(11)

Where T is the temperature in Kelvin of the planet, Lsun is the luminosity of that planet’s sun, a is the albedo of the planet, d is the distance in meters of the planet from its sun, and σ is the Stefan-Boltzman constant. This equation does not account for the greenhouse effect, however, due to the fact that the greenhouse effect serves mainly to cause planets to become hotter, it does not need to be included while taking this conservative measure. The lowest luminosity recorded of a star with a system within 10 parsecs is Teegarden’s Star with 0.00073 L _☉, or 2.79444 x 10^23 Watts¹². The highest albedo ever recorded in an exoplanet was 0.8 in LTT 9779 b¹³. Yet even given these extremes, a planet must be at least 0.235835 astronomical units away from its star in order to be cold enough to allow nitrogen to freeze on its surface.

Within ten parsecs of this solar system, there exist about 500 stars, around 60 of which have planetary systems¹⁴. 103 exo-planets are shared between these 60 stars¹⁵. 31 of these are over 0.235835 AU away from their stars. A star with 0.01 L _☉ luminosity will be hot enough to ensure nitrogen does not freeze to a distance of 0.87286 AU. 19 of the 31 planets are either too distant from their star or have a star with too little luminosity to be within this range and therefore may possibly be in the freezing temperature of nitrogen. These 19 planets are cataloged and their calculated temperatures are listed in Table 1.