Well whew it missed us. I think you are not surprised, though, because everybody who looked at its trajectory knew it would miss Earth by something like 17 million kilometers. No big civilization-busting slammer this time. Lucky that. Apophis is likely a third of a *kilometer* wide, though, enough to do some serious penetration and damage if it were ever to hit ground (or ocean). Compare that to the Meteorite Crater in Arizona, estimated to have been a mere 50 *meters* across. It left a 1.5 kilometer crater there. The recurrence interval of Earth-impactors of Apophis size is something on the order of 100,000 years. After some early calculations, scientists were 100% confident that Apophis would not hit us. But with that, there was also an odd, disquieting note.

That’s because that level of confidence against impact does not seem to exist for the return of Apophis in 2068. David Tholen of University of Hawai’i has said that certain non-gravitational effects are causing Apophis to drift slowly away from a purely gravitational orbit, which is “enough to keep the 2068 impact scenario in play.” But if you look at a pure Keplerian orbit for Apophis for 2068 right now, you wouldn’t think there is a problem, but that’s almost half a century away and little things can add up. Personally, I am most intrigued by looking at what’s going to happen sooner, in __April of 2029__. Earth will have a much closer pass by that asteroid than we just had. And it will perturb Apophis’s orbit too.

The asteroid’s orbit is tilted slightly with respect to earth. Its orbital inclination is 3.33°. Because it’s tilted, the two orbital planes of those bodies intersect. The thing I want you to notice is the *node*, where the plane of Earth’s orbit intersects with the plane of Apophis’s orbit. You can see it in the picture below. The ecliptic longitude of that *ascending* node (the point where Apophis emerges from below the ecliptic plane to above it) occurs at about 204°. Let’s remember what that means: imagine looking down on the solar system, sun in the middle. Start with the vernal equinox as the x axis (where longitudes begin – it’s like the prime Meridian on earth) and go counterclockwise around until you pass 180° and hit 204°; there you’ll find the node, the intersection point. The orbit of the asteroid is slightly smaller than that of the Earth, and at the node intersects with the Earth’s path, like a pair of woman’s bracelet bands that connect in one place. Anyway, it’s at this one place, the node, that offers the possibility of bringing the asteroid incredibly close to the earth. (Nodes are important in astronomy; it is the alignment of the moon’s shifting nodes with the ecliptic that gives us eclipses.)

Think of the node here as a rural intersection without a stoplight. The roads converge at a slight angle, like a skinny ‘x’, and are lightly traveled. Imagine for the sake of illustration a two-person bicycle race through the countryside. This is not the Tour d’Italia: this one takes a full year for the complete circuit and has no rest stops! Every Spring from your porch you watch them approach the intersection. The first racer, sporting the *Earth* logo, passes through the intersection every April on the same day at the same time, like clockwork. You remark on his regularity, but notice the other hot cyclist, *Apophis*, rounds the full course faster, in about 323½ days. Every eight years near the intersection *Apophis* is either ahead or behind *Earth*. Neither slows down as they approach it, and you’re worried they might hit each other on one of those eight-year intervals. So you decide to do some calculating based on what you’ve seen:

You can see *Apophis* was closing the gap each ‘synodic’ cycle from 2013 on in this chart, arriving at the intersection about 9 days earlier than *Earth* each time, until 2029, then opening it thereafter. On one day in April of 2029, Earth and Apophis are only hours away from meeting at the nodal intersection.

Here's a little problem for you number-fans. See if you can derive the slightly more than 9 day interval mentioned above. Hint: take the ratio of the Apophis’s orbital period to that of the Earth (0.8860692196 by my calculation), and put it in your calculator; add it repeatedly till you get the smallest fractional residual. Find out what part of a year that smallest residual is. Here is a (slightly jazzed-up by me) screenshot from NASA/JPL website (the link is below) showing the relation of the two bodies (moving counterclockwise) at the time of closest encounter on March 21, 2021. The nodal intersection is off to the right of them.

You can play with these images and numbers on JPL’s Small-Body Database Browser, at https://ssd.jpl.nasa.gov/sbdb.cgi. Type Apophis in the search bar, hit enter and you’ll see the orbital elements for Apophis. Then click Orbit Diagram. Try animating the paths and watch them circle like bikers on a velodrome, where each biker has a path, but they cross in one place, at the node. You’ll confirm that the actual closest encounter of the two in 2021 is not April 14th (they were 9 days apart in crossing the node) but was earlier, on March 6th (above image). At that time, Earth on the inside lap (at that part of its orbit) overtook Apophis and came about 17 million kilometers from it before it reaching the node. But on April 14, 2029 they meet fate at the node, in the wee hours, coming *far* closer. You can watch them in the JPL animation seemingly (not actually!) collide at the node.

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