According to the following diagram it would require ~648.69 km/s to do all of the intermediate transfers that would land you at or around the sun's surface at perigee. Is this a real number? How would they have calculated this number? Is the sun's mass and other quantities known well enough for this to be absolutely accurate? It seems like a massive number; am I reading this wrong?
I understand partially the vis-viva equations, but not in terms of the sun. It seems odd to use it around the body you're currently orbiting. Do I have to think of it in terms of a different frame of reference? I was thinking this is the delta-v for a non-circularized orbit with a lowest point being at the suns surface and the highest at Low Sun Orbit (that's my thought on the 440 number)... but I'm not sure.