this post was submitted on 17 Mar 2024
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There are no spiral orbits. Canceling the forward motion is exactly what you need to do, to bring down the next periapsis to 0. Now, you can go with a periapsis of about half a million km, because the sun is pretty big, but that is not a significant difference. Getting anywhere near the sun, is the hard part.
It's much more efficient in this case to do a bi-elliptic transfer: raise apoapsis very far out, then lower your periapsis once you are at apoapsis. Wikipedia says you could do it with about 8.8 km/s delta v. Versus 24 or so for a basic Hohman transfer (still a bit better than 30)
Sadly the bi-elliptic transfer requires two burns so you can't do it with a kick.