The military falls under the jurisdiction of the legislative portion of the government because Congress (which is the legislative branch) has the ability to declare war. Since Congress has the ability to declare war, not having a military would greatly affect their ability to protect the US. This was one of several problems within the Articles of Confederation. The Articles of Confederation was America's first constitution and was eventually replaced after less than a decade by the US Constitution (still in use today).
"In the US it would be up to the administration to direct the building
and formation of military assets and up to the legislative branch to
approve the funds and give their permission to send the troops to an
official war. The judicial branch would be called upon to make sure that
what both the administration and legislature does to and for the
military is legal. Economics will determine what is possible from a
monetary standpoint."
