Search: a070058 -id:a070058
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A003678
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Decimal expansion of the SI unit c (speed of light in vacuum), c = 299792458 meters/second.
(Formerly M1912)
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+10
76
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OFFSET
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9,1
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COMMENTS
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Since 1983, the speed of light has been defined to be exactly 299792458 m/s. - Ron Marcinski (ronmarcinski(AT)hotmail.com), Apr 18 2002
General context: Within current metrological systems (SI + IAU definitions), several physics constants have been "assigned" immutable values. They thus became metrological reference points, no longer subject to experimental assessment. These should not be confused with "conventional" values of some empirical quantities (such as Josephson's constant) used in applied metrology, but not assigned, and therefore subject to possible future revisions.
Assigned metrological constants [before the inception of the 2019 SI, which introduced some changes, see below for references] and some of their combinations that appear in the OEIS include the speed of light (this sequence); magnetic permeability of vacuum (A019694); electric permittivity of vacuum (A081799); characteristic impedance of vacuum (A213610); standard gravity acceleration (A072915), standard atmosphere (A213611), Julian year (A213612), Gregorian year (A213613) and the light-year (A213614), all in basic SI units.
(End)
Prime factors of this number are 2^1, 7^1, 73^1, 293339^1. - John W. Nicholson, Jun 15 2014
c is also the speed of gravity. - Omar E. Pol, Jun 23 2017
In the 2019 SI system of units (see the second BIPM link, and A322415) one of the seven defining constants is c = 299792458 m/s. - Wolfdieter Lang, Feb 12 2019 [corrected by Ivan Panchenko, May 20 2019]
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REFERENCES
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CRC Handbook for Chemistry and Physics, 75th edition, (1994-1995), Page 1-1.
H. J. Fischbeck and K. Fischbeck, Formulas. Facts and Constants, Springer-Verlag, NY, 2nd ed., 1987.
R. F. Fox and T. P. Hill, An exact value for Avogadro's number, American Scientist, 95 (No. 2, 2007), 104-107.
K. R. Lang, Astrophysical Data: Planets and Stars, Springer-Verlag, NY, 1991.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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c = 299792458 m/s (equals 299792.458 km/s).
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MATHEMATICA
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CROSSREFS
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More assigned constants: A003676 (h), A230458 (Δν_{Cs}), A081823 (e), A322578 (N_A), A070063 (k), A021687 (1/K_{cd}); A182999 (c^2), A183000 (c^3), A183001 (c^4), A019694, A081799, A213610, A072915, A213611, A213612, A213613, A213614.
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KEYWORD
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AUTHOR
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STATUS
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approved
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A070063
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Decimal expansion of the Boltzmann constant k in the 2019 SI system in units J/K.
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+10
23
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OFFSET
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-22,2
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COMMENTS
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The exact Boltzmann constant is one of the seven units in the 2019 system of units. See the BIMP link with the CGPM resolutuions from November 2018 which will become effective May 20 2019. See also A322415. - Wolfdieter Lang, Feb 12 2019
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REFERENCES
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CRC Handbook for Chemistry and Physics, 75th edition, (1994-1995), Page 1-1.
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LINKS
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BIPM, CGPM-2018 [See the link ``Resolutions of the CGPM" there.]
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FORMULA
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k = 1.380649×10^{-23} J/K. Joule J = kg m^2 s^(-2).
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CROSSREFS
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KEYWORD
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AUTHOR
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Ron Marcinski (ronmarcinski(AT)hotmail.com), Apr 18 2002
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EXTENSIONS
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Updated to conform with CODATA 2010 value by Ivan Panchenko, Jan 27 2015
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STATUS
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approved
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A070064
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Decimal expansion of the molar gas constant R according to the 2019 SI system in units J mol^-1 K^-1.
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+10
16
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8, 3, 1, 4, 4, 6, 2, 6, 1, 8, 1, 5, 3, 2, 4
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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CROSSREFS
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Cf. A081822 (constant according to IUPAC).
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KEYWORD
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AUTHOR
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Ron Marcinski (ronmarcinski(AT)hotmail.com), Apr 18 2002
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EXTENSIONS
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Updated to the May 20 2019 redefinition of the SI base units by Sean A. Irvine, Jun 20 2019
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STATUS
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approved
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A070059
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Decimal expansion of proton mass (in kilograms).
