Acceleration to lightspeed using gravity Suppose we have a very advanced spaceship that (aside from colliding with planets or entering a blackhole) is indestructable, and can go very fast, but is incapable of moving at lightspeed on it's own. 
Under these circumstances is it theoretically possible to accelerate the ship to light speed using the gravity well of a massive entity?
For example, if the ship perhaps entered Jupiter's gravity well, and attempted to revolve around Jupiter x amount of times, is it possible to use that force to "slingshot" away from the planet at lightspeed?
What would likely be the most time efficient entity to use in this way considering the nearest black hole is 6,070 light years away? Roughly how long might this take?
 A: I quite sure it's not theoretically possible. Without doing any actual calculations, I recall that accelerating a massive object to light speed would require an infinite amount of energy. Some energy certainly can be gained with the "slingshot" method, but definitely not an infinite amount.
Specifically, it's the Lorentz factor that prevents objects from reaching speed of light. It's a correction factor for many quantities (time, length, etc.) that has to be taken into account at high speeds, when things stop being classical. It's negligibly small in everyday situations, but goes to infinity when speed approaches the speed of light:
$\gamma = \frac{1}{\sqrt{1-v^2/c^2}},$
where $c$ is the speed of light and $v$ is the speed of the object (or a frame of reference). For an object to accelerate from rest to a speed $v$ the requires energy is
$\frac{mc^2}{\sqrt{1-v^2/c^2}}-mc^2,$  
where $m$ is the object's mass.
More reading:
http://en.wikipedia.org/wiki/Lorentz_factor
http://en.wikipedia.org/wiki/Kinetic_energy#Relativistic_kinetic_energy_of_rigid_bodies
A: Light speed is something of a cosmic speed limit.  Nothing can exceed the speed of light, and only massless particles can travel at light speed. Any particle with mass would require an infinite amount of energy to accelerate to the speed of light. 
