English: Chang in orbit of Apophis in 2029. The red curves show the orbit before the April 13, 2029, close encounter with the earth, while the green curves show the orbit afterwards. The x-axis is the heliocentric ecliptic longitude (increasing towards the east). The solid curves show the distance of Apophis from the sun as a function of its longitude. The dashed curves are the sum of the distance from the sun and the distance north of the ecliptic plane. When the two curves meet, Apophis is in the ecliptic plane (this is called being at one of its nodes). One can then see how far it is from the earth's orbit. When the solid curve meets the yellow curve, Apophis is at the same distance from the sun as the earth, and one can then see how far north or south of the ecliptic it is, which tells us how far north or south of the earth's orbit it passes. If these two distances are denoted ${\displaystyle a}$ and ${\displaystyle b}$, then the minimum distance of Apophis from the orbit of Earth is approximately ${\displaystyle ab/{\sqrt {a^{2}+b^{2}}}.}$

We see that before the 2029 encounter, the orbit of Apophis comes close to that of the earth around longitude 90° (where the earth is in late December) and again around longitude 210° (where the earth is in mid April). The first of these gave the possibility of close approaches in December, such as on December 18, 1939, when Apophis came within 0.06 AU from the earth. The second gives the very close approach in April 2029, when Apophis comes to less than 40,000 km from Earth. This encounter changes the orbit significantly, but afterwards Apophis still comes back every 423 days or so to that point very close to where the earth is in mid April. Apophis no longer passes close to Earth's orbit around longitude 90°, but a new point at which the orbits are close is created, around longitude 350°, where the earth is in the middle of September. This point of approach is even closer than the one in December that exists before 2029, and a close encounter with Earth occurs on September 11, 2102, at a distance of 0.023 AU. After this encounter the position of Apophis becomes uncertain, with the uncertainty increasing with time. However Apophis will continue to have a close approach to Earth's orbit around longitude 350° until a close approach with Earth around longitude 210° or with Venus or Mars abolishes this. Approaches with Venus and Mars could happen after another close encounter with Earth around longitude 210° or 350° makes another large change to the orbit of Apophis, but we cannot predict this because of the uncertainty after 2102.

Information on close encounters can be found at the Small-Body Database Lookup.