Observations of the Moon

Joachim Köppen Strasbourg 2011

• Basics
• Observational Procedures
• Analysis and Interpretation
• More about our results
• Lunar Challenge
• Results from 2011

The Moon is a difficult but very interesting object: It is a rather faint source, usually 0.5 dB above the level of the empty sky, which is comparable to the normal fluctuations of the background noise. Its emission is the thermal radiation from its surface. Since the surface is heated by the solar radiation, the temperature depends on the lunar phase. The fascinating thing is that the average temperature is not highest at Full Moon, when all the surface is lit, but several days later. This was discovered in the 1950s and indicated that the surface was not solid rock, but covered with a layer of dust, which takes some time to heat up under sunlight. This finding caused quite some concern for the program to land men on the Moon, as it was not clear how thick this layer was, and whether it would be able to support a landing vehicle ... These temperature variations are only about 10 percent, which presents quite a challenge in view of the faint signal and the difficulties to obtain sufficiently good quality observational material. But what would we do without challenges?

Observational procedure

Important notes:

• Because the positioning system of this telescope has only a limited accuracy and stability, good observations require the your presence during the observing run, because you have to manually optimize the pointing of the antenna to your source.
• During its monthly cycle around the Earth, the Moon is visible only at certain times of the day, which also change ... Sometimes it is visible only at rather inconvenient times in the night, and during the day, it may be above the horizon, but hidden in the bright sky ... It is necessary to plan well the times for observation, by consulting prediction software, such as this tool.
• Our experience so far shows that the Moon is quite visible even through fog and clouds. Even if there was no hint of moonlight in the sky, we successfully found and observed the Moon repeatedly. It seems that only thick rain clouds are opaque and bright enough to prevent lunar radio observations. So give it a try, but whatever you find, please record it (and the sky situation) in the Observatory Log!

After starting up the system, described here, we recommend to follow this sequence:

• from now on: whatever you do, don't forget to keep the Observatory log
• click on goto Calibrator and Start, so that the observation run begins with a flux calibration, and all data are recorded in a file
• Stay at the calibrator a few minutes. The tracing will show some fluctuations on a basically flat curve. After about two minutes you have acquired sufficient data points to permit you to determine a reliable average value
• The choice of the frequency and polarization is not so important, but in later observations you might want to change them from the default values
• click on the Moon now button. The current position of the Moon will be displayed in the text fields. Click on Goto to move the telescope there ...
• However, when the movement stops, you may notice the the current position does not agree with want you had wanted: The positioning system of the telescope is neither sufficiently accurate nor stable to move the antenna to the exact location. By using the direct control keys at the Yeasu controller, and watching the measurements you have to manually find the best position:
  • interrupt your measurements by clicking on Stop: this will cause the receiver to display its measurements more frequently!
  • you can use the sliders to the left to zoom in on the signal in the tracing. For the Moon, it is best to go to the strongest zoom to see better the small differences in the signal!
  • use the keys on the controller to move the antenna Up, Down, Left, or Right, perhaps with touching the keys only shortly ... until you get a maximum signal
  • but after each move, wait for a couple of measurements: after a move, the antenna wobbles a bit, and furthermore there are always fluctuations of the signal!
  • move about the source until you find the really largest signal. Sometimes, even a slight maneuver or going back a bit may bring the best position ... do not bother about the fact that the displayed position may not have changed!
  • when you find a maximum in azimuth, try in elevation to get an even better signal, then again in azimuth ...
  • be patient: after some practice, you notice that there is one position which is slightly brighter than the neighbouring positions!
  • when you are happy with the position, Resume your measurements
• now wait and watch. Wait until the signal goes down, as the Moon starts moving out of the antenna beam. This will take a few minutes.
• move the telescope several degrees to the Left (or East) and measure the background signal from the empty sky - since there is some contribution from the sky emission, the background depends on elevation: so we do the measurement without changing the elevation! Do this for also for several minutes.
• click Moon now and also Stop.
• move the telescope manually to the Right (and if necessary Up or Down), while observing the readings on the AMA receiver's LCD display. And again search for the lunar signal ... Resume and stay on that best position for some minutes ...
• ... carry out this alternation between Moon and nearby sky as often as you like ... but after a couple of these procedures, do a flux calibration!
• when you are really done with your observations, end the run by clicking Stop+Finish, and shut down the system.
• You find your recorded data in the text file at: C:/JKStuff/, named: UTyear/month/day/time.txt for example: UT1004141630.txt if I observed starting at 16:30 on April 14th 2010 (all times are given in UTC). Copy the file to your USB stick or flash drive to transfer onto your computer.

