Patent Publication Number: US-2023148176-A1

Title: Apparatus and methods for detecting massive particles, locating their sources and harvesting their energy.

Description:
BACKGROUND OF THE INVENTION 
     (1) Field of the Invention 
     The invention pertains to solid-state devices including vibrators, oscillators, pendulums, electric conductors and their usage in the sensors of external physical factors and, more specifically, to detectors of small masses and particles. 
     The invention is devoted to the detection of natural massive particles, which may be part of so-called cosmic rays emitted by stars, or solar “wind” emitted by the Sun. The word massive indicates that a particle has a rest mass, in contrast to photons with zero rest mass or neutrinos with close to zero rest mass. The cosmic rays consist of different particles and electromagnetic radiation, which enter Earth&#39;s atmosphere. The so-called visible or luminous matter may be detected by contemporary astronomical and high-energy-physics instruments that usually employ optical and electromagnetic sensors, which operate with the photons of different energy, electro-magnetic waves of different wavelengths, and electric currents or potentials due to electrically charged particles. 
     (2) Description of the Related Art 
     The Parker Solar Probe (PSP) launched by NASA measures the near-Sun solar wind of electrically charged particles (J. Kasper, et al.,  Nature  576, 228-231 (2019)), fine structure of the solar corona (Howard, R., et al.,  Nature  576, 232-236 (2019)), slow solar wind (S. Bale, et al.,  Nature  576, 237-242 (2019)), and energetic charged particles emitted by the Sun (D. McComas, et al.,  Nature  576, 223-227 (2019)). The magnetic fields, electrons, protons and ions of some elements were also detected using PSP. The detectors in the above-mentioned investigations employed an interaction between solar emissions and electromagnetic-type sensors. 
     However, the Sun and other stars may emit massive particles of much higher mass-energy than those already detected including those that do not demonstrate electromagnetic interaction. The existence of natural particles heavier than the protons or neutrons is proven by experimentally observed energy spectra of cosmic rays (A. Corstanje, et al.,  Phys. Rev . D 103, 102006 (2021)), and by detection of high-energy neutrinos in the Ice-Cube collaboration experiments (M. G. Aartsen, et al.,  Eur. Phys. J. C  78, 831 (2018)). 
     Recently, a crystal-star effect has been reported in Igor Ostrovskii,  Proceedings of Meetings on Acoustics,  34, 045007 (2018) (hereinafter “Ostrovskii (2018)”). In one prior art, the direct detection of cosmic dark radiation is disclosed in Ostrovskii (2018). The word dark indicates that these particles are invisible to electromagnetic sensors employed in contemporary astronomical and high-energy-physics instruments, and consequently are not yet known. This art is shown in  FIG.  1 A , where quartz crystal  101  is the sensor of cosmic radiation. It operates due to interaction of massive particles with crystal  101  being under ultrasonic excitation by input voltage  107 . The output voltage  104  may be altered owing to the influence of massive particles on  101 . Direct detection of gravitating massive particles was disclosed in Igor Ostrovskii,  Proceedings of Meetings on Acoustics,  36, 045006 (2019) (hereinafter “Ostrovskii (2019)”). This previous art is shown in  FIG.  1 B , where dielectric films  102  are absent and crystal  101  is coated with metal electrodes  103  to increase the ultrasound amplitude in  101 . It allows the recording of nonlinear phenomena in a dependency of output voltage  104  versus the frequency of voltage  107 . The nonlinear effects in  104  appeared when the massive particles hits  101  under ultrasonic excitation. 
     Both the arts shown in  FIG.  1 A  and  FIG.  1 B  require externally excited ultrasonic oscillations inside  101 , which makes sensor  101  depend on the external voltage  107  and ultrasound in  101 . This may result in errors in the detection of massive particles because sensor  101  is under ultrasonic excitation and may not be sensitive to individual particles. To solve this problem, it is necessary to eliminate the externally excited ultrasound in  101 . 
