# scattering angle derivations

1. scattering angle from sensor and solar angles

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(\theta_{0}\) | solar zenith angle | \(deg\) | solar_zenith_angle {:}
   \(\Theta_{s}\) | scattering angle | \(deg\) | scattering_angle {:}
   \(\theta_{S}\) | sensor zenith angle | \(deg\) | sensor_zenith_angle {:}
   \(\varphi_{r}\) | relative azimuth angle | \(deg\) | relative_azimuth_angle {:}

   The pattern : for the dimensions can represent {time}, or no dimensions at all.

   \[\Theta_{s} = \frac{180}{\pi}\arccos\left(-\cos\left(\frac{\pi}{180}\theta_{0}\right)\cos\left(\frac{\pi}{180}\theta_{S}\right) - \sin\left(\frac{\pi}{180}\theta_{0}\right)\sin\left(\frac{\pi}{180}\theta_{S}\right)\cos\left(\frac{\pi}{180}\varphi_{r}\right)\right)\]