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

0, 259627885, 282647041, 290272800, 293735421, 295599350, 296717583, 297441109, 297936141, 298289730, 298551077, 298749699, 298904183, 299026704, 299125511, 299206353, 299273337, 299329458, 299376946, 299417483, 299452365, 299482595, 299508967, 299532109

Offset

1,2

Comments

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.

References

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

Links

Table of n, a(n) for n=1..24.

Albert Einstein, Zur Elektrodynamik bewegter Körper, Annalen der Physik, vol. 322, Issue 10, pp. 891-921. [gallica]

Wikipedia, Albert Einstein

Wikipedia, Special relativity

Formula

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

Example

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

Mathematica

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

Prog

(Magma) c:=299792458; [Ceiling(c*Sqrt(1-1/n^2)) : n in [1..24]];
(PARI) c=299792458; vector(24, n, ceil(c*sqrt(1-1/n^2)))

Crossrefs

Cf. A003678.

Sequence in context: A246224 A205934 A375975 * A226448 A250433 A329464

Adjacent sequences: A231199 A231200 A231201 * A231203 A231204 A231205

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Nov 05 2013

Status

approved