     German Pat. No: DE102013006563A1 discloses theoretical method and apparatus for direct detection of dark matter by antimatter and their annihilation with the elementary particles of dark matter. This theoretical idea is based on possible interaction of not known dark matter particles with another not known particles of antimatter. 
     U.S. Pat. No. 5,083,028A discloses a neutron detector constituted by two identical diodes and a special cover for one diode that convert neutrons into charged particles. 
     U.S. Publication No: 2005/0017185A1 discloses a radiation detector of low energy neutrons. It is using a neutron capture material and sensing element having an electrical characteristic which changes in the presence of charged particles or electromagnetic radiation. 
     U.S. Pat. No. 8,338,784B2 discloses a radiation detector in which a semiconductor or insulator single crystal serves as a radiation absorber. In this patent the electric properties of semiconductor parts are changed under energy ray action. The term radiation means electromagnetic waves and charged particles. 
     U.S. Pat. No. 8,536,527B2 discloses a method for sensing a volume exposed to charged particles. This patent and patent EP1944626A2 disclose the radiation imaging detectors operating with optical depictions generated by incoming charged particles or a radio-active source. 
     U.S. Publication No: 2013/0015360A1 discloses a radiation detector with a scintillator structure having an optical waveguiding property. U.S. Pat. No. 4,421,985A discloses a dark field infrared telescope based on an optical sensor. 
     European Pat. No: EP0228933A1 discloses a device for detecting and locating electromagnetic radiation or neutrons by using an enclosure filled with gas, in which a converter capable, under the impact of neutral particles, of emitting ionizing particles producing ionization of the gas. This art is a modified type of well-known Geiger tube. 
     U.S. Pat. No. 5,043,574 discloses an apparatus for sensing direction of a neutral particle beam emitted by an accelerator along a predetermined axis in a magnetic field. The detection system includes a lens and a pixel array located in the focal plane of the lens for detecting a selected number of photons. 
     (3) Problems Involved in the Prior Art which are Solved by the Invention 
     The main existing problems in the two previous art shown in  FIG.  1 A  and  FIG.  1 B  are their dependency on externally excited ultrasound in  101 , which interferes with the effect of incoming massive particles that does not allow unmistakable conclusions on said particle detection. The patented arts mentioned above, (2), disclose radiation detectors for electromagnetic waves or subatomic particles. The main existing problems in patented arts consist in their detectors based on the electromagnetic interactions or transformations with incoming subatomic particles. Such detectors cannot detect massive particles that do not demonstrate the electromagnetic interactions and may be much heavier than subatomic particles. 
     BRIEF SUMMARY OF THE INVENTION 
     (1) The Advantages of the Invention 
     The invention solves problems previously existent in the prior art of detecting massive particles that do not have electro-magnetic interaction with a detector, and may be much heavier than subatomic particles. 
     (2) The Nature and Gist of the Invention 
     The essence of the invention is innovative mechanical sensor, in which massive particles propagating through said sensor influence on mechanical motion of sensor constituent atoms. 
     (3) Disclosure of the Best Mode for Invented Sensor 
     The apparatus may include a crystalline sensor suspended as a bob at the end of a pendulum that starts swinging when massive particle hits it, or be a part of any oscillator or vibrator. And then said particle is detected by detecting changes in sensor physical position, while it is swinging, and/or by detecting changes in sensor physical or chemical properties or characteristics. 
     (4) Statement of the Object of the Invention 
     The invention allows the detection of massive stellar particles, which are invisible to all of the electromagnetic sensors usually employed in particle detectors. These particles may be invisible or dark parts of so-called cosmic rays emitted by the stars. An apparatus for detecting massive particles, locating their sources, and harvesting their energy comprises a mechanical sensor, which may be made of crystal, condensed matter, ceramic, or multilayer system. The apparatus may include said sensor disclosed in (3). 
     The star-source emitting massive particles is located by finding the space direction from which the particles arrive and produce changes in the said sensor. Energy is harvested using sensor energetic characteristics including mechanical motion, electromagnetic potential, and thermal or nuclear reactions. 
