With the development of the basics of technology and the improvement of both methods of information transmission, a third class of technologies was formed [2—3; 5—6] capable of sending signals over long distances with minimal losses and at a speed equal in magnitude to the speed of propagation of an electromagnetic field in a vacuum – fiber optic networks. At the same time, they had all the advantages of conductor technology regarding the possibility of increasing volumes at maximum speed, however, in this case, the speed, even taking into account its extreme indicators with the achievement of the maximum vacuum level, was insufficient with the growing needs of current technological networks. An increase in the volume of data transmission leads to an increase in the scale of installations, which does not meet the requirements of the current time, based on this, there is a need for research and development of technologies with more advanced capabilities.

With the development of quantum theory, the attention of researchers began to be attracted by the effect of quantum tunneling, now used in tunnel diodes, computer networks, tunnel microscope [4; 7], superconducting systems and many other technologies. The study theoretically did not consider new effects associated with the accelerated transfer of information between objects, therefore, the theoretical justification of the tunneling effect in the transmission of information is relevant.

Materials and methods of research

The research materials of the external probes, their parameters, and information about the studies carried out were used for the study. The methods used in the research were the method of analysis, classification, and theoretical modeling using partial differential equations.

Equations and mathematics

Initially, it is important to determine the class of tasks where the use of tunneling technology may be in demand. Due to the fact that the maximum transmission speed when using fiber—optic systems or oscillatory circuits with a transmitting electromagnetic field is the speed of light in the specified medium and in the maximum case, it is 299,792,458 m/s, capable of circumnavigating the planet Earth in 0.134 s – the maximum possible delay in the transmission system, it becomes obvious that the scope of application data transmission systems with high speeds are becoming cosmic in scale. Space probes are already being used by international organizations. The earliest probes are Pioneer 5, 6 (A), 7 (B), 8 (C) and others, the earliest are Helios A, Helios B, ISEE—3, Ulysses, Wind, SOHO, ACE and modern ones are the second exit of Ulysses, Genesis [3—7; 11—12; 14].

Also, among the probes there are Stereo A operating to date since 2006, DSCOVR since 2015, Parker Solar Probe until December 2025, ESA from 2020, ISRO from 2023 and others. Also, each of the probes is divided into different categories – Solar probes aimed at exploring the Sun and located at a comparative distance from Earth up to 1 astronomical unit, which also include Mercury probes – Mariner 10, MESSENGER, BeliKolombo and others and Venus probes – Venus 1, Mariner 1, Sputnik 19, Sputnik 2, Cosmos 27, Zone 1, Venus 8, Mariner 10, Pioneer Venus, Venus 12, Venus 11, Magellan, Galileo, Cassini and others [2—5; 7—14]. But there are also probes directed in the opposite direction, which include the Mars probes – Mars 1B No. 1, Mariner 3, Zone 2, Mars 1969A, Cosmos 419, PrOP-M, Mars 5, Mars 6, Mars 7, Phobos 1 and 2, the 2001 Martian Odyssey, Nozomi, Mars Express not counting a large number of rovers – Mars A «Spirit», Mars B «Opportunity», along with others – Rosetta, Phoenix, Dawn, Marco A «WALL—I», Marco B «Eve», Tianwen-1, Zhuron, Psyche, Hera, Europa Clipper and others [13—14; 15].