Because the Earth is really cookin’, and anything anyone you hurl toward the sun will inherit that orbital velocity as well, meaning that they’ll actually end up going around the sun, instead of into it. And due to the speed it would pick up on its way in, it would basically take up a highly-eccentric yet stable elliptical orbit.
“Well, what if we throw them in the other direction, to make up for it?” That’s called retrograde, and that’s basically exactly what you’d have to do: cancel out the Earth’s entire orbital velocity. Which would take a lot of energy, plus a couple of really exacting gravity assists from planets on the way in.
(Edit to add: I may have explained this poorly. Basically, if you don’t change your orbital speed at all, any movement you make toward or away from the host body means you just end up in an orbit of the same average distance, but in a more eccentric [elliptical] shape.)
By contrast, even though the escape velocity from the solar system is no slouch (42 km/s), you get to start with the Earth’s orbital velocity (30 km/s)–meaning you’re already a little under 3/4 of the way there. Plus, if you can make it to Jupiter and Saturn, you can get a significant gravity assist, and they’re much bigger targets for such a maneuver than Mercury or Venus are.
So, yeah, bottom line: you only need a delta-V of about 12 km/s to get out of the solar system, but a delta-V of 30 km/s to get to the sun without going into orbit.
That’s assuming all cows are a point on a frictionless 2 dimensional plane.
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you don’t need to hit the sun dead center to be incinerated.
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the sun is huge
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you aren’t in a frictionless environment, your orbit will decay into the sun.
These are all technically correct but fairly inconsequential. Even just to graze the sun you need to lose 90% of your orbital velocity. And although everything orbiting the sun will eventually fall in, the friction is really low. It will take billions of years to lose enough velocity to fall in.
So, yeah, bottom line: you only need a delta-V of about 12 km/s to get out of the solar system, but a delta-V of 30 km/s to get to the sun without going into orbit.
This is true, but the possibility of gravity assists mostly nullifies the difference. If you can get out to Jupiter you can basically choose: either let it sling you out of the system, or let it cancel out all your orbital velocity so you fall into the sun.
I feel like that might be difficult to do without just falling into Jupiter, but I am no rocket scientist.
Why would you need to entirely cancel the earths orbital velocity, surely you just need to cancel a tiny bit of orbital velocity?
Edit: https://space.stackexchange.com/questions/43913/do-you-need-0-km-s-velocity-to-crash-into-the-sun
Good question, but if you cancel out only a little bit of orbital velocity, you just orbit in a little bit closer. Without any appreciable drag acting on you, there’s nothing that will keep your orbit decaying. You’ll just be in a smaller, perhaps slightly more eccentric orbit.
You can just change the shape of your orbit (but not your orbital energy) with the help of a sufficient gravity well from solar orbit, so it intersects with the Sun. Drag (aerobraking!) within the Sun will slow whatever is left of you enough to sap your orbital energy
