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Astronomy.com's Here's why we can't just rocket nuclear waste into the sun is an excellent explanation of the delta-V required to launch from Earth orbit into the Sun (30 km/s) vs. to escape from the solar system (11 km/s). So a minimum energy strategy to hit the Sun would be to reach nearly escape velocity, wait to reach apogee at a near-infinite distance, then kill all angular velocity at apogee.

But is it possible to slingshot angular velocity to zero within the solar system in order to hit the Sun using less than 11 km/s of acceleration? Something like skimming just ahead of Jupiter in its orbital path and being flung backwards?

It shouldn't be too hard to write a 2d numerical simulation to visualize the possibilities, but surely someone has already answered the question of whether the minimum delta-v is less than that required for the near-infinite distance maneuver. (see Has any object launched from Earth gone into the Sun?, @StarMan's answer to Do you need 0 km/s velocity to crash into the sun?).

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As already pointed out in @Slarty's answer and other linked answers, 0 velocity (w.r.t Sun) is not required to hit the Sun. I did a search for trajectories that launch from Earth within the next year and fly by Jupiter (without hitting Jupiter) within the next 10 years before hitting the Sun within the next 12 years from now.

The most efficient trajectory from that search is (Earth, Jupiter, Sun not to scale):

most efficient Sun crash via Jupiter

which, from a 1 AU circular orbit, requires 10.7 km/s of $\Delta V$ versus the 12.3 km/s required of the solar system escape approach (not 11 km/s as stated in the question). It is also significantly faster (time wise).

Interpreting the plot; there is no out of plane hidden motion here. Jupiter slows the spacecraft to near 0 speed (~600 m/s w.r.t Sun) and it proceeds to fall more or less directly into the Sun.

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    $\begingroup$ Awesome, thanks! $\endgroup$
    – Dave
    Oct 3 at 14:40
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The inner planets can be used for gravity assist to increase or decrease velocity. As an example in order to get directly to Mercury the delta V is around 12.5km/s or more. However if you are prepared to have a spacecraft shuttle around the inner solar system for 7 years or more then the delta V can be reduce to 4km/s https://issfd.org/ISSFD_2014/ISSFD24_Paper_S6-5_jehn.pdf The amount of deltaV required depends on the time of launch, the alignment of the planets at the time and how long you are prepared to let the craft drift around for.

So the deltaV might be relatively low if a suitable alignment of the planets can be found. But calculating these orbits is far from easy as there is a vast array of possibilities involving the 3 inner planets and expenditure of deltaV to make adjustments at any point over a period of perhaps tens of years makes the problem even harder.

A direct hit on the centre of the Sun is not required as the Sun is almost 700,000km in radius, so an orbit of 500,000km radius is in fact a hit. Although it is doubtful much of a space craft would survive to reach the Sun itself.

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