Aiming at the Radio Moon
Joachim Köppen ... Kiel, Aug. 2022

Some brief explanations

This tool displays the distribution of radio brightness temperature on the face of the Moon for any frequency, time, and location of the observer. The radio image shows the Moon as oriented with respect to the local horizon (parallel to the X-axis) and the vertical (Y-axis). The apparent orientation of the Moon changes with its position in the sky during its daily journey across the sky, with its position relative to the Sun during a month, and also with the changing position of the Sun during its yearly round.

These images are computed with the simple model for the heat transfer in the lunar soil.
In brief: The lunar soil is heated by the solar radiation. This heats up the top layer of a few mm thickness. Since the soil is not a solid rock, but consists of a loose mixture of dust, sand, and small pieces of rock (called 'regolith') due to the break up of the material by the constant impacts of meteroites, there is very little thermal contact between individual pieces. Hence the thermal conductivity of this material is very low, and the transport of heat from the top layer to the layers below is very slow. Thus, while the top layer can follow the solar illumination rather quickly and with a large temperature variation, the temperature of the deeper layers not only lags behind the top layers by a couple of days but also varies much less strongly.

The thermal radio emission comes mainly from a depth comparable with the wavelength. At a frequency of 1000 GHz (wavelength 0.3 mm) we see the hot top-most layer when under full sunshine and very cool at 'local night', but at 1 GHz (30 cm) the radio waves reach deep enough to let us observe a nearly constant temperature.

Since the Moon's face is illuminated after New Moon first on the western limb, then at the central face, and finally on the eastern limb, the region of high temperature moves across the Moon's face from West to East. At 1000 GHz the Moon looks very similar as in the optical, but at lower frequencies the delay in the heat-up makes the 'radio full moon' come later.

The thicker part of the white line through the centre points to the Sun. Note that at New and Full Moon this line will turn around rather rapidly.

Technical detail: The variation of the vertical temperature profile was computed during an entire lunation for a number of lunar latitudes. From these profiles the radio brightness temperature for any frequency is computed with the assumption tanδ = 0.0143. For any pixel of the Moon's face the brightness temperature is computed from its latitude and the phase corresponding to its longitude. The darkening of the limb is due to the inclination-dependent reflection coefficient for the smooth surface between the soil (ε = 1.5) and vacuum (ε = 1).

Hit the Enter key after changing the value in one of the input fields, to show the new image.

The data can be shown as a false colour image. The colour bar at right codes the temperature between minimum (black/violet) and maximum values (red), which normally are adjusted automatically. For the image with a fixed range and the contour plot the user may set appropriate values.

Furthermore, one may inspect the image without smoothing by the antenna beam - which corresponds to an image from an optical telescope - or smoothed by the antenna beam whose HPBW needs to be specified, which gives a rendering of the moon if one would take an image using the radio antenna.

Please note that the HPBW usually should be larger than the pixel size in the image. Otherwise the program will take a minimum value for the HPBW in order to prevent computational problems. This is indicated by a light yellow background of the textfield.

Temperature in beam: gives the value when a Gaussian antenna beam (with specified HPBW) is placed at a position offset in X and Y from the face centre. A white circle shows the beam's half-power level.

Fill factor in antenna beam: is the fraction of the antenna beam filled with the Moon. A narrow beam is completely filled with the lunar radiation, and the antenna temperature measures the true temperature of the lunar surface. But in a wide beam the Moon fills only a small fraction, which gives results in a low antenna temperature.

Positions on the maps are given in arcmin.

Note that the left side of the image is the Eastern side of the Moon, when it culminates in the South. But while the Moon rises in the East, a position just 'left' of the center is in the lower left corner of the face; similarly, the same position on a setting Moon in the West corresponds to its upper left corner!

Please be aware that the model data displayed in LunarTemps are not exactly the same as in this tool. This is because some computational economies had to be taken in the interest of a faster display.
You might also notice that the images with smoothing by the antenna beam appear to be more squarish than circular in the outer parts. This is because the smoothing does not extend beyond the edges of the image ... again for the benefit of a better speed, this was left out, as there is no lunar signal.

Station: longitude [W]  latitude [N] 
Date [YMD]  day of year               
Time [UT]        
Ra  Dec 
Az  El 
Ang.Diameter [deg] 
Ra  Dec 
Az  El 
Phase [0 = Full Moon] 
Angle to Sun [clockwise from top] 
Distance [km] 
Ang.Diameter [deg] 
Frequency [GHz]
No. of bins

Antenna beam HPBW [°]

contour start, step [K]
min/max temp. [K]

Average temperature
Temperature at disc centre

Beam offsets in X, Y [°]
Temperature in beam
Fill factor in antenna beam

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