Joachim Köppen DF3GJ ... Kiel Mar 2023

### Some brief explanations

Measurements of the radio noise of the Sun, Moon, the ground, and the empty sky are used to determine three estimates for the system temperature (or noise figure) of a radio telescope. It makes use that the Sun, Moon, and the ground emit thermal radiation, which corresponds to their physical temperatures. The ground can well be assumed to have the ambient temperature, which is close to 290 K. At frequencies above about 15 GHz, the Sun's radio emission is independent of its acitivity, and the temperature can be taken as that for the quiet Sun (Benz, 2009). The Moon's average surface temperature is 213 K, but varies during one month within a range which increases with frequency, from ±10 K at 10 GHz to ±100 K at 300 GHz (Foster 1969; see also here). Thus, the three bodies can be considered to have known temperatures, and to serve as calibrating sources.

• Enter the frequency, the HPBW of the antenna and the (preferably) measured value of the atmospheric attenuation towards the zenith.
• Enter your measured values in the light green fields. Note that the measurements of Sun and Moon comprise the value on the source, the comparison value of the empty sky nearby at the same elevation as the source, and the elevation. For the ground measurement, point the antenna to the ground, to a wall or a house, or a dense group of trees, all large enough to fill completely the antenna beam, and take a comparison with the empty sky at some elevation.
• Select the Moon noise temperature appropriate for the current phase of the Moon (see here)
• The plot shows as a function of the system noise figure curves of the expected Y-values for the Sun, Moon, and ground, together with the measured values (as dots). The vertical magenta line marks the value deduced from the Sun. The numerical values of noise figure and system temperature are also displayed.
• Interpretation: Ideally, all three estimate should give the same system temperature. Otherwise, the measured data are not consistent with each other. If for instance, the estimate from the Moon (blue dot) is found to the left of the magenta line, the measured Y-value for the Moon was overestimated. As the Moon is much fainter than the Sun, noise has a greater influence on its measurement.
• The radiation pattern of the antenna is assumed to be from an evenly illuminated circular dish. Sun and Moon are represented by evenly bright discs.

Antenna:
Frequency [GHz]
HPBW [°]

Measurements:

Sun
Moon
Ground

Zenith attenuation [dB]

at Elevation [°]
Line-of-sight attenuation

Moon noise temp.
xrange
yrange

Mouse position

Noise figures and System temperatures
from:
Sun
Moon
Ground

Notes on the examples:
• SRT is the Small Radio Telescope, devised by the MIT Haystack Observatory, for spectroscopy at the 1420 MHz line of neutral hydrogen. Its diameter is 2.3m, and the system temperature about 250 K. With a HPBW of 6.5° the Moon is barely detectable.
• The ESA-Dresden radio telescope uses conventional satellite TV equipment: a 1.2 m offset dish and a normal LNB, with a system temperature of about 170 K and HPBW of 1.5°. It is used for solar and lunar observations.
• The 24 GHz antenna at DL0SHF has a diameter of 3.7 m. After improvements of the feed, its system temperature has been brought to about 250 K (2021).
• The 47 GHz antennas of CT1BYM (measured data from PA0EHG's 47 GHz Performance Table)