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How come? Don't you "just" have to escape the earth's gravity?

Orbital mechanics, Earth does not fall to Sun because it is going around Sun pretty fast. To drop in Sun you have to lose this velocity. And there is no mentionable drag. Kinda similar how satellites around Earth need to go fast too to stay up. Go fast enough and you get out, but you are still stuck with sun.

To expand on and put numbers to this: to escape the solar system from Earth, you need to add about 17 km/s on top of the energy you start with by working from Earth's orbital energy. Earth is going about 30 km/s around the Sun, which helps quite a lot!

However, this also means that to hit the Sun, you need to remove more or less all of the energy that Earth starts you with. This is the key insight - if you do a bit too much or a bit too little, it slingshots around the Sun (getting close to it but not going into it) and stays in orbit rather than landing in the Sun.

Nope. You’re in orbit around the sun too. You have to modify your solar orbit so the short axis of your ellipse is close enough to fall in with atmospheric drag.

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