# 榭赫倫實驗

## 測量

### 勘測

1778年赫頓[17] 現代值[18]

## 數學步驟

$F = \frac {G m M_M} {d^2} ,\quad W = \frac {G m M_E} {r_E^2}$

$\frac {F} {W} = \frac {(G m M_M) / d^2} {(G m M_E) / r_E^2} = \frac {M_M}{M_E} {\left( \frac {r_E}{d} \right)}^2 = \frac {\rho_M} {\rho_E} \frac {V_M} {V_E} {\left( \frac {r_E}{d} \right)}^2$

$W = T \cos \theta ,\quad F = T \sin \theta$

$\tan \theta = \frac {F} {W} = \frac {\rho_M}{\rho_E} \frac {V_M}{V_E} {\left( \frac {r_E}{d} \right)}^2$

$\frac {\rho_E}{\rho_M} = \frac {V_M}{V_E} {\left( \frac {r_E}{d} \right)}^2 \frac {1}{\tan \theta}$

$\theta_N + \theta_S = \frac{r^2}{GM_E}(F_N+F_S)$

$\rho_E=\frac{3(F_N+F_S)}{4\pi r G (\theta_N+\theta_S)}$

## 參考資料

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2. ^ 2.0 2.1 Newton. Philosophiæ Naturalis Principia Mathematica II. : 528. ISBN 0521076471. Translated: Andrew Motte, First American Edition. New York, 1846
3. ^ 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Sillitto, R.M. Maskelyne on Schiehallion: A Lecture to the The Royal Philosophical Society of Glasgow. 31 October 1990 [28 December 2008].
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6. ^ 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 Poynting, J. H. The mean density of the earth. 1894: 12–22.
7. ^ Maskelyne, N. A proposal for measuring the attraction of some hill in this Kingdom. Phil. Trans. Royal Soc. 1772, 65: 495–499. Bibcode:1775RSPT...65..495M.
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10. ^ 10.0 10.1 The "Weigh the World" Challenge 2005. countingthoughts. 23 April 2005 [28 December 2008].
11. ^ 11.0 11.1 Poynting, J.H. The Earth: its shape, size, weight and spin. Cambridge. 1913: 56–59.
12. ^ 12.0 12.1 12.2 12.3 Maskelyne, N. An Account of Observations Made on the Mountain Schiehallion for Finding Its Attraction. Phil. Trans. Royal Soc. 1775, 65 (0): 500–542. doi:10.1098/rstl.1775.0050.
13. ^ 13.0 13.1 13.2 13.3 Poynting, J. H.; Thomson, J. J. A text-book of physics. 1909: 33–35. ISBN 1406773166.
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15. ^ Chalmers, A. The General Biographical Dictionary 25. 1816: 317.
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17. ^ 17.0 17.1 17.2 17.3 17.4 Hutton, C. An Account of the Calculations Made from the Survey and Measures Taken at Schehallien. Phil. Trans. Royal Soc. 1778, 68 (0): 689. doi:10.1098/rstl.1778.0034.
18. ^ 18.0 18.1 Planetary Fact Sheet. Lunar and Planetary Science. NASA. [2 January 2009].
19. ^ Boys, C. Vernon. On the Newtonian constant of gravitation. Nature. 1894, 50 (1292): 330–4. Bibcode:1894Natur..50..330.. doi:10.1038/050330a0.
20. ^ McCormmach, Russell; Jungnickel, Christa. Cavendish. American Philosophical Society. 1996: 340–341. ISBN 978-0871692207.
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22. ^ Hutton, Charles. On the mean density of the earth. Proceedings of the Royal Society. 1821.
23. ^ James. On the Deflection of the Plumb-Line at Arthur's Seat, and the Mean Specific Gravity of the Earth. Proceedings of the Royal Society. 1856, 146: 591–606. JSTOR 108603.
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