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A231202 The smallest possible speed in m/s (rounded up) of an object whose relativistic mass is n times its rest mass. 1


%S 0,259627885,282647041,290272800,293735421,295599350,296717583,

%T 297441109,297936141,298289730,298551077,298749699,298904183,

%U 299026704,299125511,299206353,299273337,299329458,299376946,299417483,299452365,299482595,299508967,299532109

%N The smallest possible speed in m/s (rounded up) of an object whose relativistic mass is n times its rest mass.

%C First compute s(n) = c*sqrt(1 - 1/n^2), where c = 299792458 is the speed of light in vacuum (m/s). Then round up. Note that a(n) = c for n >= 12244, which implies that lim n -> infinity s(n) = c.

%D Lawrence S. Lerner, Physics for Scientists and Engineers, vol. 2, Jones and Bartlett, 1996, p. 1088.

%H Albert Einstein, <a href="http://users.physik.fu-berlin.de/~kleinert/files/1905_17_891-921.pdf">Zur Elektrodynamik bewegter K├Ârper</a>, Annalen der Physik, vol. 322, Issue 10, pp. 891-921. <a href="http://gallica.bnf.fr/ark:/12148/bpt6k2094597/f896.image.langEN">[gallica]</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Albert_Einstein">Albert Einstein</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Special_relativity">Special relativity</a>

%F a(n) = ceiling(A003678*sqrt(1 - 1/n^2)).

%e a(2) = 259627885 because 299792458*sqrt(1 - 1/4) = 259627884.4909793640....

%t c = 299792458; Table[Ceiling[c*Sqrt[1 - 1/n^2]], {n, 24}]

%o (MAGMA) c:=299792458; [Ceiling(c*Sqrt(1-1/n^2)) : n in [1..24]]

%o (PARI) c=299792458; vector(24, n, ceil(c*sqrt(1-1/n^2)))

%Y Cf. A003678.

%K nonn,easy

%O 1,2

%A _Arkadiusz Wesolowski_, Nov 05 2013

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