Ignoring that it burned up and ignoring losses due to drag if it somehow didn’t. Isn’t the point of escape velocity that it explicitly won’t come back down.iar least not on earth. Your trajectory won’t matter as you have enough velocity to escape the gravity of earth and will orbit the sun. Further if you managed the solar system escape velocity you will end up orbiting the galactic core. Trajectory doesn’t matter if you have escape velocity. Correct trajectory just minimizes the delta v needed to reach that escape velocity.
At least that’s all my recollection.
Swedneck@discuss.tchncs.de 1 week ago
correction to your correction: it would not fall into the sun, falling into the sun is basically impossible, it would just end up in a highly eccentric orbit around the sun.
merc@sh.itjust.works 6 days ago
Yeah, “fall into the sun” was sort of hyperbole. If it truly got out into space and was going fast enough to escape Earth’s gravity, it would start orbiting with earth’s orbit plus some delta. Out of all the possible angles it could leave the earth, there are probably 2 angles where it would directly hit the sun One is the angle that cancels out all the orbital velocity of the earth and sends it directly at the sun, the other is the one that does the same but sends it directly away from the sun. Of all the possible trajectories on the surface of a sphere, only those two tiny solutions would end up with it contacting the sun, everything else would result in an orbit.
Of course, given enough time, it’s pretty likely that if it isn’t collected by a planet, it will eventually end up in the sun. There isn’t much friction in space, but there’s a tiny bit: solar wind, micrometeoroids, etc. Eventually its orbit would decay and it would stray too close to the sun.