocity or specific impulse (ve), and the resulting delta-V:

Delta-V = ve * log(mi/mf)

where log is the natural-logarithm function.

 Comparison of orbital rocket engines gives the numbers for existing rocket engines. The best high-thrust engines are hydrogen-oxygen ones, and they can have exhaust velocities as 4.5 km/s. Kerosene-oxygen can do 3 km/s, as can UDMH/N2O4 and similar combinations. Solid fuel can do around 2.5 km/s.

This means a mass ratio of 20 - 30 for going into low Earth orbit.


A smaller Earth-composition planet would be easier to travel from, and a larger Earth-composition one harder. From http://astrozeng.com I find these numbers (rock, 30% Fe):
[table="class: grid"]
[tr]
[td]Mass[/td]
[td]Radius[/td]
[td]Surf Grav[/td]
[td]LO Velocity[/td]
[/tr]
[tr]
[td]1.00[/td]
[td]1.005[/td]
[td]0.99[/td]
[td]7.71[/td]
[/tr]
[tr]
[td]2.22[/td]
[td]1.26[/td]
[td]1.41[/td]
[td]10.33[/td]
[/tr]
[tr]
[td]4.29[/td]
[td]1.50[/td]
[td]1.92[/td]
[td]13.19[/td]
[/tr]
[tr]
[td]8.00[/td]
[td]1.75[/td]
[td]2.62[/td]
[td]16.69[/td]
[/tr]
[tr]
[td]13.93[/td]
[td]2.02[/td]
[td]3.42[/td]
[td]20.54[/td]
[/tr]
[/table]
So it would be hard to depart from a super-Earth planet.

The escape velocity is sqrt(2) or 1.414 times the orbit velocity. So one needs 3.22 km/s to escape from low Earth orbit, while for super-Earths, it would also be difficult.


Proxima Centauri b's minimum mass is 1.27 +0.18 -0.17 Earth masses, the minimum figure being reached only for an edge-on orbit. For an orbit tilted with inclination i, one must divide it by sin(i). An inclination of 60d would make it 1.47, 45d 1.80, and 30d 2.54. So that planet is more difficult to depart from than the Earth, but not impossible.

 

[lpetrich]

Now for escape into interstellar space. The Earth's orbit velocity is about 30 km/s, giving a Solar-System escape velocity of 42 km/s. The best case for departing is to depart in the direction of the Earth's motion around the Sun, and one needs only 12 km/s. If one can get the necessary delta-V for departing in 30 minutes or less, then one needs only 8.5 km/s. This is courtesy of the "Oberth effect", a consequence of conservation of energy. But that is still large, and every spacecraft that has gone out into the outer Solar System has gotten a gravity assist from other planets, like Jupiter.

Proxima Centauri seems much easier to depart from, since its mass is only 0.123 times the Sun's, about 1/8. But Proxima Centauri b is about 0.0485 AU from the star, about 1/21. This gives an orbital velocity of 47 km/s and an escape boost of 20 km/s.

Some red dwarfs are known to have multiple planets, like TRAPPIST-1. These arguments also apply to interplanetary travel in such systems, so it would be hard to travel from planet to planet in the TRAPPIST-1 system.

From the SciAm article,

Nevertheless, this global perspective should make us feel fortunate that we live in the habitable zone of a rare star as bright as the sun. Not only that we have liquid water and a comfortable climate to maintain a good quality of life, but that we also inhabit a platform from which we can escape at ease into interstellar space. We should take advantage of this fortune to find real estate on extrasolar planets in anticipation of a future time when life on our own planet will become impossible.

More massive stars would be better for that, but they don't last as long on the Main Sequence. But less massive stars like Proxima Centauri and TRAPPIST-1 will outlast the Sun by a large factor.

I wouldn't call the Sun a rare sort of star, either. Less common, certainly, but not nearly as rare as (say) OB stars.