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+10
11
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OFFSET
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-26,2
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REFERENCES
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CRC Handbook for Chemistry and Physics, 75th edition, (1994-1995), Page 1-1.
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LINKS
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FORMULA
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1.672621777(74) * 10-27 kg (2010 value).
1.672 621 923 69(51) * 10^(-27) kg (2018 value). - Ivan Panchenko, May 30 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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Ron Marcinski (ronmarcinski(AT)hotmail.com), Apr 18 2002
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EXTENSIONS
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Corrected by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 16 2004
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STATUS
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approved
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A183001
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Decimal expansion of the integer c^4 where c = 299792458 (exactly) is the speed of light in vacuum (m/s).
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+10
7
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8, 0, 7, 7, 6, 0, 8, 7, 1, 3, 0, 6, 2, 4, 9, 0, 2, 2, 9, 2, 6, 3, 8, 0, 0, 7, 4, 6, 1, 5, 1, 6, 9, 6
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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34,1
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COMMENTS
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Also decimal expansion of the product of Newtonian constant of gravitation and Planck force. - Omar E. Pol, Sep 29 2013
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LINKS
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FORMULA
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EXAMPLE
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c^4 = 299792458^4 = 8077608713062490229263800746151696 [meter^4/second^4].
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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A228817
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Decimal expansion of Planck force: F_P = c^4/G, in SI units.
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+10
6
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OFFSET
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45,2
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COMMENTS
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According to the law of universal gravitation, the attractive force (F) between two bodies is proportional to the product of their masses (m_1 and m_2), and inversely proportional to the square of the distance, r, between them. Newton's formula is F = G*m_1*m_2/r^2, where G is the constant of gravitation. Using both the Planck force (F_P) and Einstein's formula E = m*c^2, the law of universal gravitation could be written as F = (G/c^4)*m_1*c^2*m_2*c^2/r^2 = E_1*E_2/(F_P*r^2), where E_1 and E_2 are the energies of the bodies.
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LINKS
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FORMULA
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EXAMPLE
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F_P = c^4/G = 8077608713062490229263800746151696 (m^4/s^4)/(6.67384...*10^-11 (m^3)/(kg*s^2)) ~ 1.2103...*10^44 (kg*m/s^2), where c is the speed of light in vacuum and G is the Newtonian constant of gravitation.
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A228818
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Decimal expansion of G/c^4 in s^2/(kg * m), where G is the gravitational constant and c = 299792458 m/s is the speed of light in vacuum.
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+10
6
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OFFSET
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-44,1
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COMMENTS
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Also decimal expansion of 1/F_p where F_p is the Planck force, see A228817.
According to the law of universal gravitation, the attractive force (F) between two bodies is proportional to the product of their masses (m_1 and M2), and inversely proportional to the square of the distance (r) between them. The Newton's formula is F = G*m_1*m_2/r^2, where G is the constant of gravitation. Using both the Planck force (F_P) and the Einstein's formula E = m*c^2 the law of universal gravitation could be written as F = (G/c^4)*m_1*c^2*m_2*c^2/r^2 = E_1*E_2/(F_P*r^2), where both E_1 and E_2 are the energies of the bodies.
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LINKS
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FORMULA
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EXAMPLE
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G/c^4 = 6.67384...*10^-11 [(m^3)/(kg*s^2)]/299792458^4 [m^4/s^4] = 8.262...*10^-45 [s^2/(kg*m)] = 0.000000000000000000000000000000000000000000008262... [s^2/(kg*m)].
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A353769
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Decimal expansion of the gravitational acceleration generated at the center of a face by a unit-mass cube with edge length 2 in units where the gravitational constant is G = 1.
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+10
5
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6, 4, 9, 2, 2, 4, 1, 4, 4, 5, 6, 4, 5, 9, 1, 2, 6, 4, 7, 1, 2, 4, 7, 4, 7, 4, 2, 4, 4, 6, 6, 8, 2, 0, 3, 1, 5, 3, 5, 9, 5, 0, 1, 6, 4, 6, 9, 1, 0, 4, 1, 9, 3, 1, 3, 4, 8, 7, 8, 0, 0, 3, 3, 4, 0, 3, 3, 2, 2, 1, 2, 8, 6, 1, 7, 1, 1, 1, 5, 9, 9, 4, 3, 1, 3, 1, 4, 4, 2, 9, 8, 3, 8, 6, 5, 2, 6, 4, 0, 8, 2, 9, 9, 0, 0
(list;
constant;
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listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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The absolute value of the gravitational attraction force between a homogeneous cube with mass M and edge length 2*s and a test particle with mass m located at the cube's center of face is c*G*M*m/s^2, where G is the gravitational constant (A070058) and c is this constant.
