I was trying out a simulation about escape velocity to understand why direction has no impact on it here :http://highered.mheducation.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/0072482621/78778/Escape_Nav.swf::Escape%20Velocity%20Interactive
I understand that gravitational fields should be conservative, that is, getting from one equipotential line to another should require the same amount of energy no matter the path taken. That's what surprised me about this simulation (pictured below)
The "bottom" rocket (orange) was launched horizontally from earth whilst the "top" rocket (yellow) was launched vertically from earth at the same speed (exactly escape velocity). I would expect that for the same distance away, both rockets should have the same speed. What I'm not getting, is that the bottom rocket (orange) is both further away from earth AND has greater velocity (and hence energy) than the top rocket (yellow).
This to me seemingly tells me that the conservative nature of gravity is violated as it seems like it does depend on the path taken? Could someone please tell me where my interpretation is falling short?