Analysis

Let's suppose that we use Microsoft Excel to do the interpretation of the data. Then we recommend to follow this sequence:

• To import your text file go to: File -> Import-> Text File -> Select your Text File -> Delimited Text file -> Delimiter is spaces -> Finish
• Each row represents a single measurement taken by the telescope at a certain time instant. The columns from left to right represent: Time, Azimuth, Elevation, Power measured in dBµV.
• We shall need only the times and the power
• To reduce the fluctuations in the data, we put in the column to the right of the powers an array of smoothed values: in each cell, say E100, you put in the average of the powers of the neigbouring times, such as: = AVERAGE(D95:D105) Make sure that the averaging region is centered on the particular row; the length of +/-5 points of this smoothing region is a compromise between smoothing out the fluctuations but not the interesting time dependence. You may use other values. Do this for all your data points. Obviously the first and the last points are not suitable for this procedure, so simply copy their values.
• make a scatter plot of the original and the smoothed powers as function of time, which would look like this: From this plot, we see that most observations show the Moon leaving the antenna lobe. Only once we had been lucky enough to catch the Moon also when it entered the lobe ...
• Next, insert a couple of rows where you can put in some cells with parameters for the background and calibrator levels, as seen below: Here I marked with yellow the cells which need my input.
• Go through your data and locate the row numbers which correspond to the midpoints of the calibration measurements. It is a good idea to mark these times, as I did above in red colour. You also note that I write these row numbers in the small table, to make life easier!
• This means, we have divided the entire data set into a number of sections for whose two endpoints we have the measured flux from the calibrator and the sky background. Since during an observing run, both the background and the calibrator measurement may change - because the LNB warms up - we must estimate for each time their current values. We shall do this by assuming that in each section, the two quantities change linearly with time.
• fill the table with guess values for background and calibrator powers
• to the right of the last column, make two new arrays, and fill them with formulae that compute for each time values for background and calibrator which are linearly interpolated from the guess values in the table. You have do to this for each section separately, accessing the corresponding guess values. As seen in the screen shot above, the formula for the background in row i is background(i) = bguess(i1) + (time(i)- time(i1))*(bguess(i2)-bguess(i1))/(time(i2)-time(i1)) where i1 and i2 are the row numbers of the start and the end of that section. The formula for the calibration values is similar. This is a tedious job, but it needs to be done, if one wants nice results!
• add the curves for these columns to your graph - as seen above.
• now adjust the guess values in the table for each section, until the background curve always comes close to your measurements of the empty sky (but not above!) and the calibration curve goes nicely through your calibrator measurements. Well done!
• Now we make another column, in which we put the relative powers relative_power(i) = (power(i)-background(i))/ (calibration(i)-background(i)) by subtracting the background and normalizing with the calibrator signal. Plotting these relative powers as a function of time, you get something similar to this: But please be aware that this is based only on a simple interpretation of the noise background. See here for proper flux calibration.
• Finally, you can plot a horizontal line into this graph, and adjust its y-value until it best matches the highest peaks that you had observed, and you get the antenna temperature of the Moon: T_ant(Moon) = 290 K * 0.085 = 24.6 K

To determine the temperature on the surface of the Moon, we also need to know the fraction with which the Moon's disk fills the antenna beam:

• We can take the antenna's HPBW from measurements of the Sun, which give about HPBW = 1.5°
• Since the Moon has an angular diameter of about 0.5°, much smaller than the antenna beam, its temperature must be correspondingly hotter than our calibrator, the Holiday Inn hotel which fills the entire antenna beam. Thus the true solar temperature is T_moon = T_ant(Moon) * (HPBW/0.5))² = 287 K
• There is fine detail: the lunar diameter varies during the month due to the ellipticity, of the Moon's orbit. The diameter of the Moon you may obtain from here.

Finally, it is worth estimating the errors on the temperature. What are the sources of error:

• the fluctuations of the noisy signal amount to about 0.15 dB
• the slow time variation of the background and the calibration may have not been properly represented by the interpolation
• we may have placed the background not accurately enough
• we may have missed in all the individual measurements the true maximum signal to some extent. This would tend to underestimate the true temperature.
• the clouds in the sky may have been not sufficiently transparent. Again, a lower temperature would be the result.
• the value of the HPBW has only a certain accuracy
• not using the true lunar diameter may also introduce some error
• the exact temperature of the calibrator ... etc
• ...

Which error is the dominant one? Can we improve our technique, and where?

More about our results

Our first successful observation, after the refocussing the the telescope, was done on 26 April 2007. We got full scans like shown below, which was taken five days before Full Moon:

The signal is only 0.5 dB over the background level, but with some practice, one can locate the moon ... The observations shown also display the flux calibrations on the Holiday Inn hotel; if we assume that it has a temperature of 300 K, the antenna temperature for the moon was 15 K; from the scan profile, one deduces an antenna HPBW of 1.9° (which is larger than measured with the much better profile obtained with the Sun - obviously an effect of the greater imporatnce of noise), and it gives a temperature averaged over the lunar surface of 211 K! A second scan taken one hour later gave the same numbers. The small wiggle just before 18:45 was the manual search about the expected position for the lunar signal. Once found, we placed the telescope a bit to the west and a bit higher, and waited for the moon to pass through the beam ... and sometimes it does so!