The centers of the faces are the positions where the gravitational field that is generated by the cube attains its maximum absolute value.
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LINKS
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Murray S. Klamkin, Extreme Gravitational Attraction, Problem 92-5, SIAM Review, Vol. 34, No. 1 (1992), pp. 120-121; Solution, by Carl C. Grosjean, ibid., Vol. 38, No. 3 (1996), pp. 515-520.
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FORMULA
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Equals Pi/2 + log((sqrt(2) + 1)*(sqrt(6) - 1)/sqrt(5)) - 2*arcsin(sqrt(2/5)).
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EXAMPLE
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0.64922414456459126471247474244668203153595016469104...
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MATHEMATICA
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RealDigits[Pi/2 + Log[(Sqrt[2] + 1)*(Sqrt[6] - 1)/Sqrt[5]] - 2*ArcSin[Sqrt[2/5]], 10, 100][[1]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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A353770
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Decimal expansion of the gravitational acceleration generated at a vertex by a unit-mass cube with edge length 2 in units where the gravitational constant is G = 1.
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+10
5
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4, 1, 9, 7, 5, 7, 3, 3, 9, 8, 8, 7, 1, 0, 6, 2, 9, 1, 8, 7, 3, 7, 4, 7, 6, 8, 7, 2, 0, 0, 8, 1, 3, 9, 0, 9, 6, 0, 5, 8, 5, 6, 1, 0, 2, 7, 6, 1, 7, 7, 2, 6, 6, 1, 3, 8, 7, 8, 2, 7, 5, 6, 1, 7, 1, 2, 7, 6, 5, 7, 4, 5, 1, 0, 4, 7, 7, 6, 7, 5, 7, 6, 6, 1, 4, 8, 8, 7, 0, 3, 0, 2, 5, 9, 9, 8, 8, 7, 0, 6, 4, 5, 9, 7, 1
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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The absolute value of the gravitational attraction force between a homogeneous cube with mass M and edge length 2*s and a test particle with mass m located at the cube's vertex is c*G*M*m/s^2, where G is the gravitational constant (A070058) and c is this constant.
The vertices are the positions where the gravitational field that is generated by the cube on its surface attains its minimum absolute value.
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LINKS
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Murray S. Klamkin, Extreme Gravitational Attraction, Problem 92-5, SIAM Review, Vol. 34, No. 1 (1992), pp. 120-121; Solution, by Carl C. Grosjean, ibid., Vol. 38, No. 3 (1996), pp. 515-520.
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FORMULA
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Equals (sqrt(3)/2)*(Pi/12 + log(sqrt(2) + 1) - log(sqrt(3) + 2)/2).
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EXAMPLE
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0.41975733988710629187374768720081390960585610276177...
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MATHEMATICA
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RealDigits[(Sqrt[3]/2)*(Pi/12 + Log[Sqrt[2] + 1] - Log[Sqrt[3] + 2]/2), 10, 100][[1]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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A125125
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Decimal expansion of the geocentric gravitational constant (mass of Earth's atmosphere included) of the World Geodetic System 1984 Ellipsoid, second upgrade.
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+10
4
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OFFSET
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15,1
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COMMENTS
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Closely aligned with ITRF93, 29 Sept 96 onwards.
The new World Geodetic System is called WGS 84. It is currently the reference system being used by the Global Positioning System. It is geocentric and globally consistent within +-1 m.
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REFERENCES
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H. Moritz, Geodetic Reference System 1980, Journal of Geodesy 74 (1): 128-162, 2000. (not WGS 84)
Thaddeus Vincenty, Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations, Survey Review XXII (176): 88-93, 1975.
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LINKS
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U.S. Dept. of Commerce, NOAA, National Geodetic Survey, Survey Review, Thaddeus Vincenty, Direct and Inverse Solutions of Geodesics on the Ellipsoid with Application of Nested Equations, Vol. XXIII, No. 176, April, 1975. (an application)
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FORMULA
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EXAMPLE
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GM = (3986004.418 +- 0.008) * 10^8 m^3/s^2.
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MATHEMATICA
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(* first do *) Needs["GeometricalGeodesy`ReferenceEllipsoids`"]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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