# Has anyone back-calculated previous close encounters between the Apophis asteroid and Earth?

The Apophis asteroid was only discovered in 2004, and shares an orbit similar to Earth's orbit, leading to many close encounters on the scale of decades.

Most of the stories about this asteroid are about predicting future encounters between Earth and Apophis. It occurs to me that you can use the same models that predict future encounters to show past encounters as well.

Has anyone done this, and shown any past events when the asteroid has come extremely close to the Earth?

The JPL Small Body Database lists Apophis close approaches dating back 100 years before discovery. Three fairly close ones were:

• 1907-04-13, 0.029 au
• 1949-04-14, 0.028 au
• 1990-04-14, 0.033 au

While it's possible to run a dynamical integrator arbitrarily far backward or forward in time, any given pos(t), vel(t) state is only a point in a cloud of possibilities. Observations (MPC database, NASA news) constrain that cloud; close encounters accelerate its dispersion. Specific predictions before ~1900 or after ~2050 should not be regarded with much confidence.

• Many thanks! It's difficult to find these "deep web" searches without prior knowledge. – Steve Sether Mar 28 at 21:21

If you visit https://ssd.jpl.nasa.gov/horizons.cgi and enter Apophis as the target body (full name "99942 Apophis (2004 MN4)"), you can go to the "Time Span" link and see "Available time span for currently selected target body: 1599-Dec-12 to 2500-Dec-30"

It's possible others have calculated its position beyond this time span, but I would regard NASA's HORIZONS as canonical.

• Thank you! This is exactly what I'm looking for, and difficult to find via Google searches unless you know that it exists, and what to search for. – Steve Sether Mar 28 at 21:20
• Any guidance on how to get earth->target distance? The tool is powerful, which means it's also extremely complex. – Steve Sether Mar 28 at 21:37
• @SteveSether The default settings for "OBSERVER" ephemeris print a column titled delta, which is the observer-to-body distance in AU, (and deldot is the change of distance in km/s). In the table settings these are option #20, Observer range & range-rate. The default observer location "geocentric" gives you the distance from the Earth's centre to the target body. – Dronir Mar 29 at 13:16

Using the calculator posted by Guest, I've calculated some previous close approaches going back as far as 1600. None are anywhere near the 2029 encounter where Apophis will be close to the geostationary orbit of satellites.

Going back to 1600 (the limit the tool is capable of calculating for this object), the closest Apophis encounters was on April 12, 1748, where Apophis was approximately .0068 AU away from earth. For reference, this is about 2.5 times the average earth/moon distance.

By comparison, the April 13, 2029 encounter will bring Apophis 0.000254 AU away from the earth, about 27 times closer than the 1748 encounter.

• Before the 0.011±0.004 au encounter on 1823-04-14, the uncertainty of Apophis's position grows quite large. Ephemeris type Vectors, table type 1 with XYZ state uncertainties, shows σ≈20 au on 1748-04-12, i.e. all bets are off. – Mike G Mar 31 at 13:09
• @MikeG Interesting. So I guess this answer is pretty much wrong then. I saw the accuracy field, but wasn't sure how to use it, or what units it was in. This is the problem with being a neophyte, and using a powerful tool beyond your ken. Any idea why we can calculate the position 100 years into the future after the VERY near 2029 encounter, but not the 1823 encounter that's so much farther away? – Steve Sether Apr 1 at 3:22
• The uncertainties grow rapidly after the 2029 encounter too, e.g. the time of closest approach in Sep 2102 has a 1.6 day uncertainty, and in Apr 2138 it's ±8.5 days! – Mike G Apr 1 at 4:30
• @MikeG Is it possible a different, more accurate model is being used to calculate the post 2029 encounters? I read that NASA ruled out any impacts in the next 100 years. Any idea what the source of inaccuracy in the model is? – Steve Sether Apr 1 at 4:57
• Probably the same model. Every close encounter multiplies whatever uncertainties are in the observations; see the butterfly effect. – Mike G Apr 1 at 5:11