Mass-energy equivalence and conservation of momentum I do not have a background with relativity, so expect some faux pas in this question.
Let's say I have a system of three balls moving through space. The three balls have a known total mass and a center of gravity with a known velocity, so we can calculate the the system's linear momentum. Now, let's say that some uranium on the balls undergoes fission, converting mass into energy. The total mass of the system has now been reduced. Does this violate conservation of momentum, as the momentum of the system have been reduced?
 A: The law of conservation of momentum applies to isolated systems. That is, in an isolated system the total momentum (of one, or many bodies) remains constant (unless an external force is applied).
If we consider your 3-body system to be isolated, and provided we include the momentum of the decay products, and the change in momentum of the objects that lost mass to decay, the total momentum of the system stays the same.
Provided there is no matter or energy leaving the system under consideration, the total momentum (and energy) is conserved.
A: This was, more or less, the subject of Einstein's second 1905 paper on relativity:  "Ist die Trägheit eines Körpers von seinem Energiegehalt abhängig?" (or in English, "Does the Inertia of a Body Depend upon its Energy Content?").  Einstein showed how the internal energy of a body contributed to the mass, energy, and momentum, and the paper is the origin of famous $E=mc^{2}$ equation—although the actual result in the paper was that $m=E/c^{2}$:  that the mass of a composite object depends on the internal energy $E$ of its components.
This means that, when the decay occurs, the mass of the composite does not actually change.  After the decay, the system is no longer just a three-body system, since there are additional decay products.  However, if we suppose that the initial mass is a large enough that the the decay products (including, say, an $\alpha$-particle/$^{4}$He nucleus from the decay of an atom of $^{235}$U) are still gravitationally bound, then the observed inertial mass of the whole composite system will be the same before and after the decay.  The potential energy stored in the parent $^{235}$U has been converted largely into kinetic energy for the $^{4}$He; however, both types of energy make the same contribution to the mass $m=E/c^{2}$ of the composite system.