     The invented sensor has directly detected massive particles from the Sun, central region of our Galaxy, and star Deneb. The average mass-energy of solar massive particles is 3.1×10 15  eV and mass-energy density near Earth˜0.78 GeV/cm 3 . 
     (5) The Figures and Examples 
     The Figures and Examples demonstrate the validity of the Invention and Claims, its embodiments, the best mode of practical operation, and application for the characterization of detected stellar massive particles. 
     Example 1 and  FIG.  5 A ,  FIG.  5 B  evidence that vibrations of the invented mechanical sensor suspended as a bob at the end of a pendulum cannot be explained by seismic and ambient noises. 
     Example 2 and  FIG.  6 A ,  FIG.  6 B  prove that massive particles detected by invented mechanical sensor put sensor atoms into mechanical oscillating motion. 
     Example 3 and  FIG.  7 A ,  FIG.  7 B  validate a method of locating azimuth/direction to a source of massive particles detected by the invented mechanical sensor suspended as a bob at the end of a pendulum in accordance with a disclosure of the best mode for invented sensor. 
     Example 4 and  FIG.  8 A ,  FIG.  8 B  present a practical application of the invention for characterization of massive particles emitted by the Sun by finding their mass and their mass-energy density near Earth. 
     Example 5 and  FIG.  9 A ,  FIG.  9 B ,  FIG.  9 C ,  FIG.  9 D  demonstrate that massive particles may be produced and emitted by the Sun. 
     Example 6 and  FIG.  10 A ,  FIG.  10 B  demonstrate the direct detection of massive stellar particles from the central region of our Milky Way Galaxy by using invented mechanical sensor suspended as a bob at the end of a pendulum. 
     Example 7 and  FIG.  11 A ,  FIG.  11 B  demonstrate the direct detection of massive stellar particles from the star Deneb in the constellation Cygnus by using invented mechanical sensor suspended as a bob at the end of a pendulum. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1 A . Previous art with fixed crystal  101  between the two dielectric films  102 . 
         FIG.  1 B . Previous art with fixed crystal  101  without dielectric films  102 . 
         FIG.  2   . The embodiment of an apparatus for detecting massive stellar particles, locating their sources and harvesting their energy. 
         FIG.  3   . The schematic diagram of the method for detecting stellar particles and locating their sources. 
         FIG.  4   . The schematic diagram of a method for energy harvesting from massive particles. 
         FIG.  5 A . Time waveform detected from swinging quartz  32 QXM 7 ; while it is hit by solar massive particles. 
         FIG.  5 B . The seismic and ambient noise waveform  502  detected by noise sensor  207  simultaneously with  501 . 
         FIG.  6 A . Time waveform detected from swinging quartz  28 QAT 6 ; while it is hit by solar massive particles. 
         FIG.  6 B . MHz-range electric current through swinging quartz  28 QAT 6 ; while it is hit by solar massive particles. 
         FIG.  7 A . Time waveform  701  detected from swinging quartz  32 QM 7 ; while it is hit by solar massive particles. 
         FIG.  7 B . Plot  702  is a time dependency of an amplitude of waveform  701 . 
         FIG.  8 A . Fast Fourier transform spectrum  801  obtained from the time dependent vibration waveform  601 . The  801  reveals natural resonance frequency F 0  and driven frequency Fin  601 . 
         FIG.  8 B . Fast Fourier transform spectrum  802  obtained from the time dependent vibration waveform  701 . The  802  reveals natural resonance frequencies F 0  and driven frequencies F in  701 . 
         FIG.  9 A . Time waveform  901  detected from swinging quartz  4 QY 7 ; while it is hit by solar massive particles. 
         FIG.  9 B . Fast Fourier transform spectrum  902 , obtained from the time dependent vibration waveform  901 , reveals the frequency components of F=5.9 Hz, F 0 =7.3 Hz, and F2=8 Hz in  901 . 
