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## Main Question or Discussion Point

Could somebody please explain the following equation for me?

ds^2 = −c^2 dt^2 + [dx − v

I've wrestled with it for a while, but quite frankly do not get it. I'm only up through Calc II, but I'm more than happy to learn a few new concepts, should the need arise. This uses the familiar coordinates, (t, x, y, z) and curve x = x

ds^2 = −c^2 dt^2 + [dx − v

_{s}(t)f(r_{s})dt]^2 + dy^2 + dz^2 where f(r_{s})=(tanh(σ(r_{s}+ R)) − tanh(σ(r_{s}− R)))/(2tanh(σR).I've wrestled with it for a while, but quite frankly do not get it. I'm only up through Calc II, but I'm more than happy to learn a few new concepts, should the need arise. This uses the familiar coordinates, (t, x, y, z) and curve x = x

_{s}(t), y = 0, z=0 where x is analogous to what is commonly referred to as a spacecraft’s trajectory.