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However, the Moon is a very difficult customer, as Zahrah Musa found out during many nights in 2008: Not only rain clouds make it impossible to pick up the weak lunar signal, and the thermal emission from the clouds themselves can be stronger than that of the moon. Also the slightest veil of clouds can upset the signal by its emission. So when you try to locate the Moon, and find some enhancement of the signal, you may also find that this signal fades away as slowly as the Moon would do it ... since clouds also move across the sky ... but then the signal may go up again ... eventually you get really confused and frustrated.

The plot below (from Marina Lemberg's data) shows the signals during a day when sun, rain, and winds came and went in succession: The high signal at lunchtime is the transit of the Sun, but the other peaks are simply rain clouds passing over:

It is clear that against these clouds, the Moon - at about +42.5 dBµV on that day - would have little chance to be observable!

On the next day - sunny and blue skies - Marina had the chance observation of the New Moon following the Sun in its lunchtime transit:

The dark blue curve is the lunar signal multiplied by ten, for better visibility. The green curve is a smothed version of the blue curve. Both show that the Moon has an antenna temperature of about 20 K, which is - within the error bars - the same as we had observed at full moon. To further improve our techniques of observation and analysis were our next steps ...

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We thus learned that a major limitation is not due to our instrument ... it is the natural weather which we can do nothing about! The Moon remains a nice and challenging target, but you need a cloudless sky for that! ..... ... but it ain't necessarily so!!!!! The following observations were done when the Full Moon was behind a layer of fog. It was still fairly easy to distinguish the dark mare and bright highlands on its face, but I would not have bothered to bring out an optical telescope to view the Moon. However, the radio data are as good as those taken during a cloudless evening a few days earlier!

More details of our results and techniques may be found here:

• How to do Lunar drift scans (1.1 MB)
• Improved Lunar observations (200 kB)

The Lunar Challenge

How does the lunar surface temperature vary with lunar phase? The lunar surface is heated by the solar radiation and emits thermal radiation in the infrared and radio range. Already in 1949, J.H.Piddington and H.C.Minnitt (Australian Journal of Scientific Resaerch A, vol.2, p.63) showed that the radio flux from the Moon varies with the lunar phase. The temperature, averaged over the lunar face, is highest not at Full Moon, as one might have guessed, but about 4 or 5 days later. They fit the results with

This time delay revealed (long before the human lunar landings) that the surface of the Moon is composed not of solid rock, but that it is made from broken-up material, such as dust and small pebbles. Because of the smaller thermal contact between the solid particles the layers below the immediate surface heat up only slowly. This temperature variation has been shown to be detectable by conventional satellite TV receiver equipment (C.Monstein, 2001 or here).

... so, can ESA-Dresden do it?

Results from 2011

Employing this improved technique possible with the new software, Mary-Anne Fobert was able to take 106 individual measurements of the Moon, covering the entire lunar phase range. To our great surprise, meaningful measurements were obtained during nearly all weather conditions that were present this winter: clear sky, mist, fog, and overcast sky. Only during a snowfall the lunar signal could not be pickd up. A comparison of her data with Monstein's curve (in red) is shown below:

The average values correspond well with these other observations, however the scatter is still too large to detect the systematic relation with lunar phase. Some data - like the one with a very low value of 50 K - obviously come from observations where the Moon did not pass through the center of the antenna lobe. A careful look reveals that the readings taken when the Moon was observed at elevations less than 20 degrees (orange dots) are systematically higher than the ones taken at higher elevations (blue diamonds). The reason is quite simple: at lower elevation we observe through a larger airmass and hence we receive a larger amount of thermal radiation from the atmosphere than if the Moon is observed closer to the zenith (see also here). Since in our analysis we do not yet separate the elevation-dependent atmospheric noise from the constant receiver noise, as it would require numerous additional measurements, we overestimate the lunar temperatures!

An even closer look shows that the weather does not affect the measurements

Blue diamonds indicate clear skies, green squares overcast skies, fog, or mist, but all taken at elevations higher than 20 degrees. Yellow symbols refer to observations at low elevation, the circles showing clear sky conditions. It is clearly the elevation effect that dominates!

Lastly, we had become aware that our previous elevation for the flux calibration was not sufficiently low enough for the Holiday Inn building to fill the antenna beam completely. Hence, we now use point 2 degrees lower. As a consequence, the system temperatures (and hence the derived lunar temperature) now are significantly lower, as shown below:

A more reliable method of flux calibration is described here, and how to interpret the measurements. .

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last update: oct 2020 J.Köppen