1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047 Russia Lavochkin Research and Production Association, Khimki, Moscow oblast, Russia E.L. Akim, G.S. Zaslavsky, I.M. Morskoy, E.G. Ruzsky, V.A. Stepanyants, A.G.Tuchin, V.A. Shishov Delivery of the Samples from Phobos to Earth—The Phobos–Grunt Project: Ballistics, Navigation, and Flight Control 2010

2. 2 The main purpose of the project of the Federal space program "Phobos-grunt" is to deliver ground samples of the minor celestial body — Natural Mars’s satellite Phobos The implementation of the "Phobos-grunt" project is planned to begin in 2011. The mission will be finished in 2014 The implementation of the project "Phobos-grunt" will allow to solve the important for our country scientific and technical task of creation an interplanetary spacecraft of a new generation for scientific researches in deep space.

3. Trajectory corrections Transfer to the Mars orbit Phobos The Mars-Earth cruise Sun Transfer to the Mars –Earth orbit Mars Start Insertion on the intermediate orbit Insertion on the reference orbit on the transfer orbit Earth-Mars Insertion

4. 4 FOUR SEQENTIAL STAGES the SC puts on the departure from Earth trajectory Flight from Earth to Mars finished by transition on the artificial satellite of Mars (ASM) Orbiting Mars with maneuvers aimed to maintain a close approach of the SC with Phobos, landing of the SC on its surface, taking of rock sample, lift-off of the returning vehicle and its flight around Mars along the wait orbit Start from the wait orbit of the returned SC and flight to Earth finished by reentry in it’s atmosphere and landing in the certain region of territory of our country

5. 5 BALLISTIC DESIGNING OF THE FLIGHT "PHOBOS-GRUNT "

6. 6 EARTH-MARS CRUISE PHASE The argument of pericenter of the ingoing hyperbola must be equal 180º and the inclination is near 30º The SC flyby trajectory distance from Mars center is near 800 km The radio vision from tracking stations in Ussuriisk and Medvezy Ozera must be ensured After inserting the SC on the outgoing trajectory the errors due to motions near Earth may be high. The error of the asymptotic velocity may consist ~70 m/sec. That’s why the correction is needed. As a result an cast error will consist 1.5 million km. It has to do during first 10 days of flight, no more. In the cruise phase main target of the navigation and flight control is insertion of the SC to the Mars flyby orbit with the errors not exceeded about 300 km. It will be done by two corrections: the former for 80 days before reaching, the latter 14 days. Arrival to Mars 10.09.2012 After finishing this phase the following requirements must be met :

7. The initial stage of the SC motion around Mars Earth at the time of arrival Sun at the time of arrival The ingoing trajectory The burn of main engine The main engine separation The correction of initial orbit around Mars The YH-1 separation The initial orbit

8. The incoming hyperbola The first intermediate orbit The second intermediate orbit The maneuver to up the pericenter Deimos &Phobos orbits The observation orbit The braking maneuver The maneuver to transfer on the observation orbit The cell size : 10x10 th. km Orbital motion in the vicinity of Mars

9. 9 Main task of the Mars satellite phase is to insert the SC in the space area located 40-80 km above of the given Phobos surface point The errors of the spacecraft predicted motion relative the Phobos should not exceed of 1-3 km in position and 1 m/s in velocity Two types of orbit are used to approach the Phobos: - an orbit of observation (putting on January 2013) - a quasi-synchronously orbit (QSO) (orbit insertion 09.02.2013) For an orbit of observation is selected the one, which has a semi- axis exceeding a semi-axis of Phobos’s orbit up 500 km The transition from the orbit of observation to QSO can execute by three maneuvers. The total delta V ` of the maneuvers does not exceed 150 m/s. The sum of delta V of the two final impulses is ~ 60 m/s

10. Works on the observation orbit Observations of Phobos with on-board television facilities to obtain measurements; Radio sessions with the SC to obtain numerous Doppler and range measurements ;I Improving states vectors both the SC and Phobos on these measurements solving the orbit determination task; Adjusting of the Phobos gravity constant in the above mentioned process; As the a priory information in the measurement processing for Phobos will be taken data of the Phobos motion theory.

11. Types of measurements used for the construction of the adaptable Phobos motion theory Mars Spirit, Opportunity Transits of Phobos across the solar disk Phobos Earth Television images Laser ranging Mariner-9 Viking Mars Express Gravity influence Phobos-Grunt Phobos-2 Mars Global Surveyor Tracking stationsTelescopes Astrometry

12. The quasi-synchronous orbit (QSO) For classification of QSO the maximal distance between Phobos and SC, and also number of revolutions of SC round the Phobos are used. The distance is considered in two directions: – in a direction of the Phobos movement on orbit around Mars ( ), – in a direction of the line-of-sight Mars- Phobos ( ). The number of revolutions of the SC around Phobos for the given number of revolutions Phobos around of Mars is calculated

13. QSO with minimum removing drift of the Phobos surface about 50, 55 and 60 km The annular areas containing QSO have wides: 5.3, 6.7 and 8.3 km The mean relative difference of angular velocities of the SC and Phobos to the angular velocities of Phobos is in ranges 0.215–0.234, 0.182–0.199 и 0.154–0.170 The transfer from the observation orbit on the QSO 2013/02/09 The first impulse: 04:27:15.321, Δv=21.975 m/sec The second impulse: 08:15:00.000, Δv=43.794 m/sec Compare with Hohmann transfer: 58.345 m/sec

14. Basic conditions to realize the landing Getting television pictures of the land region in a few days before the beginning of the landing operation; Forecasting the SC motion relative Phobos on the QSO departure with errors not exceeding 3 km in position and 1 m/sec in velocity; Having ability to repeat the landing session, if it was not started in its proper time; Making departure from the QSO, approach and soft landing in frame of trust ability and propellant store of the SC. Checking capacity for work of the main on-board facilities, ensuring the landing, in advance; The angular value Sun-Phobos-SC has to be in the range from 20° to 70° during landing session and on the final stage from 20° to 50°; Having radio vision of the SC from tracking stations in Ussuriisk, Medvezy Ozera; Having radio vision of the Earth in acceptable angle band for sharply directed antenna

15. The landing windows (February 2013) The duration 90 minutes 07/02 10:00 14/02 10:30 15/02 09:30 22/02 10:00 23/02 09:00

16. 16 The landing on Phobos Departure from the QSO The first correcting impulse The second correcting impulse The transfer impulse for the vertical descent The site of the precision braking

18. 18 The SC returning on Earth with a ground The selected scheme of correction realization gives conditions, at which the error of bringing does not exceed 30 km in position, and error of forecasting of landing point - 5 km. The mission schedule for the returned SC assumes realization of 4 corrections of trajectory: · Realization of the first correction through ~ 10 day after putting the SC on a trajectory of flight to Earth · Realization of the second correction through ~ 5 months after the first correction · Realization of the third correction before ~ 2 months of meeting with Earth · Realization of the final fourth correction 72-12 hours prior to meeting of the SC and Earth

19. 19 The theory of qusi-syncronouse orbits is developed that permits to correct parameters operatively during approach stage, The new adaptable theory of the Phobos motion is constructed that permits just-in-time corrections of parameters on the observation orbit and on the qusi- syncronouse orbit, The developed methods and algorithms, and also the results of simulation have shown, that the problems of mechanics and motion control in the project “PHOBOS-GRUNT” can be successfully solved, The implementation of the project will be an essentially new experience in the field of the mechanics and the motion control of space vehicles CONCLUSIONS