         FIG.  9 C . Time waveform  903  of a squared magnetic field (B 2 ) of the Sun at the time when particles  304  have been emitted by the Sun. 
         FIG.  9 D . Fast Fourier transform spectrum  904 , obtained from the time waveform  903  of a squared magnetic field of the Sun, reveals the frequency components of F=5.9 Hz and F2=8 Hz in  904 . 
         FIG.  10 A . Time waveform  1001  detected from swinging quartz  28 QAT 6 ; while it is hit by massive particles from the central region of our Milky Way Galaxy. 
         FIG.  10 B . Fast Fourier transform spectrum  1002 , obtained from the time waveform  1001 , reveals the main driven vibrational frequency of F=7.3 Hz in  1001 . 
         FIG.  11 A . Time waveform  1101  detected from swinging quartz  28 QAT 1 ; while it is hit by massive particles from the star Deneb in the constellation Cygnus. 
         FIG.  11 B . Fast Fourier transform spectrum  1102 , obtained from the time waveform  1101 , reveals the main driven vibrational frequency of F=7.8 Hz in  1101 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the description to follow, like reference numbers are used to identify like elements. 
     (1) A description of the preferred embodiments of the invented mechanical sensor: The embodiment of the invented mechanical sensor  201  is presented in  FIG.  2   , where it is suspended in its housing  202 .
 
(2) A description of the preferred embodiments of the invented apparatus:  FIG.  2    shows an embodiment of an apparatus for detecting massive stellar particles, locating their sources and harvesting their energy with the help of a sensor  201  in its housing  202 , which is installed on optical bench  206 , as shown in  FIG.  2   . The registration means  203 ,  204 ,  205  detect said particles by detecting changes in the physical characteristics and position of sensor  201 . The noise sensor  207  detects the seismic and ambient noises. The optical bench  206  may be orientated in three dimensions by 3-dimensional rotation fixture  209  connected to a fixed base plate  208 , which is installed on a supporting pedestal  210  through vibration insulation  211 .
 
(3) A description of the preferred embodiments and the mode of operation of the invented method for detecting massive particles and locating their sources: The registration means  203 ,  204 , and  205  detect said particles by detecting changes in the physical characteristics and position of sensor  201 . The noise sensor  207  detects the seismic and ambient noises. The optical bench  206  may be orientated in three dimensions by a 3-dimensional rotation fixture  209 ,  FIG.  2   . It is connected to a fixed base plate  208 ,  FIG.  2   , which is installed on a supporting pedestal  210  through a vibration insulation  211 ,  FIG.  2   . The  FIG.  3    shows a schematic diagram of the method for detecting massive stellar particles and locating their sources. The sensor  301  is oriented in space by setting its axis  302  at variable azimuth (AZ) and altitude (AL), as presented in  FIG.  3   . The detection means  305  detect the changes in characteristics of  301  including deviations of the position of sensor  301  in its housing  306 , and changes in physical characteristics counting optical, electrical, electromagnetic, acoustical, mechanical, high-energy or particle physics, nuclear physics, thermal, or any combination of the physical characteristics. The changes in said characteristics of  301  are detected by  305  when massive particle  304  emitted by  303  hits  301 ; and in this way  304  is detected. The space direction of  302  given by its AZ, AL reveals sky location of star  303  that emitted particle  304 . The search and locating  303  is completed by varying AZ and AL of  302 , as disclosed in the  FIG.  3   , together with detecting changes in the above-mentioned characteristics of  301 .
 
(4) A description of the preferred embodiments and the mode of operation of the invented method for energy harvesting from massive particles:  FIG.  4    shows a schematic diagram of a method for energy harvesting from massive particles by using energy of the mechanical motion of a suspended sensor  401  in its housing  402 , with an attached magnet  403 . The magnet  403  vibrates along with  401  over an electric coil  404 , and then a variable magnetic field near the tip of  403  penetrates electrical coil  404  generating an electric current  405 . The electric current  405  occurred when particles  304  hit sensor  401  and activated a swinging motion of  401  with  403  over coil  404 .
