Aliens around Tau Ceti

There are several planets other than Earth that are thought to be able to sustain life of the form we have on Earth, one of the basic requirements for which is to have liquid water on its surface.

One of the Sun-like stars is Tau Ceti. Its radius is \(79 \%\) of Sun's radius, and its surface temperature is \(T = \SI{5344}{\kelvin}\). What is the width of the spherical shell around Tau Ceti \((\)in \(\si{\kilo\meter})\) in which planets can have liquid water?

Details and Assumptions:

  • The radius of the Sun is \(\SI{695500}{\kilo\meter}.\)
  • Planets and stars can be approximated to behave like black bodies.
  • For the sake of simplicity, assume the atmospheric pressure on the surface of potentially inhabitable planets is the same as on Earth.
  • Only one side of a planet is exposed to Tau Ceti's radiation.

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