A radio calibrator seen through the air

Adapted from IOAA 2015 (Magelang), theory problem S6. We have restated it in our own words and kept the original data. The solution was last checked on 20 October 2026.

Before each observation a radio telescope is pointed at a calibration source whose flux density above the atmosphere is known to be 21.86 Jy. On one day the telescope measured only 14.27 Jy from it, with the source at an altitude of 35°. Estimate the optical depth of the atmosphere at the zenith, ${\tau }_z$. A jansky (Jy) is a unit of flux density used in radio astronomy.

AnswerThe optical depth at the zenith was about 0.24.