1. Deflecting APOPHIS with a Flotilla of Solar Sails Jean-Yves Prado Olivier Boisard, Alain Perret,Guy Pignolet U3P France

2. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 ■ The case of Apophis ■ Keyholes and resonant orbits ■ The Yarkovsky Effect ■ Mitigation mission ■ Comparison with other deflection techniques Outlines

3. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 APOPHIS Discovery Discovered by: Roy A. Tucker, David J. Tholen, Fabrizio Bernardi Discovery date:June 19, 2004 Orbital characteristics Aphelion distance:1.099 AU Perihelion distance:0.746 AU Orbital period:323.6 d (0.89 year) Inclination:3.331° Physical characteristics Dimensions:~250 m (estimated) Mass: Rotation period ~30h 2×10 10 kg (estimated) Mass of APOPHIS ~ 200 x @V=40,000 km/h

4. 426 Days =>2036 417 Days =>2037 APOPHIS Fly by of the Earth on April 13, 2029

5. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 KEYHOLES Orbit Uncertainty + - Earth asteroid + Earth Gravity Assist

6. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 426.125 d 417.43 d Possible Resonant Orbits 2037 2036 1  Resonance Condition: T ap =m/n T Earth

7. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 KH distance distribution XX = Year – 2K ‘safe area’

8. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 The Yarkovsky Effect Ivan Osipovich Yarkovsky 1844-1902 From PhD thesis Miroslav Broz, Charles University, Prague 2006 1987: Small variations in motion of LAGEOS explained using Yarkovsky theory 2003: First time measured on an asteroid GOLEVKA (Chesley) based on 1991-1999 data May 2003

9. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 The Diurnal Yarkovsky Effect YE depends on: Distance to the Sun Asteroid size Asteroid shape Rotation axis obliquity Rotation rate Thermal properties: surface conductivity thermal inertia Very sensitive for the 1 m / 10 km class of Asteroids Seasonal effect can be neglected for >100m asteroids

10. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 ■ Tiny effect (10 -10 / 10 -13 m/s 2 ) but permanent ■ Main effect on semimajor axis ■ Order of magnitude for da/dt variation of tens to hundreds meters per year ■ Position error varies with t 2 ■ Example: with da/dt =10m/year position shifts 100m in 1 year, 400 m in 2 years… 100m1km 4 km ■ Can be positive (outward spiral) or negative (inward spiral) depending on obliquity ■ Determination of its direction and magnitude for propagating orbit parameters with an accuracy coherent with keyhole sizes ■ General question, not specific to APOPHIS Impact of the Yarkovsky Effect on the asteroid orbit

11. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 ■ A Transfer Module using SEP carries 4 x 200 kg solar sails to be deployed near APOPHIS ■ Formation Flying mode of the sails controlled by the TM ■ The sails hover a few km over the asteroid ■ They can shadow only the surface which is the most effective w.r.t. YE ■ No direct link from the Earth to individual sails ■ Chemical propulsion needed for balancing the photonic pressure (  V ~1.1 m/s/day) ■ Photonic pressure could be decreased by using a mesh instead of a film screen ■ 2 sets of TM+SS required (so 2 launches) can be required for efficiency and reliability Mission Design

12. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 ■ High  V needed => Use of solar electric propulsion ■ Soyouz Fregat launch from Kourou assumed ■ Typical mission profiles Cruise 2011 option 2016 option 2019 option Departure dateDec. 14, 2011 Mar. 30, 2016 Dec. 5, 2019 Departure conditionsv-inf = 3km/s, dec = -20.4deg v-inf=3.76 km/s, dec =-40 deg v-inf = 3km/s, dec = -18.4deg Launch mass1200kg Date of the Earth swing-byApr. 18, 2013 No Earth Swing-By Apr. 11, 2021 Characteristics of the swing-byh p = 78000km, v-inf = 4.38km/sh p = 60000km, v-inf = 4.50km/s Date of the rendezvousMar. 5, 2014 Dec.22, 2018 Jan. 18, 2022 Total cruise duration813 days (27 months) 997 days (33 months) 775 days (26 months) Total Delta-V1520m/s 1620 m/s 1350m/s Xenon mass95kg 100 kg 85kg Final S/C dry mass1105kg 1100 kg 1115kg

13. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 2016 Departure No Earth Swing By

14. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 2019 Departure

15. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 Image Credit Olivier Boisard

16. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 ■ 2 categories: Impulsive/Slow Push Techniques ■ Impulsive techniques can be seen as a preliminar to send weapons in space ■ Slow Push Techniques (from NASA report to US Congress):  Focused Solar Boil off material using large mirror Low TRL, complex  Pulsed Laser Boil off material with a laser Low TRL  Mass Driver Needs to land, Asteroid characteristics dependant Low TRL  Gravity Tractor Efficiency in D -5, High TRL  Asteroid Tug Needs to land, Asteroid characteristics dependant Low TRL  Enhanced YE Heavy, Asteroid characteristics dependant Low TRL  YES Efficiency in ~D -1, High TRL but applicable only if YE is present Comparison with Other Deflection Techniques

17. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 ■ Cancelling YE can be an efficient and reliable method for deflecting a NEO < km ■ Effort in such technology would benefit several types of missions ■ Canceling YE for a given period of time, even if not needed for APOPHIS, would validate the feasibility of the method ■ The required technology is very similar to the one required for solar sailing ■ International coordination required Conclusions

18. ISSS 2010 Deflecting Apophis with a flotilla of solar sails New York July 20-22 APOPHIS in the Egyptian mythology