This article is the first of a two-part series by physicist Eric Hedin and is reprinted with permission from Evolution News. Next is part 2.
Reports of newly discovered exoplanets, especially those that share even the slightest overlap in parameters similar to Earth, are a staple of science news. While these discoveries are exciting from an astronomical point of view, attention often relies on speculation that these planets might one day become homes to humans. The idea of extraterrestrial life operating on the surfaces of planets that are not hellishly hot, or trapped in the frozen outer reaches of distant star systems, also tends to pique interest in such reports.
For example, in a recent article Science News The report “Discovery of a Habitable Earth-Size Exoplanet around Gliese 12” describes the discovery of a planet orbiting an M-type dwarf star about 40 light-years away from Earth. The planet, named Gliese 12b, is so close to its host star that it takes just 12.76 days to complete one orbit. For planets orbiting such typical dwarf stars, there are several obstacles to habitability, including tidal locking.
But the tidal forces that stars exert on planets orbiting this close are enormous: a planet orbiting an M dwarf star close enough that liquid water could exist on its surface would be tidally locked, meaning one of its hemispheres would always point towards the star (just as one hemisphere of the Moon always points towards the Earth).
Fascinating Hope
What about the enticing hope of interstellar travel for humanity in the future? Ocean How much space would be needed to build an Earth outpost on one of these exoplanets? Astronomers have determined a number of possible stellar destinations in our “close” galactic neighborhood. There are roughly 2,000 stars within 50 Lyles of Earth, while the Milky Way has about 200 billion stars (one millionth of a percent are within 50 Lyles of Earth). By applying known laws of physics, we can place certain limits on the feasibility of interstellar space travel (either for humans or putative aliens).
Let's use special relativity to think about how much energy is needed in raw form to accelerate a spacecraft to the speed required to make the journey of 40 Lyre (say, Gliese 12b) in 5 years, as measured by the astronauts on board. First, we need to find the velocity this spacecraft must achieve relative to Earth to generate the appropriate time dilation needed to arrive in 5 years on the astronauts' clocks. Using Einstein's formula for time dilation and a little algebra, we find the required velocity to be 0.99c, where c=300,000 km/sec is the speed of light in a vacuum.
Because time flows differently in the reference frame of Earth and in the reference frame of a spacecraft moving at 0.99c, a journey that takes 5 years for an astronaut turns out to take 40.3 years according to an observer on Earth. This is a slight inconvenience, but probably manageable. However, if you calculate the energy required to accelerate a modest-sized spacecraft equipped with all the gear a team of astronauts would need for a multi-year expedition to explore an unknown destination, the answer turns out to be mind-boggling.
Using Einstein's formula for kinetic energy from Special Relativity, and assuming the mass of the spacecraft is equivalent to that of a fully loaded 747 airplane (m=400,000 kg), we find that the energy required to accelerate the spacecraft to a cruising speed of 0.99c is 70 quadrillion kWh. If we assume that the astronauts wish to stop in a distant star system, this amount would need to be doubled to account for deceleration for the spacecraft to fly one way from Earth to the distant star.
So how much energy is 1.4 trillion kWh? Believe it or not, this is total United States energy consumption in 2022. This means consumption of electricity, oil, natural gas and all other forms of energy. all A one-year stay in the United States would be 4,800 times too small to get a reasonably sized spacecraft to a relatively nearby star in a reasonable amount of time. It is no exaggeration to say that with our current knowledge of physics and technology, interstellar space travel is simply not possible.
This is part two of a two-part series: “But why shouldn't we dream?”
