# How accurately can an asteroid's path be calculated?

I have read a bit about the asteroid 99942 Apophis, and I have found that its approach in 2029 is predicted to be as close as 31,200km.

I may be oversimplifying this a little, but given the Earth orbits the Sun at 30km per second, then surely the "ETA" of the asteroid on Earth's orbit only has to be wrong by just over a thousand seconds for it to hit Earth.

I appreciate that even if the predictions are wrong, the likelihood of an impact on Earth is still relatively small, but surely it isn't possible to predict the position of an asteroid in 11 years time to within just over a quarter of an hour? Therefore, how come the possibility of an impact with Earth has been completely eliminated?

• It could be that the 31,200 km distance refers to how far apart the planes of orbit of Earth and Apophis will be, instead of how far ahead or behind they will be from where the paths cross. – Tom B. Mar 22 '18 at 17:43
• @TomB. I hadn't thought of that actually. Reading Wikipedia though, it does say that the asteroid will pass within the orbits of geosynchronous satellites, so one would assume that this means it is on the same plane as these satellites and therefore the same would be true for Earth's orbit. – PhysicsGuy123 Mar 22 '18 at 18:34
• Huh, interesting. But that brings up the possibility of an in-plane but "sideways" miss, and I just looked up geosynchronous orbit and it's 35,786 km! Coincidence? I hope someone answers definitively. – Tom B. Mar 22 '18 at 18:40
• @TomB. Having done some more research, it appears that the plane is inclined at 40 degrees to the Earth's equator. – PhysicsGuy123 Mar 22 '18 at 18:43
• @PhysicsGuy123 - The orbital ephemeris data are updated every ~10 years or so and when this is done it is done down to 6-15 decimal places, depending on the parameter (e.g., see adsabs.harvard.edu/abs/2002P%26SS...50..217F). That being said, they often update near Earth object trajectories whenever new data is presented and the projections almost always change, at least a little. – honeste_vivere Mar 23 '18 at 14:01