Exoplanetary Exploration

Classical Mechanics Level 4

So, here you are, about to embark on an epic journey to calculate the planetary equilibrium temperature of our theoretical exoplanet, Sigma 239.

Through observations of Sigma 239, we found that it is potentially habitable in terms of temperature (as well as other features). The distance from Sigma 239 to its star is an average of 1.02 astronomical units. The star it orbits is a G-type star with a diameter of 1,425,000 kilometers and a surface temperature of 5900 K. While the atmospheric constituents of the planet are unknown at the moment, the average albedo is calculated at 38%, slightly higher than Earth's.

This is the planetary equilibrium temperature formula, it is your map:

\({ T }_{ eq }\) \({ = }\) \({ T }_{ ʘ }\) \((1-a)^{ 1/4 }\) \((\) \({ R }_{ ʘ }\) \(/\) \(2D\) \()\)\(^{ 1/2 }\)

A few things to know before you compute:

  1. " \({ T }_{ ʘ }\)" is temperature of the star expressed in Kelvins
  2. "\(a\)" is the planetary albedo expressed in percentage / decimal
  3. " \({ R }_{ ʘ }\)" is the radius of the star
  4. "\(D\)" is the distance from star to planet expressed in kilometers

Round to the nearest whole number if any intermediate calculations use decimals (except for the albedo measurement).

Express the answer by including any decimals to the thousandths place; omit the Kelvin unit.

Good Luck on your travels!


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