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The Allais Effect and the Cause Analysis of Gravity Valley Formation
DOI: 10.12677/AAS.2023.112002, PDF, HTML, XML, 下载: 211  浏览: 452

Abstract: Usually, in addition to the gravitational force of the earth and the centrifugal force of the earth’s rotation, the surface materials are also affected by the gravitational force of the sun, the centrifugal force of the sun, the gravitational force of the moon, and the centrifugal force of the earth and the moon. This paper illustrates the main factors affecting the Allais effect and the double-valley phenomenon of gravity by calculating the change of the resultant force of these forces in the direction of gravity and the horizontal direction. For the surface matter, the direction of the ordinary matter’s force is relatively large. When the solar eclipse begins, the centrifugal direction of the sun and the moon does not change much, but the direction of the sun’s and moon’s gravitational forces is almost the same. At this time, the combined force of the sun and the moon reaches its peak. During the so-lar eclipse, the gravitons emitted by the sun are partially absorbed by the moon. The quantity is the same. At this time, the resultant force of the sun and the moon is the same as the gravitational force of the sun alone. When the solar eclipse is restored, the moon escapes from the shadow of the sun. At this time, there is no problem of graviton occlusion. The resultant force of the gravitational force of the sun and the moon is the second highest for the material on the ground. Then, as the angle between the moon and the sun increases, the resultant force of gravitation decreases and returns to normal. During a solar eclipse, the matter on the ground appears double peaks due to the gravitational force of the sun and the moon, and the corresponding gravity appears double valleys. The Foucault pendulum will have the Allais effect where the horizon elevation angle is greater than 40˚; when the horizon elevation angle is 20˚~65˚, it is easy to measure the phenomenon of gravity double valleys. The actual measured gravity double valley value has a lot to do with the selected tidal force curve and parameters.

1. 引言

1851年的巴黎，在法兰西共和国的先贤祠(国葬院)的大厅里，让·傅科进行一项有趣的实验 [1] 。傅科在大厅的穹顶上悬挂了一条67米长的绳索，绳索的下面是一个重达28千克的摆锤，摆锤的下方是巨大的沙盘。每当摆锤经过沙盘上方的时候，摆锤上的指针就会在沙盘上面留下运动的轨迹。按照日常生活的经验，这个硕大无比的摆应该在沙盘上面画出唯一一条轨迹。实验开始后，人们惊奇的发现，傅科设置的摆每经过一个周期的震荡，在沙盘上画出的轨迹都会偏离原来的轨迹，后经研究这种偏离是地球的自转造成的。在地球南半球这个偏转是逆时针方向，在地球北半球这个偏转是顺时针方向。图1为傅科摆的示意图。傅科摆实验首次为地球自转提供了天文学之外的证据。

Figure 1. Foucault pendulum

Figure 2. Actual measurement of gravity double valley

2. 日食期间牛顿经典理论下的引力叠加

Figure 3. Gravitational superposition of the sun and the moon

${F}_{S}=G\frac{{m}_{s}{m}_{0}}{{R}_{S}^{2}}=\text{6}{\text{.67×10}}^{\text{-11}}×\text{}\frac{\text{1}\text{.989}×{\text{10}}^{\text{30}}×\text{1}}{{\left(\text{1}\text{.496}×{\text{10}}^{\text{11}}-6.371×{10}^{6}\right)}^{2}}=\text{0}.005928\text{N}$ (1)

${\alpha }_{s}\approx \frac{1.392×{10}^{9}}{1.496×{10}^{11}}=0.\text{00}93$ (2)

${F}_{\text{m}}=G\frac{{m}_{m}{m}_{0}}{{R}_{m}^{2}}=\text{6}\text{.67}×{\text{10}}^{-\text{11}}×\frac{\text{7}.342×{\text{10}}^{\text{22}}×\text{1}}{{\left(\text{3}.844×{\text{10}}^{\text{8}}-6.371×{10}^{6}\right)}^{2}}=\text{3}\text{.4268}×{\text{10}}^{-\text{5}}$ (3)

${\alpha }_{m}=\frac{3.476×{10}^{6}}{3.844×{10}^{8}}=0.00904$ (4)

