Conservation law at high speeds

[stevebd1]

While I understand (in principle) the relationship of gravitational potential energy, kinetic energy and the conservation law in a system for an object falling towards a large mass, I'm not so familiar with how this is applies to an object traveling at high speeds. Say in the example of a spaceship, are we supposed to assume that the potential energy is the fuel on board which is slowly converted to kinetic energy as the object builds up in speed (allowing for some 'work done' quantity) so that the conservation law applies as potential energy reduces (fuel being used) kinetic energy increases? Also how does the conservation law apply at ultra-high speeds where the kinetic energy increases exponentially relative to the Lorentz factor?

 

[Dale]

Here is a good page for relativistic rockets.

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html