 
(5) The best mode contemplated by the inventor of carrying out his invention: The best mode of a practical usage of the invention includes three parts: 1) The best mode for invented sensor. It may be made of a crystalline media, and be suspended as a bob at the end of a pendulum,  FIG.  2   . It will be swinging when a massive particle hits it, and causes changes in sensor position and its physical characteristics. 2) The preferred embodiment and the mode of operation of the invented method presented in  FIG.  3   . 3) The use of optical,  204 , and/or electrical,  205 , means of detection of the changes in the characteristics of a swinging sensor  201 , as disclosed in  FIG.  2   .
 
(6) The Examples for clarification and verification of the present invention: The Examples below are included to provide additional explanations for a more systematic clarification of the present invention. In order to provide a more thorough formulation of the invention, reference is made to the following non-limiting examples. To verify the feasibility and performance of an apparatus for detecting massive stellar particles and locating their sources, in the examples that follow, the sensors are made of crystalline quartz plates or disks of milligram range weight available on the market place. The sensor axis  302  in  FIG.  3    is oriented along one of the crystallographic quartz axes, for example X-axis, Y-axis or rotated Y-axis.
 
     Equipment used in the examples comprised a laser Doppler vibrometer Polytec PDV-100 (LDV) for optical means of detection,  203  in  FIG.  2   , spectrum analyzer Siglent SSA-3021 as electrical means of detection,  204  in  FIG.  2   , digital storage oscilloscopes Tektonics TBS2024B and Keysight DSOX-2012A along with computers for data acquisition system,  205  in  FIG.  2   , some small components and chemicals. The experimental errors of the method include calibration accuracy ±1% of LDV, spectrum analyzer and digital storage oscilloscopes accuracy of 1-5% depending on signal amplitude, and ±0.5 deg in setting crystal axis toward a star. The resultant signal-to-noise ratio was from near 10 to more than 100 in different examples below. The LDV gauges the vibrational speed S of the crystal-sensor  201 / 301  from 0.05 micrometer/s and higher over a frequency range from 0.05 Hz to 22 KHz. Its readings are specified in Volts used in some figures below, and 1 V corresponds to S=5 mm/s. 
     The LDV detected deviations in the physical position of sensor  201  in its housing  202 . The pendulum vibrations of a suspended  201 ,  FIG.  2   , occur when particles  304  periodically hit sensor  201 , and consequently  203  in  FIG.  2    detects periodic changes in a position of 201, which is represented by a sinusoidal time waveform of sensor vibrational speed in the examples below. 
     The exact location in the sky of the Sun, the star Deneb and center region of our Galaxy is obtained with the astronomy software “TheSkyX Professional Edition” along with the calculated time of propagation, Tp=(Lse/Vp), needed for massive particles  304  to travel the distance Lse from the Sun to sensor  302  on Earth,  FIG.  3   . The speed Vp=249 km/sec (Ostrovskii (2018)). Then, solar time Ts for determining solar AZ, AL is Ts=(Te−Tp), where Te stands for a time of experiment on Earth. The distance Lse is changed every second due to not-circular orbit of Earth around the Sun, and therefore must be calculated for exact date and time Te of the experiment on Earth. 
     Example 1: This example demonstrates that vibrations of invented mechanical sensor suspended as a bob at the end of a pendulum,  FIG.  2   , cannot be explained by seismic and ambient noises. 
     The details of the invented mechanical sensor are schematically presented in  FIG.  2   ,  FIG.  3    and  FIG.  4   ; where  202  is a sensor housing. 
       FIG.  5 A  demonstrates the detection of massive stellar particles  304  from the Sun by optical means of detection  203  LDV,  FIG.  2   . The LDV returned a time waveform  501  occurring when particles  304  hit  201 / 301 .  FIG.  5 B  presents the seismic and ambient noise waveform  502  detected by the noise sensor geophone  207 ,  FIG.  2   , simultaneously with the detection of  501 . There is a significant difference between the time waveform  501  occurring due to particles  304  and noise the waveform  502  owing due to seismic and ambient noises. The plot  501  was is taken from the quartz sensor  32 QXM; while Azimuth of axis  302  set to 240° coincides with Sun&#39;s AZ. This example evidences an important fact that the time waveform  501  occurs due to solar massive particles  304  and cannot be explained by the seismic and ambient noises. 