${\alpha }_{SM}=\frac{\text{1}}{\text{2}}{\alpha }_{m}+\frac{\text{1}}{\text{2}}{\alpha }_{s}=\frac{\text{1}}{\text{2}}×\text{0}\text{.00904}+\frac{\text{1}}{\text{2}}×\text{0}\text{.0093}=\text{0}\text{.00917}$ (5)

$\begin{array}{c}{F}_{SM1}=\sqrt{{F}_{S}^{2}+{F}_{M}^{2}+2{F}_{S}{F}_{M}\mathrm{cos}{\alpha }_{SM}}\\ =\sqrt{{0.005928}^{\text{2}}+{\left(3.4268×{10}^{-5}\right)}^{\text{2}}+\text{2}×0.005928×3.4268×{10}^{-5}\mathrm{cos}\text{0}\text{.00917}}=0.005962\end{array}$ (6)

$\Delta {F}_{SM1}={F}_{SM1}-{F}_{S}=0.005962-0.005928=0.000034\text{}\left(\text{Gal}\right)=3.4\text{}\left(\text{mGal}\right)$ (7)

$\begin{array}{c}{F}_{SM\text{2}}={F}_{S}+{F}_{M}\\ =0.005928+3.4268×{10}^{-5}=0.005962\end{array}$ (8)

$\begin{array}{c}\Delta {F}_{SM2}={F}_{SM2}-{F}_{S}\\ =0.005962-0.005928\\ =0.000034\text{(Gal)}=3.4\text{(mGal)}\end{array}$ (9)

Figure 4. The difference between the gravitational force of the sun and the moon (Newton) and the gravitational force of the sun during a solar eclipse

3. 日食期间量子引力理论下的引力叠加

Figure 5. Graviton occlusion during a solar eclipse

Figure 6. The difference between the gravitational force of the sun and the moon (quantum gravity) and the gravitational force of the sun during a solar eclipse

4. 影响重力双谷和阿莱效应的主要因素

${F}_{S}=2G\frac{{m}_{s}{r}_{E}}{{R}_{SE}^{3}}=2×6.67×{10}^{-11}×\frac{1.989×{10}^{30}×6.371×{10}^{6}}{{\left(1.496×{10}^{11}\right)}^{3}}=5.049×{10}^{-7}\text{g}=50.49\text{uGal}$ (10)

${F}_{M}=2G\frac{{m}_{M}{r}_{E}}{{R}_{ME}^{3}}=2×6.67×{10}^{-11}×\frac{7.342×{10}^{22}×6.371×{10}^{6}}{{\left(3.844×{10}^{8}\right)}^{3}}=1.09857×{10}^{-6}g=109.857\text{uGal}$ (11)

Figure 7. The angle between the object’s gravity and centripetal force

${r}_{W}={r}_{E}\mathrm{cos}\beta$ (12)

${F}_{W//V}=m{\omega }^{2}r={\omega }^{2}{r}_{E}\mathrm{cos}\beta$ (13)

${F}_{E}=G\frac{{m}_{E}{m}_{W}}{{r}_{E}^{2}}=G\frac{{m}_{E}}{{r}_{E}^{2}}$ (14)

${F}_{G}^{2}={F}_{W//V}^{2}+{F}_{E}^{2}-2{F}_{W//V}{F}_{E}\mathrm{cos}\beta$ (15)

${F}_{G}^{2}={\left({\omega }^{2}{r}_{E}\mathrm{cos}\beta \right)}^{2}+{\left(G\frac{{m}_{E}}{{r}_{E}^{2}}\right)}^{2}-2\left({\omega }^{2}{r}_{E}\mathrm{cos}\beta \right)\left(G\frac{{m}_{E}}{{r}_{E}^{2}}\right)\mathrm{cos}\beta$ (16)

$\mathrm{tan}{\theta }_{G}=\frac{CD}{AB-DB}=\frac{CB\mathrm{sin}\beta }{AB-CB\mathrm{cos}\beta }$ (17)

