Limitations of Chemical Propulsion for Interstellar Escape from Habitable Zones Around Low-mass Stars

Abstract

On Earth, current and past space missions have been reliant on chemical rockets (Crawford 1990). A notable issue with chemical rockets is that the mass of the fuel required (for a given payload) scales exponentially with the final speed that one wishes to achieve. Fortunately, this issue is not particularly important for humanity because the escape velocities from the Earth and the Solar system are roughly within an order of magnitude of the velocities achievable by chemical rockets. However, the use of chemical rockets for undertaking interstellar travel is likely to become more problematic for habitable planets around low-mass stars, for reasons outlined below. In this work, we carry out calculations to quantify, and further develop, the general points raised in Loeb (2018).The rocket equation developed by Tsiolkovsky (1903) states thatwhere m 0 and m f are the initial (payload and fuel) and final (only payload) masses respectively, v ex is the exhaust velocity and ∆v is the maximum velocity change that can be achieved. For state-of-the-art rockets that use liquid oxygen-hydrogen fuel, v ex = g ⊕ I sp where g ⊕ = 9.8 m/s 2 is the Earth's surface gravity and I sp ∼ 450 s is the specific impulse. If we wish to exit the planetary system, ∆v v esc is necessary, with the escape speed v esc defined asfor a given stellar mass (M ) and semi-major axis of the planet (a). We have not considered the conditions for escaping the planet's gravity, which has been investigated in Hippke (2018). It can, however, be verified that the corresponding velocity for escaping the planetary surface is likely to be lower than v esc for M M if we consider rocky planets in the habitable zones of their host stars. In our discussion below, we will adopt the criterion ∆v > (1 − 1/ √ 2)v esc instead, where the additional factor has been introduced to account for the boost from gravitational assists. This reduction in ∆v is achievable by launching the rocket such that it will be parallel to the planet's motion (Loeb 2018). In this scenario, the planet's speed in a circular orbit is v c = GM /a and therefore ∆v = v esc − v c is given by ∆vAlthough v esc depends on two independent parameters, we can reduce this to just one parameter by demanding that the technological species inhabit an "Earth-analog", i.e. a habitable planet that receives the same insolation as the Earth so as to possess surface liquid water, which is necessary for the chemistry of "life as we know it". In this event, we have a ∝ L 1/2 with L denoting the stellar luminosity. Thus, using the above data in (1), we find that the lower bound on m 0 /m f is given byand we can make use of the mass-luminosity relation from Loeb et al. (2016) to express the right-hand-side purely as a function of M . The final result has been plotted in Fig. 1, and it is evident that m 0 /m f becomes very high for

Electric sails are potentially more effective than light sails near most stars

“…A similar hypothesis was advanced by Ref. [27] while studying the feasibility of chemical propulsion around low-mass stars. There are several reasons as to why d could constitute an optimal choice.…”

Role of stellar physics in regulating the critical steps for life

“…Our discussion also ignored the possible transfer of life between stars. Such transfer may involve lithopanspermia (Arrhenius 1908; Burchell 2004; Wickramasinghe 2010), directed panspermia (Crick and Orgel 1973; Mautner 1997) or interstellar travel and habitation by technologically advanced species (Shklovskii and Sagan 1966; Crawford 1990; Lubin 2016; Lingam 2016b; Lingam and Loeb 2018c). If such transfer events are common enough, which might be the case in some environments (Belbruno et al 2012; Di Stefano and Ray 2016; Lingam and Loeb 2017a; Chen et al 2018; Ginsburg et al 2018), they could blur the quantitative conclusions of this paper because of diffusion processes and Galactic differential rotation (Newman and Sagan 1981; Lingam 2016a).…”

Relative Likelihood of Success in the Search for Primitive versus Intelligent Extraterrestrial Life

“…7 https://www.cfa.harvard.edu/events/2013/postkepler/Exoplanets_in_the_Post_Kepler_Era/Program_files/Seager.pdf 8 It should be noted that electromagnetic signals may also be detectable due to the leakage radiation emitted as a consequence of powering light sails (Guillochon and Loeb, 2015;Benford and Benford, 2016;Lingam and Loeb, 2018b) even at extragalactic distances (Lingam and Loeb, 2017b).…”