     Example 2: This example evidences that massive particles detected by the invented mechanical sensor disclosed in  FIG.  2    put sensor atoms into mechanical oscillating motion, which allows sensor to be a part of any pendulum or oscillator. 
     The waveform  601  in  FIG.  6 A  evidences a swinging oscillating motion of sensor  201 , here quartz sample  28 QAT 6 ; while it detects massive stellar particles  304  emitted by the Sun,  303  in  FIG.  3   , with optical means of detection  203  LDV, indicated in  FIG.  2    and returning plot  601  when particles  304  from the Sun are hitting  201 / 301 ; while Azimuth of axis  302  set to 204° coincides with Sun&#39;s AZ.  FIG.  6 B  presents the detection of massive stellar particles  304  emitted by the Sun using electrical means of detection  204 , plots  603 ,  604 . Time waveform  601  becomes approximately zero-level noise in the absence of  304 . Electrical means  204  detected the time dependency of the MHz-range electric current through sensor  201 / 301 . The plot  602  is a smooth time dependency taken without particles  304  when axis  302  does not coincide with AZ angle of  303 ,  FIG.  3   . The pulse-type plot  603  is detected when particles  304  start hitting  201 / 301  as soon as axis  302  is approaching AZ toward  303  within ±1-degree difference from the AZ of  303 . The low-amplitude plot  604  is detected when particles  304  hit  201 / 301  once axis  302  coincides with the AZ of  303 . The plot  601  was taken from the quartz sensor  28 QAT with axis  302  set at AZ 204° toward the Sun. The data in  FIG.  6 B  were taken from the same sensor and the same axis  302  settings. However, the initial undistorted plot  602  is registered at 20 h: 55 min: 51 s UTC, when Sun AZ=191.8°, and does not coincide with axis  302  AZ=204° and then particles  304  do not hit  201 / 301 . The plot  603  is taken later at 21 h: 13 m: 59 s UTC when Sun AZ=203.3°, that is 0.7° smaller than AZ of 302°. The plot  604  is taken at 21 h: 15 m: 52 s UTC when Sun AZ=204°=AZ of  302 ; then the maximum possible number of particles  304  hit sensor  201 / 301 , and the amplitude of the initial plot  602  becomes very small. With time goes on, the alternating electric current through  301  restores from  604  to the initial plot  602 , and plot  601  decreases to a near-zero noise. 
     The detection of time waveforms  601  and  604  occurs because massive particles  304  put sensor atoms into vibrational motion with low frequency F below 10 Hz, and consequently  201 / 301  starts swinging resulting in  601 . However, high-frequency electric current of MHz range is not transmitted through dielectric quartz sensor  301  resulting in plot  604 , because sensor atoms do not oscillate at high-frequency. 
     Example 3: This example validates a method of locating source of massive particles,  FIG.  2    and  FIG.  3   , in accordance with a disclosure of the best mode of carrying out the invention. 
     The details of the invented apparatus and method of detecting massive particles, locating their source, and harvesting their energy are schematically presented in  FIG.  2    and  FIG.  3   . The dimensions of 202, 203, 206, 207, 208, and 209 may vary, and are presented in  FIG.  2    schematically to clearly show the details of the invented apparatus and method. 