$\mathrm{tan}{\theta }_{G}=\frac{{F}_{W//V}\mathrm{sin}\beta }{{F}_{E}-{F}_{W//V}\mathrm{cos}\beta }=\frac{{\omega }^{2}{r}_{E}\mathrm{cos}\beta \mathrm{sin}\beta }{G\frac{{m}_{E}}{{r}_{E}^{2}}-{\omega }^{2}{r}_{E}{\mathrm{cos}}^{\text{2}}\beta }$ (18)

Figure 8. The effect of inclination on the gravitational double valley

${\theta }_{S}=\pi -\left(h+\frac{\pi }{2}+{\theta }_{G}\right)-art\mathrm{sin}\left[\frac{{r}_{E}}{{R}_{SE}}\mathrm{sin}\left(h+\frac{\pi }{2}+{\theta }_{G}\right)\right]$ (19)

${\theta }_{M}=\pi -\left(h+{\alpha }_{SM}+\frac{\pi }{2}+{\theta }_{G}\right)-art\mathrm{sin}\left[\frac{{r}_{E}}{{R}_{ME}}\mathrm{sin}\left(h+{\alpha }_{SM}+\frac{\pi }{2}+{\theta }_{G}\right)\right]$ (20)

${R}_{SW}^{2}={R}_{SE}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{SE}\mathrm{cos}{\theta }_{S}$ (21)

${F}_{SW}=G\frac{{m}_{S}}{{R}_{SW}^{2}}=G\frac{{m}_{S}}{{R}_{SE}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{SE}\mathrm{cos}{\theta }_{S}}$ (22)

${F}_{SWC}=G\frac{{m}_{S}}{{R}_{SE}^{2}}$ (23)

${R}_{MW}^{2}={R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{M}$ (24)

${F}_{MW}=G\frac{{m}_{M}}{{R}_{MW}^{2}}=G\frac{{m}_{M}}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{M}}$ (25)

${F}_{MWC}=G\frac{{m}_{M}}{{R}_{ME}^{2}}$ (26)

$\begin{array}{c}{F}_{\perp }={F}_{SWC\perp }+{F}_{MWC\perp }-{F}_{SW\perp }-{F}_{MW\perp }\\ =G\frac{{m}_{s}}{{R}_{SE}^{2}}\mathrm{cos}\left({\theta }_{G}+{\theta }_{S}\right)+G\frac{{m}_{M}}{{R}_{ME}^{2}}\mathrm{cos}\left({\theta }_{G}+{\theta }_{M}\right)-G\frac{{m}_{S}\mathrm{sin}\left(h\right)}{{R}_{SE}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{SE}\mathrm{cos}{\theta }_{S}}-G\frac{{m}_{M}\mathrm{sin}\left(h+{\alpha }_{SM}\right)}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{M}}\end{array}$ (27)

$\begin{array}{c}{F}_{\text{//}}={F}_{SWC\text{//}}+{F}_{MWC\text{//}}-{F}_{SW\text{//}}-{F}_{MW\text{//}}\\ =G\frac{{m}_{s}}{{R}_{SE}^{2}}\mathrm{sin}\left({\theta }_{G}+{\theta }_{S}\right)+G\frac{{m}_{M}}{{R}_{ME}^{2}}\mathrm{sin}\left({\theta }_{G}+{\theta }_{M2}\right)-G\frac{{m}_{S}\mathrm{cos}\left(h\right)}{{R}_{SE}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{SE}\mathrm{cos}{\theta }_{S}}-G\frac{{m}_{M}\mathrm{cos}\left(h+{\alpha }_{SM}\right)}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{M2}}\end{array}$ (28)

Figure 9. Schematic diagram of lunar orbit and yellow-white intersection angle

${\theta }_{Mn}=\pi -\left(h+n{\alpha }_{SM}+\frac{\pi }{2}+{\theta }_{G}\right)-art\mathrm{sin}\left[\frac{{r}_{E}}{{R}_{ME}}\mathrm{sin}\left(h+n{\alpha }_{SM}+\frac{\pi }{2}+{\theta }_{G}\right)\right]$ (29)

