  The equivalence of mass and energy is indelibly linked with relativity, both
by scientists and in the popular mind. I prove that E = mc^2 by demanding
momentum conservation of an object that emits two equal electromagnetic wave
packets in opposite directions in its own frame. In contrast to Einstein's
derivation of this equation, which applies energy conservation to a similar
thought experiment, the new derivation employs no effects that are greater than
first order in v/c and therefore does not rely on results from Special
Relativity. In addition to momentum conservation, it uses only aberration of
starlight and the electromagnetic-wave momentum-energy relation p=E/c, both of
which were established by 1884. In particular, no assumption is made about the
constancy of the speed of light, and the derivation proceeds equally well if
one assumes that light is governed by a Galilean transformation. In view of
this, it is somewhat puzzling that the equivalence of mass and energy was not
derived well before the advent of Special Relativity. The new derivation is
simpler and more transparent than Einstein's and is therefore pedagogically
useful.
