2018-04-23 14:54:30 UTC
A civilization in the habitable zone of a dwarf star like Proxima
Centauri might find it hard to get into interstellar space with
By Abraham Loeb on April 16, 2018
Escape from Proxima b
Artist's impression of the exoplanet Proxima Centauri b. Credit: ESO
Almost all space missions launched so far by our civilization have been
based on chemical propulsion. The fundamental limitation here is easy to
understand: a rocket is pushed forward by ejecting burnt fuel gases
backwards through its exhaust. The characteristic composition and
temperature of the burnt fuel set the exhaust speed to a typical value
of a few kilometers per second. Momentum conservation implies that the
terminal speed of the rocket is given by this exhaust speed times the
natural logarithm of the ratio between the initial and final mass of the
To exceed the exhaust speed by some large factor requires an initial
fuel mass that exceeds the final payload mass by the exponential of this
factor. Since the required fuel mass grows exponentially with terminal
speed, it is not practical for chemical rockets to exceed a terminal
speed that is more than an order of magnitude larger than the exhaust
speed, namely a few tens of kilometers per second. Indeed, this has been
the speed limit of all spacecraft launched so far by NASA or other space
By a fortunate coincidence, the escape speed from the surface of the
Earth, 11 kilometers per second, and the escape speed from the location
of the Earth around the sun, 42 kilometers per second, are close to the
speed limit attainable by chemical propulsion. This miracle allowed our
civilization to design missions, such as Voyager 1 and 2 or New
Horizons, that could escape from the solar system into interstellar
space. But is this fortune shared by other civilizations on habitable
planets outside the solar system?
Life “as we know it” requires liquid water, which can exist on planets
with a surface temperature and a mass similar to Earth. Surface heating
is needed to avoid freezing of water into ice and an Earth-like gravity
is needed to retain the planet’s atmosphere, which is also essential,
since ice turns directly into gas in the absence of an external
atmospheric pressure. Just next door to Mars, which has a tenth of an
Earth mass and lost most its atmosphere long ago.
Since the surface temperature of a warm planet is dictated by the flux
of stellar irradiation, the distance of the habitable zone around any
arbitrary star scales roughly as the square root of the star’s
luminosity. For low mass stars, the stellar luminosity scales roughly as
the stellar mass to the third power. The escape speed scales as the
square root of the stellar mass over the distance from the star.
Taken together, these considerations imply that the escape speed from
the habitable zone of a star scales inversely with stellar mass to the
power of one quarter. Paradoxically, the gravitational potential well is
deeper in the habitable zone around lower mass stars. A civilization
born near a dwarf star would need to launch rockets at a higher speed
than we do in order to escape the gravitational pull of its star, even
though the star is less massive than the Sun.
As it turns out, the lowest mass stars happen to be the most abundant of
them all. It is therefore not surprising that the nearest star to the
sun, Proxima Centauri, has 12 percent of the mass of the sun. This star
also hosts a planet, Proxima b, in its habitable zone at a distance that
is 20 times smaller than the Earth-Sun separation. The escape speed from
the location of Proxima b to interstellar space is about 65 kilometers
per second. Launching a rocket from rest at that location requires the
fuel-to-payload weight ratio to be larger than a few billions in order
for the rocket to escape the gravitational pull of Proxima Centauri.
In other words, freeing one gram’s worth of technological equipment from
the position of Proxima b to interstellar space requires a chemical fuel
tank that weighs millions of kilograms, similar to that used for liftoff
of the space shuttle. Increasing the final payload weight to a kilogram,
the scale of our smallest CubeSat, requires a thousand times more fuel
than carried by the space shuttle.
This is bad news for technological civilizations in the habitable zone
of dwarf stars.
Their space missions would barely be capable of escaping into
interstellar space using chemical propulsion alone. Of course, the
extraterrestrials (E.T.s) can take advantage, as we do, of gravitational
assists by optimally designing the spacecraft trajectory around their
host star and surrounding planets.
In particular, launching a rocket in the direction of motion of the
planet would reduce the propulsion boost needed for interstellar escape
down to the practical range of 30 kilometers per second. The E.T.s could
also employ more advanced propulsion technologies, such as light sails
or nuclear engines.
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.
This unfortunate fate will inevitably confront us in less than a billion
years, when the sun will heat up enough to boil all water off the face
of the Earth. With proper planning we could relocate to a new home by
then. Some of the most desirable destinations would be systems of
multiple planets around low mass stars, such as the nearby dwarf star
TRAPPIST-1 which weighs 9 percent of a solar mass and hosts seven
Once we get to the habitable zone of TRAPPIST-1, however, there would be
no rush to escape. Such stars burn hydrogen so slowly that they could
keep us warm for ten trillion years, about a thousand times longer than
the lifetime of the sun.
The views expressed are those of the author(s) and are not necessarily
those of Scientific American.
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ABOUT THE AUTHOR(S)
Abraham Loeb is chair of the astronomy department at Harvard University,
founding director of Harvard's Black Hole Initiative and director of the
Institute for Theory and Computation at the Harvard-Smithsonian Center
for Astrophysics. He also chairs the advisory board for the Breakthrough
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