Background

Insects can use the sky polarization from the Sun and the Moon for their spatial orientation. A lots of researchers and mainly examinations with aquatic insects deal with this theme. It has been well known since decades that the polarized light of the sky has an important part in the orientation of certain insects. In opinion of Dacke et al. (2003) many animals are able to use the solar polarization pattern of the sky for their orientation, but the Dung Beetle (Scarabeus zambesianus Péringuey, 1901) is the first insect, who is able to use for this purpose in the moonlight million-fold less than the brightness of the solar polarization (Dacke et al., 2003). 

The polarization pattern of the sky in various sky conditions is nowadays well known thanks to the spread of full-sky imaging polar meters. The degree of polarization is maximal along a great circle of the sky being 90 degrees from the Sun, and minimal at the Sun and anti-Sun (Horváth et al., 1998). The degree of polarization also depends on the atmospheric conditions. In cloudy (Horváth et al., 2002) and foggy (Hegedűs et al., 2007a) skies, as well as under canopies (Hegedűs et al., 2007b) the degree of polarization are much smaller compared to clear skies. However the direction of polarization pattern is very robust, the typical 8-shaped pattern as well as the axis of symmetry is well recognizable.

The direction of polarization pattern is very robust, the typical 8-shaped pattern as well as the axis of symmetry is well recognizable. When the Sun is well below the horizon and the moonlights the atmosphere, then the axis of symmetry is the celestial great circle containing the Moon (Gál et al., 2001; Barta et al., 2014) inspected the transition of characteristics of sky polarization between sunlit and moonlit skies during twilight. 

Researchers, however, has been as yet concentrated primarily on insects flying in daytime or at dusk and entomologists have paid less attention to species active at night. Horváth and Varjú (2004) discovered that some insects are able to use the polarization pattern of the sky in daytime and at dusk. 

Kyba et al. (2011) found that in the bright moonlit nights in a highly polarized light bands stretching from the sky at 90 degrees to the Moon, and has recently shown that the nocturnal organisms are able to navigate it. We did not find any study, apart from our own one (Nowinszky et al., 2017) in the literature which investigate the effectiveness of light trapping in the context of gravitational potential of celestial bodies.

Our aim was to find out whether the change in the gravitational potential of celestial bodies influences the effectiveness of light trapping of the moths.

Of course, we do not know the number of species in each species from spec. indet. data. However, it is reasonable to assume that more species can be found from the caught by the light-trap in the field. And even if we take into account that the same species in the country are not in the same masses, then we can assume that the material available to us is a realistic picture of the behavior of the majority of the moth (Microlepidoptera) species in relation to the gravity of the Sun and the Moon. 

1 Results

1.1 Calculation results of the negative and positive gravitational potential of celestial bodies

The gravitational potentials of celestial bodies (Sun or Moon) is given in Figure 1. And the critical elevation depending on the gravitational potential of the celestial bodies is given in Figure 2.

If the celestial body has a gravitational potential of 500 μJ/kg and the moth’s body mass is 40 mg, the celestial body increases the flying up of moth with 500 * 10^-6 * 40 μJ = 20 mJ energy, but in case of -500 μJ/kg of gravitational potential it is reduced in the same value.

For example in the gravitational force field of Earth if the rise is h = 1 mm =10³ μm, the necessary energy is: 9.808,52 * 106 μm/s² * 10 μm * 40 mg * 10^-6 = 392,340.8 μJ = 392 mJ. Therefore, the required energy is 392 mJ ± 20 mJ.

For example, a lighter or harder effect on insect elevation means on 1 mm with ± 5 percent less or more energy. Naturally the required energy can change, but the ± 5 ratio will be the same. In the case of further elevation, this effect gradually will disappear.

1.2 Results of the light-trap catch of moths in connection with the negative and positive gravitational potential of celestial bodies

Based on our findings, we have determined that the gravitation potential of Sun and Moon change the catch all night, even when the celestial body is not above the horizon. We assume that the influence we have found is real in case of gravity. The negative sign in gravity does not mean negative numbers, but the fact that the gravity of the celestial body is suction, it reduces the gravity of the Earth it. The gravity of the Moon may reduce Earth’s gravity to a very small extent, with a millionth part, and the Sun with even much less. Surprisingly, it is a fact that the insects perceive even these small values and our results justify this fact (Nowinszky et al., 2018).

The Light-trap catch of Microlepidoptera spec. indet. in connection with the gravitational potential of Sun is given in Figure 3. The Light-trap catch of Microlepidoptera spec. indet. in connection with the gravitational potential of Moon is given in Figure 4. And the Light-trap catch of Microlepidoptera spec. indet. in connection with the gravitational potential of Sun + Moon is given in Figure 5.

