Adam Hibberd
Apophis gets awfully close on Friday April 13th 2029 (within GEO altitude). Its orbit is altered by the encounter with Earth and the obvious question is will there be any further possible encounters?
Some of you may remember I have worked on the practicalities of sending laser-accelerated sails to intercept Apophis as it gets up close to Earth on this day of high anxiety for all humanity. My previous work for i4is on this can be found here.
An animation of Apophis's encounter with the Earth/Moon system can be found at my Youtube channel link here, or below. Alternatively look at the heliocentric trajectory of Apophis for the next few years here.
I've been doing some calculations. According to the NASA Horizons SPICE kernel file for Apophis, after the encounter the period of its orbit will be equivalent to around 423.18734 days.
What will be the synodic period, TS, between Earth and Apophis?
TS= 1/(1/365.256-1/423.18734)=2668.1881 days
This means that every 2668.1881 days the Earth and Apophis should realign with the Sun BUT NOT NECESSARILY at the same location in space as the encounter in 2029 (so in other words not on 13th April).
In fact this realignment will take place after 2668.1881/365.256 = 7.304 Earth years WHICH IS NOT AN INTEGER (whole number). Never has humanity been so relieved that this calculation is NOT AN INTEGER.
BTW 7.304 years is around 2029 + 7 = 2036, this is why Apophis gets close again in the year 2036.
What we need to do to determine when there is a next collision, is to wind time forward n*7.304 years, where n is an integer, until we get another integer. This also assumes that Apophis's orbit isn't significantly altered by perturbing forces.
Obviously n=10 is a possibility, so after 73 years, and so on, but this might miss out on multiplers n in between different powers of 10, for which n*7.304 is still nonetheless an integer. And of course I have neglected the fact that Apophis reaches 1.0 au from the Sun at two points in its orbit, and so I have missed the possibilties of collisions at the other point.
If you look on the Wiki page for Apophis, we find that there is another close encounter in 2051, that is 22 years following the encounter in 2029. This fits nicely with the above analysis since if we take n=3 above (a whole number) then 3*7.304=21.912, which is very close to 22 thus we expect there to be a fairly close encounter on this year.
What is clear is that there is PLENTY OF OPPORTUNITY for Apophis to be catastrophic to Earth into the distant future.
This thing just keeps buzzing around like an unwelcome mosquito, and packs a deadly punch far worse than malaria