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I've already searched Physics StackExchange for some similar question but I didn't find anything about this.


  • Earth is a perfect sphere with it's core (X,Y,Z) -> (0,0,0) as a reference-frame center
  • Air resistance can be ignored
  • Earth rotation can be ignored
  • Moon gravity-effect can be ignored

And if I know (projectile starting properties):

  • Current Earth GPS-coordinates
  • Starting angle
  • Starting direction (relative to (0,0,0))
  • Starting velocity (can be larger than Earth-escaping speed)
  • (mass of the projectile is irrelevant (I guess) when we know starting velocity of the projectile)

How could I calculate aprox. coordinates of a projectile landing somewhere around the Earth globe (OR detect that projectile will "leave" the Earth)?

EDIT: I've found tons of links on the net about projectile trajectories when starting velocities are quite small (& Earth can be considered like a flat plane), but non about upper situation.

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You can do it with Keplar's laws. The formulas do not come out particularly simple. – Steve B Nov 21 '11 at 13:51
As Steve says: compute the orbit and find the intersections with the surface. But neglecting air resistance is silly for cases where the projectile lands far around the globe (because small changes in the speed and course when leaving the atmosphere will make a big difference in range.) and even sillier for projectiles very near escape speed (because small changes can switch which behavior is exhibited). – dmckee Nov 21 '11 at 16:17
Thx both of you for your comments! I know air resistance has a huge influence on a trajectory, but in my (specific) case (-> computer game) it can be neglected. Anyways, thx again! :-) – sabiland Nov 22 '11 at 11:42
@sabiland: if you're doing a computer game, then you are just timestepping the projectile, right? You know that it's coming down because you do the simulation, and you see it coming down. – Jerry Schirmer Apr 1 '13 at 20:17
Might this be what you're looking for? – David Z Sep 5 '14 at 23:14

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