Adam Hibberd
There have been some developments. I have been addressing the problem of how to deflect Apophis from its path if it were indeed on a collision course with Earth.
My Apocalypse Plot gives the magnitude of ΔV at different points in Apophis's orbit to send it on a course to JUST strike the Earth's surface. See below:
This in itself is pretty useless stuff, but then I made the observation that should a ΔV be applied in the OPPOSITE DIRECTION to this, then that would force Apophis FARTHER AWAY.
Of course this would be a foolish thing to do under the CURRENT circumstances, but what IF APOPHIS HAD GENUINELY BEEN ON A COLLISION COURSE WITH EARTH? Then this would be very important knowledge to have. So let us pursue this hypothetical.
Might an impactor then sent from Earth be able to deflect it by a sufficient ΔV in this direction to cause it to miss Earth altogether on April 13th 2029?
The first thing to note is that the required ΔV would NOT necessarily be that shown in the above APOCALYPSE PLOT. This ΔV shifts the perigee of Apophis in 2029 by 31,000 km towards Earth, but in our hypothetical, Apophis is already targeting Earth and we need to shift it - let's say on the safe side by one Earth Diameter (12756 km) - so that it misses it by a fairly safe distance.
We can observe in the Apocalypse Plot that an impactor arriving in January 2026 would only need to shift Apophis by 0.1*12756/31000 = 0.041 m/s, or 4.1 cm/s.
At this point in our hypothetical, we refer to the DART mission, where the spacecraft managed to shift Dimorphos by 2.7 mm/s (0.0027 m/s or 0.27cm/s).
We need to change Apophis's velocity by at least an order of magnitude higher than DART achieved with Dimorphos and what's more Dimorphos has a mass of only ~5.5 billion kg as opposed the Apophis's mass of ~27 billion kg. This is also an order of magnitude difference, so we need an impactor with TWO ORDERS OF MAGNITUDE higher momentum than the DART mission (570 kg at 6.6km/s). Is this possible? I decided to set out and see.
For my findings read the up-coming November issue of Principium, the quarterly publication of the Initiative for Interstellar Studies (i4is).
For a taster, look for example at the following optimal trajectory animation, created by my own software development Optimum Interplanetary Trajectory Software (OITS). It is optimal in the sense of resulting in the LARGEST arrival velocity component at Apophis relative to the optimal deflection direction, to ensure maximum likelihood of increasing the perigee distance of Apophis when it subsequently encounters Earth on April 13th 2029.