Our calculations are justified by the light-trap catching results of the Microlepidoptera species.

2 Discussion

When the gravitational potential of the Sun, Moon, or Sun and Moon together is high, then the catching result of the Microlepidoptera species caught by light-traps is the highest. In contrast, in case of the highest positive gravitational potential value, the catch is the lowest. It is assumed that the cause of this fact may be to make easy or more difficult the flying up of moths.

Our results are unpublished in the literature and require explanation. 

2.1 Conclusions

Our current research draws the attention of researchers to the importance of an environmental factor not yet studied earlier. These are the gravitational potential of the Sun and Moon. When the moth flies up to height of 1 mm, the greatest positive or negative value of the gravitational potential decreases with ± 5% the energy to flying up.

3 Materials and Methods

3.1 The catching data

The light-trap network with the same Jermy-type light-traps has been operating continuously in Hungary since 1958. There were about 130 light-traps, which have been operating for six decades, have provided invaluable data for scientific researches. The studies of Hungarian researchers enriched the literature with many valuable new scientific results. 

Lepidoptera (Macro- and Microlepidoptera) is the best-processed group. Until now, however, no studies were published on the most injured moths. The reason for this is understandable that the unidentified specimens were recorded as “Microlepidoptera spec. indet.” name. Because they were not known according to by species, it was not possible for further investigations. However, if we consider that there is a huge amount of collection data, we could see possibility for this research. 

In our study, we looked for correlation between the gravitational potential of the Sun and the Moon and the sky polarization they generate, and also the effectiveness of light-trap catches of Microlepidoptera spec. indet.

The light source of the Jermy-type light-trap is a 100W normal electric bulb and the killing agent is chloroform. (Jermy, 1961). It consists of a frame, a truss, a cover, a light source, a funnel and a killing device. All the components are painted black, except for the funnel, which is white. The frame is fixed to a pile dug into the ground.  

Before putting on the appliance, they put on cotton wool pads at the bottom, which reduces the risk of injury to the collected insect material. The captured insects are often unsuitable for the species definition because the killing effect of chloroform does not prevail immediately, and in particular small insects are still often damaged.

Specialists found in the field of specialty capture species of the various insect species from the captured material and this data is registered. For our investigations, all Microlepidoptera spec. indet. data were used from 49 traps of the nationwide light trap network in 1962, 1963, 1964, 1966, 1967, 1968 and 1969. We did not have data from 1965, so we processed data for seven years. During 1,479 nights 590,139 moths were caught. However, because more light-trap worked during one night, we could work more than catching nights. Our total catching data was 21,761. 

We have calculated the relative catch values (RC) of the number of caught moths by basic data were the number of moths caught by one night. In order to compare the differing sampling data, relative catch values were calculated from the number of moths for each sampling night from spring to autumn until the trap of the year worked. The relative catch was defined as the quotient of the number of moth specimen caught during a sampling time unit (1 night) per the average catch (number of moths) within the same catching period to the same time unit. For example, when the actual catch was equal to the average moth number captured in the same catching period, the relative catch was 1 (Nowinszky, 2003).

3.2 Methods for calculating of gravitational potentials of the Sun and Moon

The astronomical data were calculated with a program based on the algorithms and routines of the VSOP87D planetary theory for Solar System ephemeris and written in C by J. Kovacs. The additional formatting of data tables and some further calculations were carried out using standard Unix and Linux math and text manipulating commands. For computing the tidal potential generated by the Sun and the Moon we used the expansion of the gravitational potential in Legendre polynomials and expressed the relevant terms as a function of horizontal coordinates of the celestial objects.

3.3 Methods for calculating of light-trap catch of Microlepidoptera species in connection with gravitational potentials of the Sun and Moon

We calculated the change in the gravitational potential of Sun and Moon depending on the height of flying up. We also calculated the critical elevation depending on the gravitational potential of the celestial bodies.

The gravitational potential values of the Sun and Moon were arranged into groups. The number of groups was determined according to Sturges’ methods (Odor and Iglói, 1987). The gravitational potential groups and groups and the corresponding catch data were arranged into groups. We depicted the values of these groups in Figures. Figures also show the confidence intervals.

Authors’ contributions

LN processed the catching data of moths as a function of the gravitational potential of celestial bodies. MK calculated the negative and positive gravitational potential values that facilitate or make heavier the fly up of insects. JP participated in the design of the study, helped in statistical analysis and correction of the manuscript. All authors read and approved the final manuscript.

Acknowledgments

We would like to thank J Kovács (ELTE Astrophysical Observatory, Szombathely) for calculating the Moon and Sun data and describing the method of investigation. 

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