$\begin{array}{c}{F}_{\perp n}={F}_{SWC\perp n}+{F}_{MWC\perp n}-{F}_{SW\perp n}-{F}_{MW\perp n}\\ =G\frac{{m}_{s}}{{R}_{SE}^{2}}\mathrm{cos}\left({\theta }_{G}+{\theta }_{S}\right)+G\frac{{m}_{M}}{{R}_{ME}^{2}}\mathrm{cos}\left({\theta }_{G}+{\theta }_{Mn}\right)-G\frac{{m}_{S}\mathrm{sin}\left(h\right)}{{R}_{SE}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{SE}\mathrm{cos}{\theta }_{S}}-G\frac{{m}_{M}\mathrm{sin}\left(h+n{\alpha }_{SM}\right)}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{Mn}}\end{array}$ (30)

$\begin{array}{c}{F}_{\text{//}n}={F}_{SWC\text{//}n}+{F}_{MWC\text{//}n}-{F}_{SW\text{//}n}-{F}_{MW\text{//}n}\\ =G\frac{{m}_{s}}{{R}_{SE}^{2}}\mathrm{sin}\left({\theta }_{G}+{\theta }_{S}\right)+G\frac{{m}_{M}}{{R}_{ME}^{2}}\mathrm{sin}\left({\theta }_{G}+{\theta }_{Mn}\right)-G\frac{{m}_{S}\mathrm{cos}\left(h\right)}{{R}_{SE}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{SE}\mathrm{cos}{\theta }_{S}}-G\frac{{m}_{M}\mathrm{cos}\left(h+n{\alpha }_{SM}\right)}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{Mn}}\end{array}$ (31)

$\begin{array}{c}\Delta {F}_{\perp n}={F}_{\perp }-{F}_{\perp n}\\ =\left[G\frac{{m}_{s}}{{R}_{SE}^{2}}\mathrm{cos}\left({\theta }_{G}+{\theta }_{S}\right)+G\frac{{m}_{M}}{{R}_{ME}^{2}}\mathrm{cos}\left({\theta }_{G}+{\theta }_{M}\right)-G\frac{{m}_{S}\mathrm{sin}\left(h\right)}{{R}_{SE}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{SE}\mathrm{cos}{\theta }_{S}}-G\frac{{m}_{M}\mathrm{sin}\left(h+{\alpha }_{SM}\right)}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{M}}\right]\\ -\left[G\frac{{m}_{s}}{{R}_{SE}^{2}}\mathrm{cos}\left({\theta }_{G}+{\theta }_{S}\right)+G\frac{{m}_{M}}{{R}_{ME}^{2}}\mathrm{cos}\left({\theta }_{G}+{\theta }_{Mn}\right)-G\frac{{m}_{S}\mathrm{sin}\left(h\right)}{{R}_{SE}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{SE}\mathrm{cos}{\theta }_{S}}-G\frac{{m}_{M}\mathrm{sin}\left(h+n{\alpha }_{SM}\right)}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{Mn}}\right]\end{array}$ (32)

$\Delta {F}_{\perp }=G\frac{{m}_{M}}{{R}_{ME}^{2}}\left[\mathrm{cos}\left({\theta }_{G}+{\theta }_{M}\right)-\mathrm{cos}\left({\theta }_{G}+{\theta }_{Mn}\right)\right]-G{m}_{M}\left[\frac{\mathrm{sin}\left(h+{\alpha }_{SM}\right)}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{M}}-\frac{\mathrm{sin}\left(h+n{\alpha }_{SM}\right)}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{Mn}}\right]$ (33)

$\begin{array}{l}\Delta {F}_{\text{//}}={F}_{\text{//}}-{F}_{\text{//}n}\\ =\left[G\frac{{m}_{s}}{{R}_{SE}^{2}}\mathrm{sin}\left({\theta }_{G}+{\theta }_{S}\right)+G\frac{{m}_{M}}{{R}_{ME}^{2}}\mathrm{sin}\left({\theta }_{G}+{\theta }_{M}\right)-G\frac{{m}_{S}\mathrm{cos}\left(h\right)}{{R}_{SE}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{SE}\mathrm{cos}{\theta }_{S}}-G\frac{{m}_{M}\mathrm{cos}\left(h+{\alpha }_{SM}\right)}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{M}}\right]\\ -\left[G\frac{{m}_{s}}{{R}_{SE}^{2}}\mathrm{sin}\left({\theta }_{G}+{\theta }_{S}\right)+G\frac{{m}_{M}}{{R}_{ME}^{2}}\mathrm{sin}\left({\theta }_{G}+{\theta }_{Mn}\right)-G\frac{{m}_{S}\mathrm{cos}\left(h\right)}{{R}_{SE}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{SE}\mathrm{cos}{\theta }_{S}}-G\frac{{m}_{M}\mathrm{cos}\left(h+n{\alpha }_{SM}\right)}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{Mn}}\right]\end{array}$ (34)

