Near-Earth asteroid (NEA) 99942 Apophis which will have a very close encounter
with Earth on 13 Apr 2029 and, with a non-negligible probability, subsequent very close encounters or even
an impact on 13 Apr 2036 Head-On Impact Deflection of NEAs:
A Case Study for 99942 Apophis
Bernd Dachwald and Ralph Kahle†
German Aerospace Center (DLR), 82234 Wessling, Germany
Bong Wie‡
Arizona State University, Tempe, AZ 85287, USA In June 2004, a NEA with a diameter of about 320m was discovered, which will have a very close
encounter
with Earth on 13 Apr 2029 and, with a non-negligible probability, subsequent very close encounters or even
an impact on 13 Apr 2036, 13 Apr 2037, or later (Refs. 1, 2, and 3). This NEA first got the provisional
designation 2004MN4 and later 99942 Apophis. The currently estimated probability that Apophis impacts
the Earth is 1/45 000 for a 2036-encounter and 1/12 346 000 for a 2037-encounter (Ref. 2, October 2006).
Note that the current probability of a catastrophic impact in 2036 is higher than, e.g., the probability for an
airplane to crash during a flight. Apophis would impact the Earth with a velocity of about 12.6 km/s and
the released energy would equal about 875 Megatons of TNT (Ref. 2). Whether or not Apophis will impact
the Earth in 2036 or 2037 will be decided by its close encounter in 2029. If the asteroid passes through one
of several so-called “gravitational keyholes”, it will get into a resonant orbit and impact the Earth in one of
its later encounters, if no counter-measures are taken.
Apophis’ size (H = 19.2) and taxonomic type are not definitely known at this time (Ref. 2). According
to Ref. 1, e.g., Apophis has a diameter of 430 − 970 m. In accordance with Ref. 2, however, we assume for
our calculations that it is a spherical 320m diameter asteroid with a typical S-class density of 2 720 kg/m3
and thus an estimated mass of 4.67 × 1010 kg.
During November and December 2005, ESA’s Advanced Concepts Team (ACT) has organized the 1st
Global Trajectory Optimisation Competition. The goal was to find the trajectory that yields the maximum
deflection of asteroid 2001 TW229 using a nuclear-electric propulsion (NEP) system within a maximum
mission duration of 30 years. The winning trajectory came from JPL’s Outer Planets Mission Analysis
Group (Ref. 4). An even improved post-competition trajectory that will be published in Ref. 4 uses an Earth-
Venus-Venus-Earth-Earth-Venus-Venus-Earth-Venus-Earth-Jupiter-Saturn-Jupiter gravity assist to make the
trajectory retrograde and impact the target at one of its perihelion passages. The flight time is 28.4 years
and the used propellant mass is only 3% of the launch mass. Therefore, a similar trajectory would also be
feasible for a chemically propelled spacecraft. Although the trajectory for such a mission concept was not
yet calculated for Apophis, the flight times for achieving a retrograde orbit would be in the same order as
for the ACT competition problem. This renders chemical and electrical propulsion systems prohibitive for
propelling a retrograde deflection mission to impact Apophis before the close Earth-encounter in 2029 or
even before the potential Earth-impact in 2036.
The solar sail might be the better propulsion system for such a mission. The use of solar sails to achieve
impacts from retrograde orbits was first proposed (and elaborated in a more general way) by McInnes in
Refs. 5 and 6. Wie employed in Refs. 7 and 8 the same idea for a fictional asteroid deflection problem by
AIAA and made a preliminary conceptual mission design. In Refs. 9 and 10, Dachwald and Wie made a
more rigorous trajectory optimization study for this fictional AIAA mission scenario. The results in Refs. 9
and 10 show that solar sail Kinetic Energy Impactor (KEI) spacecraft that impact the asteroid with very
high relative velocity from a retrograde trajectory are a realistic option for mitigating the impact threat from
NEAs. This paper is about the application of the solar sail KEI concept to remove the real threat from this
real asteroid. Read more at
www.aero.org... ... -paper.pdf