       FIG.  7 A  presents a sinusoidal time waveform  701  taken from the swinging sensor  201 / 301 , here quartz crystal  32 QXM 7 , by  203 , LDV; while  304  emitted by the Sun hit  301 . Plot  702  in  FIG.  7 B  shows the time dependency of the amplitude of waveform  701 . The AZ of axis  302  was fixed in this experiment, and peak-type dependency  702  occurred because of the changing Sun&#39;s AZ due to Earth&#39;s rotation about its axis of rotation. The maximum of plot  702  in  FIG.  7 B  was observed when AZ  302  coincided with that of the Sun, star-source  303 . The data in  FIG.  7 A  and  FIG.  7 B  were taken with axis  302  set at AZ=105°. Plot  701  is taken at 11 h:54 m:06 s UTC when Sun&#39;s AZ is also 105°. Plot  702  is taken during time interval from 11 h:41 m:18 s to 12 h:13 m:56 s UTC, during which Sun&#39;s AZ is changes from less than 105° to more than 105°, upper X-axis in  FIG.  7 B . The maximum in  702  occurs under a 105° solar AZ when the maximum number of particles  304  hit sensor  301 . The AL angle, as shown in  FIG.  3   , can be found in a manner similar to the AZ angle. This can be achieved by changing the AL angle of sensor axis  302 , as shown in  FIG.  3   . 
     Example 4: This example presents a practical application of the invention for characterization of massive particles from the Sun by finding their mass M and their mass density D near Earth. 
       FIG.  8 A  presents a fast Fourier transform spectrum  801  of the vibration time waveform  601 . Then  FIG.  8 B  presents a fast Fourier transform spectrum  802  of the vibration time waveform  701 . The plot  801  discloses two frequencies, F 0 =6.5 Hz and F′=7.9 Hz, which compose waveform  601 . The plot  802  discloses two frequencies, F 0 =6 Hz and F=7.6 Hz which compose waveform  701 . The vibrations of a driven pendulum have two main frequencies including a natural resonance F 0  and a driven frequency F=(1/T), with which an external periodic force of period T pushes said pendulum. (Fowels, G., Cassidy, G.  Analytical Mechanics,  7th edn., Ch. 3. Thomson Brooks/Cole Publishing, (2005)). The force produced by massive particle  304  hits sensor  201 / 301 , and is acting during time ΔT≈0.5 T. The particle  304  of mass M interacts with pendulum-sensor  201 / 301  of mass m. Particle mass M can be calculated from the law of energy conservation, since a kinetic energy of  201 / 301  is equal to a kinetic energy transferred by  304  to  201 / 301 , Equation (1), (Ostrovskii (2021)). 
       ( M/m )=2π( S/V ) 2 [(( F   0   2   /F   2 )−1) 2 +(γ/π F ) 2 ] 1/2  sin(πΔ T/T −φ).  (1)
 
     Where m, S, F 0 , F are experimentally measured, γ&lt;&lt;πF, sin(πΔT/T−φ)≈1, and V≈249 km/s (Ostrovskii (2018)). In the case when the 3-dimensional sensor  201 / 301  cannot be considered as a point body, the mass M is replaced by sensor&#39;s moment of inertia with respect to a pivot line, and the linear speed S is replaced by an angular speed (S/L B ) of the vibrating  201 / 301 , where L B  is a distance from the pivot point to laser beam position on a surface of  201 / 301 , which may be in a center of sensor  201  indicated by arrow  302  in  FIG.  3   . 
     The calculations by Equation (1) with the data in  FIG.  6 A  yield particle mass M=7.54×10 −21  kg with known m=0.421 g and F 0 =6.5 Hz, F=7.9 Hz, as in  FIG.  8 A . Similar calculations with the data in  FIG.  7    give M=6.34×10 −21  kg with known m=0.125 g, F 0 =6 Hz and F=7.6 Hz, as in  FIG.  8 B . The average mass, Ma, of solar massive particle from multiple experiments is Ma=5.5 −1.7   +2.2 ×10 −21  kg, and its average mass-energy Wa=Ma×C 2 =3.1 −1   +1.2 ×10 15  eV. The average mass-energy density of solar massive particles near Earth (Da) can be calculated as Da=(Wa×F)/(A×V), where A is an area of sensor  301  oriented toward the Sun. The calculations with typical F=7.7 Hz and used half-inch diameter sensor  301  give maximum Da=(0.78 GeV/cm 3 ). 