$\begin{array}{l}\Delta {F}_{\text{//}}={F}_{\text{//}}-{F}_{\text{//}n}\\ =G\frac{{m}_{M}}{{R}_{ME}^{2}}\left[\mathrm{sin}\left({\theta }_{G}+{\theta }_{M}\right)-\mathrm{sin}\left({\theta }_{G}+{\theta }_{Mn}\right)\right]-G{m}_{M}\left[\frac{\mathrm{cos}\left(h+{\alpha }_{SM}\right)}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{M}}-\frac{\mathrm{cos}\left(h+n{\alpha }_{SM}\right)}{{R}_{ME}^{2}+{r}_{E}^{2}-2{r}_{E}{R}_{ME}\mathrm{cos}{\theta }_{Mn}}\right]\end{array}$ (35)

$\Delta {F}_{SM//V}=\Delta {F}_{\text{//}}\mathrm{cos}{\beta }_{\text{0}}$ (36)

$\Delta {F}_{SM\perp V}=\Delta {F}_{\text{//}}\mathrm{sin}{\beta }_{\text{0}}$ (37)

Figure 10. Screenshot of data simulation part

5. 讨论

6. 结论

 [1] 傅科摆. 百度百科[EB/OL]. https://baike.baidu.com/item/%E5%82%85%E7%A7%91%E6%91%86/1486911?fr=ge_ala, 2023-07-14. [2] 星巴克. 日食时才出现的阿莱效应[J]. 大科技: 科学之谜(A), 2014(2): 52-53, 54. [3] 许梅. 日食时的“阿莱单摆效应”[J]. 物理通报, 2005(8): 10-12. https://doi.org/10.3969/j.issn.0509-4038.2005.08.004 [4] 王榴泉, 田景发, 刘煜奋, 等. 1976年4月29日日环食时引力效应观测——重力仪与倾斜仪的观测结果[J]. 科学通报, 1978, 23(8): 477-480. [5] 王政, 王永庆. 日环食引力观测的分析[J]. 新疆大学学报: 自然科学版, 1989, 6(4): 47-52. [6] 汤克云, 王谦身. 由漠河日全食期间的重力异常看引力实验[J]. 科学新闻, 2001(15): 3. [7] 王谦身, 杨新社, 汤克云. 漠河日全食期间的重力异常[J]. 科学通报, 2001, 46(12): 1044-1048. [8] 汤克云. 追逐重力异常[J]. Newton-科学世界, 2005(1): 44-49. [9] 崔荣花, 方剑, 王新胜. 2009-07-22湖北地区日全食期间的重力观测[J]. 武汉大学学报信息科学版, 2011, 36(11): 1332-1335. [10] 文武, 汤克云, 王谦身, 等. 利用2009年日全食的精细重力观测探寻引力异常[J]. 地球物理学报, 2013, 56(3): 770-782 [11] 姚垚, 李辉, 韦进, 等. 2009年7月22日武汉日全食重力效应研究[J]. 大地测量与地球动力学, 2013, 33(A01): 3. [12] 张登科. 自然界还存在一种新的场及新的力[J]. 科学(中文版), 2000(6): 60-61. [13] 陈军利, 康耀辉. 引力、引力场和引力子——关于引力能量波频率的推断[J]. 天文与天体物理, 2022, 10(1): 1-10. [14] 陈军利. 引力是如何产生的？—引力线在偏转物体的运动方向[J]. 天文与天体物理, 2023, 10(2): 11-24. https://doi.org/10.12677/AAS.2022.102002 [15] 周义钦. 月球地平高度的变化规律解析[J]. 地理教学, 2012(19): 11-13.