The sun's escape velocity is about 42 km/s. Earth's orbital velocity is about 30km/s.
To go straight from Earth to the sun, you'd need to shed almost all that speed, meaning you'd need to accelerate by nearly 30km/s. To leave the solar system, you'd only need to accelerate by about 12km/s.
That said, as someone else pointed out, there's an interesting irony: Since objects closer to the sun orbit faster than ones that are far away, the cost to go to the sun is generally higher the closer you are. (The exception is if you're already more-or-less on a collision course.) So, if you've got the time, it's cheaper to go away first. You can think of it as sort of a way of using the sun's gravity to do most the work of slowing you down.
If we replace "toward the sun" with "away from earth", you'd have to get to a bit over 11km/s relative to earth. From geostationary orbit (3ish km/s), that's kind of expensive. Again with the counter-intuitive, it's actually cheaper to get away from Earth from low earth orbit, where you'd be starting from a speed of more like 7km/s.
This all starts feeling really intuitive after a couple hours of playing Kerbal Space Program. :)
The sun's escape velocity is about 42 km/s. Earth's orbital velocity is about 30km/s.
To go straight from Earth to the sun, you'd need to shed almost all that speed, meaning you'd need to accelerate by nearly 30km/s. To leave the solar system, you'd only need to accelerate by about 12km/s.
That said, as someone else pointed out, there's an interesting irony: Since objects closer to the sun orbit faster than ones that are far away, the cost to go to the sun is generally higher the closer you are. (The exception is if you're already more-or-less on a collision course.) So, if you've got the time, it's cheaper to go away first. You can think of it as sort of a way of using the sun's gravity to do most the work of slowing you down.
If we replace "toward the sun" with "away from earth", you'd have to get to a bit over 11km/s relative to earth. From geostationary orbit (3ish km/s), that's kind of expensive. Again with the counter-intuitive, it's actually cheaper to get away from Earth from low earth orbit, where you'd be starting from a speed of more like 7km/s.
This all starts feeling really intuitive after a couple hours of playing Kerbal Space Program. :)