     Example 5: This example reveals the fact of identical frequencies in the vibrational spectrum of the invented mechanical sensor due to solar massive particles and in the spectrum of solar magnetic field energy, which proves that massive particles may be produced and emitted by the Sun. 
     Time waveform  901  is taken at 14 h: 51 m: 58 s UTC from the quartz sensor  4 QY 7  with axis  302  set at 185° AZ while Sun&#39;s AZ was also 185° at a time when particles  304  were emitted. The spectrum  902 ,  FIG.  9 B , of waveform  901 ,  FIG.  9 A , reveals the driven frequency of vibrations F=5.9 Hz, natural resonance frequency F 0 =7.3 Hz, and additional frequency F 2 =8 Hz, which is not expected from the theory of driven pendulum vibrations (Fowels, Cassidy (2005)). 
     The plot  903 ,  FIG.  9 C , is a time waveform of the squared solar magnetic field (B 2 ) proportional to solar magnetic energy, at the time when particles  304  have been emitted by the Sun. The components of solar magnetic field B are obtained by Parker Solar Probe launched by NASA; and they are available from the CDAWeb of the NASA Space Physics Data Facility (https://spdf.gsfc.nasa.gov). Spectrum  904 ,  FIG.  9 D , of waveform  903 ,  FIG.  9 C , also revealed two main frequencies: F=5.9 Hz and F 2=8  Hz. They coincide with the frequencies in  FIG.  9 B  detected by the quartz sensor  301 / 201 ,  FIG.  3   / FIG.  2    correspondingly; while massive solar particles hit the sensor and activate its swinging. 
     Consequently, the spectral analysis shows the identical F and F2 in both waveforms  901  and  903 , which allows us to conclude that massive particles hitting  201 / 301  were produced and emitted by the Sun. 
     Example 6: This example evidences direct detection of massive stellar particles from the central region of our Milky Way Galaxy by using invented mechanical sensor suspended as a bob at the end of a pendulum, as disclosed in  FIG.  2   . 
       FIG.  10 A  presents a time waveform  1001  demonstrating detection of massive particles from the central region of our Galaxy. The vibrational waveform  1001  is taken from sensor  201 ,  FIG.  12 A , by using LDV,  203  in  FIG.  13 F . Plot  1001  is captured from swinging quartz sensor  28 QAT 6  with F 0 =6.5 Hz on 2019 Sep. 30 at 02 h: 37 m: 06 s UTC with axis  302  set at 224° AZ aimed on the Galactic center. The frequency components of time waveform  1001  are made known from its fast Fourier transform spectrum  1002 . Main driven frequency F=7.3 Hz is below 10 Hz, the same frequency range as for solar massive particles discussed in Example 4. 
     Example 7: This example evidences direct detection of massive stellar particles from the star Deneb in the constellation Cygnus by using invented mechanical sensor suspended as a bob at the end of a pendulum, as disclosed in  FIG.  2   . 
     Time waveform  1101 ,  FIG.  11 A , demonstrates detection of massive particles arrived from the star Deneb in the constellation Cygnus. Plot  1101  is registered from swinging quartz sensor  28 QAT 1  with F 0 =0.8 Hz on 2020 Jan. 8 at 04 h: 01 m: 12 s UTC with axis  302  set at AZ=326° coinciding with that of the star Deneb. The fast Fourier transform spectrum  1102  of the time waveform  1101  revealed first-order driven frequency F=7.8 Hz that is below 10 Hz, the same frequency range as for solar massive particles discussed in Example 4. 
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                 5,083,028A 
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         R. Howard, et al., Near-Sun observations of an F-corona decrease and K-corona fine structure.  Nature  576, 232-236 (2019). 
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         Igor Ostrovskii, Direct detection of gravitating dark particles navitens by nonlinear effects in crystal vibrations and by particles track.  Proceedings of Meetings on Acoustics,  36, 045006 (2019); doi: 10.1121/2.0001129. 
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