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But that phrasing was nonsense because so much of this is kinetic vs potential energy, which doesn't really work with that phrasing. A lot of folks asked "orbiting mercury or reaching a similar orbit of Mercury?" As I phrased it it actually doesn't matter.
Ultimately the only difference between orbiting a planet and being in the same solar orbit as that planet is whether you're next to it or not. While orbiting Mercury might take less Δv than getting to the same solar orbit, the laws of physics say that can't take less energy.
The difference here is ultimately that when performing orbital insertion, you're stealing energy from Mercury relative to the sun, slowing it down slightly. That's where the difference in Δv costs comes from. (Physics degrees don't @ me about potential energy plz)
This is also why all of this is cheaper if you start from Earth instead of heliocentric orbit. When considering only 2 bodies, you're just manipulating your exhaust's kinetic energy to go faster. When considering 3 bodies, you're slowing down Earth relative to the Sun.
You can remove this from the equation by just starting from a heliocentric orbit with the same SMA as Earth, and looking at the Δv required to get to 142Mmx29 vs 58x58. You'll see that getting to the sun still takes far more Δv. (it's close though, the plane change might tip it)
Anyway, for anyone who I lost 20 tweets ago... The answer is the sun. Parker solar probe is incredible, its mission is insanely ambitious, and probably harder than anything else we'll do in our lifetimes. You should go read more about it.
For the KSP players who knew the insane Δv requirements of Mercury and also remembered that bi-elliptic transfers exist (unlike me when making this poll), you are correct. If you don't care about perihelion, that is the hardest place in this list to reach.
For those with physics degrees who are noticing that my aside about Oberth would interact with the Sun's velocity, and I should have considered Earth/AC transfer from galactic orbit by my own rules... I couldn't find enough concrete numbers to do the math.
All I could really find is that we are travelling 20km/s relative to stars in our local neighborhood, which may or may not apply to AC, and by itself doesn't imply a large enough maneuver to beat orbit of Mercury. I would love to be proven wrong here though!
I'm done. Folks with physics degrees, you can @ me now. I'm sorry for subtweeting you so hard.
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