Again Apophis

I got a few interesting questions about my first Apophis post

“Why not wait with a mission until after 2029, then it will be clearer if the Earth might be hit in 2036”
“Is it a coincidence that there are exactly seven years between the two data?”

Here is a bit more information. For some of you it may be a bit (too) technical ..:-) Don’t worry.

The present orbit of Apophis is shown in the figure below as the blue line, together with the orbits of Mercury, Venus and Earth, with the Sun in the center.
Distances are given in Astronomical Units (AU), where 1 AU = ~ 150 million km, the average distance between Earth and Sun.
Apophis has a period of  323.6 days, six weeks shorter than a year, and its orbit is quite elliptical, coming almost as close as the orbit of Venus, but also crossing the Earth orbit.

During an orbit Apophis crosses the Ecliptic twice. One crossing is no problem, but the other one is, because there it crosses the Earth orbit as well!
And Apophis, with its shorter period, is continuously overtaking Earth…..

The images come from an interesting NASA website where you can follow the course of Apophis in time.
Try it out and check that both Earth and Apophis will arrive at the Danger Point on 13-4-2029!

On that day Apophis will pass Earth at a distance of about 30.000 km and because of the Earth gravitation its orbit will be strongly disturbed.
It will get a boost from the encounter, increasing its orbit and its period. See the sketch below.

The uncertainty in the trajectory is indicated, the white bar is about 1000 km at present.

So, no need to worry about 2029. But there IS a (small) chance that Apophis might hit Earth exactly seven years later!
This could happen if Apophis, after deflection, enters into a resonant orbit with Earth.

What are resonant orbits? Two orbits are resonant if there is a simple relation between their respective periods, like 2:3, 5:6 etc
Example: two planets A and B with periods of 300 and 450 days have resonant orbits (2:3). Starting from any given position, they will be in exactly the same position after 900 days (A will have completed 3 orbits, while B has completed 2).

Back to Apophis.

There is a possibility that on 13-4-2029 Apophis will be deflected into a (6:7) resonant orbit! In that case it might hit Earth exactly 7 years later, having completed 6 orbits itself.

This will only happen when Apophis will pass through a very small “window” during its encounter with Earth in 2029. Estimated width about 600 meter(!) only. Astronomers call it a keyhole  🙂
Remember, Apophis has a size of ~ 300 m, so it just fits in the keyhole….

At this time the estimated probability that Apophis will pass through the 6:7 resonance keyhole is only about 1:250.000. Almost negligible .

Why is it then that for example the Russian Space Agency is still proposing a mission?
Well, if more accurate calculations in the coming years show that Apophis will pass through the keyhole, it will be rather easy to steer the asteroid away from it. As the keyhole is so small, just a few hundred meters will do.
That will be orders of magnitude easier than steering it away from the Earth, once it has passed the keyhole!

One last remark.
There was a question if a second hit, again on April 13, took into account leap years.
It does. A year is 365.25 days, so seven years equals 2556.75 days. And between 13-4-2029 and 13-4-2036 there are 2557 days (7 x 365 + 2 leap days).
Difference is only 6 hours. By the way 13-4-2036 will be a Sunday. Easter Sunday..:-)

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