Several Ways to Calculate the Universal Gravitational Constant <i>G</i>Theoretically and Cubic Splines to Verify Its Measured Value

• 作者: Claude Mercier
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: Universal Gravitational Constant G NEWTON Cavendish EINSTEIN Cubic Splines
• 年，卷（期）: 2020,（9）
• 页码范围: 1428-1465
• 页数: 38页
• 分类号: O17

摘要

<p align="justify"> <span style="font-family:Verdana;"></span><span style="font-family:Verdana;"></span>In 1686, Newton discovered the laws of gravitation [<a href="#ref1">1</a>] and predicted the universal gravitational constant <img alt="" src="Edit_8cc6927a-fa86-44a2-a4e4-c2b809cba958.png" />. In 1798, with a torsion balance, Cavendish [<a href="#ref2">2</a>] measured <img alt="" src="Edit_f51d8d12-e299-4f0f-918d-d4b7cb9d5b9b.png" />. Due to the low intensity of gravitation, it is difficult to obtain reliable results because they are disturbed by surrounding masses and environmental phenomena. Modern physics is unable to link <i>G</i> with other constants. However, in a 2019 article [<a href="#ref3">3</a>], with a new cosmological model, we showed that <i>G</i> seams related to other constants, and we obtained a theoretical value of <img alt="" src="Edit_a2b7158e-b2db-4c33-bab7-898a8cbe0cad.png" />. Here, we want to show that our theoretical value of <i>G</i> is the right one by interpreting measurements of <i>G</i> with the help of a new technique using cubic splines. We make the hypothesis that most <i>G</i> measurements are affected by an unknown systematic error which creates two main groups of data. We obtain a measured value of <img alt="" src="Edit_d447fba6-cde2-4b05-8b67-d1bdbacd412b.png" /><span style="font-family:Verdana;"></span><span style="font-family:Verdana;"></span>. Knowing that our theoretical value of <i>G</i> is in agreement with the measured value, we want to establish a direct link between <i>G</i> and as many other constants as possible to show, with 33 equations, that <i>G</i> is probably linked with most constants in the universe. These equations may be useful for astrophysicists who work in this domain. Since we have been able to link <i>G</i> with Hubble parameter <em>H₀</em> (which evolve since its reverse gives the apparent age of the universe), we deduce that <i>G</i> is likely not truly constant. It’s value probably slowly varies in time and space. However, at our lo