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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.

%I A231202 #34 Sep 22 2024 17:34:06
%S A231202 0,259627885,282647041,290272800,293735421,295599350,296717583,
%T A231202 297441109,297936141,298289730,298551077,298749699,298904183,
%U A231202 299026704,299125511,299206353,299273337,299329458,299376946,299417483,299452365,299482595,299508967,299532109
%N A231202 The smallest possible speed in m/s (rounded up) of an object whose relativistic mass is n times its rest mass.
%C A231202 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 A231202 Lawrence S. Lerner, Physics for Scientists and Engineers, vol. 2, Jones and Bartlett, 1996, p. 1088.
%H A231202 Albert Einstein, <a href="http://users.physik.fu-berlin.de/~kleinert/files/1905_17_891-921.pdf">Zur Elektrodynamik bewegter Körper</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 A231202 Wikipedia, <a href="http://en.wikipedia.org/wiki/Albert_Einstein">Albert Einstein</a>
%H A231202 Wikipedia, <a href="http://en.wikipedia.org/wiki/Special_relativity">Special relativity</a>
%F A231202 a(n) = ceiling(A003678*sqrt(1 - 1/n^2)).
%e A231202 a(2) = 259627885 because 299792458*sqrt(1 - 1/4) = 259627884.4909793640....
%t A231202 c = 299792458; Table[Ceiling[c*Sqrt[1 - 1/n^2]], {n, 24}]
%o A231202 (Magma) c:=299792458; [Ceiling(c*Sqrt(1-1/n^2)) : n in [1..24]];
%o A231202 (PARI) c=299792458; vector(24, n, ceil(c*sqrt(1-1/n^2)))
%Y A231202 Cf. A003678.
%K A231202 nonn,easy
%O A231202 1,2
%A A231202 _Arkadiusz Wesolowski_, Nov 05 2013