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One unique feature of Spaceflight Simulator is that you can "land" on The Sun. This would be impossible in real world. Solar atmosphere is very dense and lacks turbulences. Also, heat does not affect the ship.
The Sun has a huge gravity and the densest atmosphere in the system. You can send a ship towards it, but you will never be able to liftoff.
Reaching The Sun
A ship that escapes Earth's Sphere of Influence will be in heliocentric orbit. From there, it can lower its perigee by firing backwards. This comes with a huge fuel cost.
A more easy way to reach the Sun is to rise the apogee, beyond the orbit of Mars, maybe to Jupiter, which is not currently implemented. From there, lowering the perigee is very easy, until a crash trajectory is achieved. The ship will accelerate then will dramatically slow down in Sun's atmosphere.
Using a parachute is useless, because the ship will be slowed down. Even without a parachute, when the ship reaches altitude of 0 meters, it will move very slow.
At The Sun
After reaching altitude zero, a ship continues to descend for a long period of time, slower and slower. The ship finds itself unable to move. Even the most powerful engines cannot adjust trajectory or speed significantly. It appears that, after a long period of time, the ship vanishes. In a homage to KSP, it shall be named The Kraken.
See Heliocentric Orbit Activities for activities done around the Earth's orbit.
Scientists want to explore the environment surrounding the Sun. This is why NASA is building Solar Probe Plus, which will come very close to the Sun. This can be simulated here very well. A ship can be sent on a highly elongated ellipse that will take it very close to the Sun, even touching the atmosphere. If this happens, the ship will slowly spiral towards the Sun.
It is possible to accelerate a ship until it will fly on a hyperbolic trajectory. However, if this is done, once the ship achieves Sun escape velocity, it will no longer have an orbital path displayed on the map.
Still, it is possible to come very close to the Sun, then return. See Sun Return Mission for more details.