〈 Berger | Dillon 〉

that is an interesting question

All the masses start at zero velocity, so going relativistic means essentially having a VERY high starting point

right, but i was thinking if we just added an equivalent initial velocity to all of them

And it would need to be a VERY massive object to provide much gravitational effect. The story goes that Isaac Newton dispatched this problem in a single night, after all the continental giants had worked on Bernoulli's challenge for months. "I know the lion by his roar." J.B.

Right but we don’t have to assume gravity is what makes them speed up to relativistic speeds. We can ask what will happen if they start at those high speeds

What would be the deflecting force then that caused them to deviate their paths? 2nd Law issues arise I think? Not a physicist so...forgive my ignorance.

They don’t get deflected but there’s length contraction and time dilation effects you’d have to consider

So then the answer to the original question falls apart? I was assuming these to be freely moving bodies, not on a track. If they begin by moving at near C in the same direction, their paths will remain the same no cycloid, no right angle bend, all three same geodesic path?