J. Brit. Astron. Assoc., 109, 5, 1999, p.299

Letters

(Note: The Association is not responsible for individual opinions expressed in articles, reviews, letters or reports of any kind.)


'Measurement and analysis of radio emission from the quiet Sun'

From Dr Geoffrey H. Grayer

Some confusion exists in this paper by J. C. D. Marsh (JBAA 108(6), 317–319 (1998)) regarding voltage and power gain, which leads to an (admittedly small) error in the flux calculation.

Gain is best denoted in terms of power, for this is a conserved quantity; voltage gain on the other hand depends on the impedances of the input and output circuits. As an example, consider an audio output stage using a valve (vacuum tube); this might be considered obsolete, but it is a good example. The voltage gain measured on the primary of the output transformer (some 10,000 ohms impedance, to match that of the tube) will be very different from that measured across the loudspeaker on the secondary of the transformer (say 8 or 16 ohms impedance); the power available at the two points is however essentially the same.

Power is related to voltage by W(watts)=V^2/R, with V in volts and R in ohms. The decibel (dB) is a logarithmic unit of power ratio. The ratio G of two values of power W1 and W2 is defined as: G(dB)=10 log10 (W2/W1). In terms of V this becomes G(dB)=20 log10 (V2/V1). The resistance, being constant, drops out.

When J. C. D. Marsh quotes his 'gain' as 1.8×10^6 he does not qualify it, but he is quoting voltage gain, since the value given of 125dB corresponds to the second of the above formulae for R. The error occurs in the correction for the unmeasured polarisation component normal to that of his (linearly polarised) yagi. Under the heading 'Calculations' he states 'Allowing for the single polarisation of the aerial, Vin should be doubled...' This other polarisation would not double the voltage at the input (as he states), but would rather double the power input. The voltage would therefore only increase by (2 = 1.71. Incidentally, this correction implicitly assumes that the solar emission at this wavelength is randomly polarised; this is indeed the case for the bremmstrahlung radiation described, which is characteristic of the quiet Sun, but it should be noted that this is not true of the active component at this wavelength (see e.g. K. J. H. Phillips, Guide to the Sun, CUP 1992, p.146.)

Mr Marsh also shows a dip in his signal from solar noise during a thunderstorm, and asks for suggestions to explain this. I think the explanation is rather simple in concept, if not in detail. Thunder clouds contain a huge number of ionised particles, i.e. separated charge; it is this charge which builds up the huge potentials eventually released in a lightning discharge. A thunder cell may well extend from a few hundred meters above you up to the tropopause. This plasma (a mixture of neutral and charged particles) may be compared to the ionospheric D-layer, which absorbs frequencies below about 3 MHz, only in this case there is much greater charge, and the air is more dense giving a very short mean free path. Hence this plasma will absorb the incoming radiation, even as high as 150 MHz. Another way of looking at it is to consider the cloud as a conducting shield.

G. H. Grayer
3 Southend, Brightwalton, Newbury, Berks. RG20 7BE. [g.h.grayer@rl.ac.uk]


Unusual object 1998 DK36

From Mr Robert H. McNaught

Jean Meeus JBAA , 109(3), June 1999, p.156) is correct in noting both that this object was observed on only two nights and that a unique orbit cannot be derived from only two observations. However it is not the case with 1998 DK36 that only two observations were made. It was observed twice on both nights, thus providing knowledge of its angular velocity. It is possible to derive a limited set of orbits that fit these four positions to within the uncertainty of the observations. Most of these solutions indicate an orbit that lies wholely within the Earth's orbit, but as Gareth Williams notes, some Earth-crossing solutions do exist.

Regarding the derivation of orbits from two positions, this has been a standard practice for many years, but as Meeus notes, there is no unique solution. It is, however, often the only information one has to follow up a discovery. Simple extrapolation of these positions has no physical basis, (imagine observations near a turning point) and Meeus notes that an orbit with zero eccentricity could be used. This would be adequate to follow up a newly discovered main-belt object, although it is more often the case that such an object will be discovered close to its perihelion. The method of Väisälä incorporates the assumption of observation at perihelion into his method. Ted Bowell developed a variation of this technique.

For near-earth objects (NEOs), the assumption of the object being at perihelion is unreasonable, requiring the development of a more suitable technique. At the UK Schmidt Telescope, the AANEAS and Spaceguard Australia search projects from 1990–1996 produced many discoveries of fast-moving objects (FMOs). Most of these FMO trails were ambiguous as to the direction, and there was no information on the acceleration of the object. The technique I used was to assume the first observation was at some arbitrary distance and moving at some arbitrary angle to the line of sight. This defined a vector that had to intersect the line of sight of the second observation. This defines unique position and velocity vectors from which a unique orbit is derived. By repeating this process for a range of assumed topocentric distances and angles to the line of sight, a range of orbits is derived. Hyperbolic orbits were ignored, and the rest were given a (rough) probability depending on the orbital elements derived; a main-belt solution given high probability and an NEO solution, a probability based on empirical formulae for inclination, semi-major axis, absolute magnitude etc. If there was any main-belt solution, no follow-up was made, and if an NEO solution was possible, the direction of motion was taken as the one that gave the highest probability orbit. The software was called PANGLOSS and attempted to derive the best of all possible orbits; a belief as unfounded as that of Voltaire's Dr Pangloss who believed we lived in the best of all possible worlds!

The technique proved very useful however, as occasionally a discovery could not be followed up for several days. For an object moving at over a degree of arc per day, this is very significant. Using the range of orbits and their associated probability, an ephemeris probability map could be derived to optimise the search effort. Using this technique, we did not lose any objects that we searched for this way, although occasionally we had to switch to the other direction when the high probability region of one direction was exhausted. It also proved its value in finding additional images of FMOs on archival plates.

Brian Marsden proposed a technique of assuming a third position at the proposed observation time. This derived orbit could then be assigned a probability as above, and from a range of third positions, a probability map created. Depending on the orbit software used, this could potentially result in a failure due to an initial arc of only a few minutes. The PANGLOSS software has no limitation with a short time scale, but over longer time scales (a day or so), the process must be iterated due to curvature of the orbit.

There is thus great utility in orbits derived from only two positions, but like the Irishman who when asked how to get to Dublin, replied 'If I was you I wouldn't start from here', the most sensible course of action is never to gather such limited data in the first place.

Robert H. McNaught
Siding Spring Observatory, Coonabarabran, NSW 2357, Australia. [rmn@aaocbn.aao.gov.au]


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