1. Ballistics and navigation support for the Venera-D mission V. A. Shishov 1, V. A. Stepaniants 1, A. G. Tuchin 1, S. M. Lavrenov 2 (1)Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, (2)Moscow State Institute of Electronics and Mathematics (Technical University) Moscow 2012

2. Comparison of probable start windows by summary costs of characteristic velocities Departure date Arriving dateFlight durance (days) Departure Velocity (km/sec) Arriving Velocity (km/sec) Velocity sum (km/sec) 11.01.202025.07.2020 196 4.6773.4838.160 28.10.202106.04.2022 160 2.8004.7607.560 27.05.202327.10.2023 153 2.5733.6956.268 07.12.202415.05.2025 159 3.2952.6865.981 08.06.202608.12.2026 183 3.8572.9896.846

3. Isolines of the total characteristic velocities for the 2020 start window По оси абсцисс – даты старта, по оси ординат – продолжительность перелёта (в сутках). На перекрестье красных линий – оптимальная дата старта (11.01.2020) и продолжительность перелёта (196 суток). Optimal date to start 11.01.2020 Transition duration 196 days Dates are on the axis of abscissa Flight durations are on axis of the ordinates (in days)

4. Main ballistics tasks to be solved during the Venera-D mission Pointing for the on-Earth tracking stations Trajectory measurement raw processing Determination and forecast of the SC motion parameters Maneuver and adjustment calculations Data calculations for the on-board control system Scientific program providing

5. Flight trajectory adjustments Insertion into transfer orbit after motion on the orbit around the Earth The first correction is performed on the seventh day of the flight. The second correction is performed four days prior to the Venus approach. After performing the second correction and the DM separation the SC withdrawal maneuver is performed. The third motion correction of the SC is implemented one day before approaching for the trim purpose. The capture maneuver is performed at the outgoing hyperbola pericenter and the SC goes to the high eccentricity orbit around Venus.

6. Maneouver and correction execution errors 1.Errors of the flight path transfer impulse (the first) performance are 0.2% by value and 0.7° by direction. 2.Errors of the correction impulses (the second etc.) and the withdrawal maneouver are 0.5 m/sec by value and 0.7° by direction.

7. Orbital measurements in the project Venera-D carry on 1.up to 2 Mkm distances from tracking stations in Baikonur and Bear Lakes with Spectr-X facilities (antenna THA-57,diameter=12.5m); 2.at distances more than 1.5 Mkm from tracking stations in Ussuriisk(antenna P-2500, diameter=70 m) and Bear Lakes (antenna TNA-1500, diameter=64 m) equipped with large radars. Radiated frequency: 7.1–7.2 GHertz. On-board frequency conversion coefficient: 880/749. Zone of unambiguous measurement of the range (in the slant distance sense): 1023 km. Measurement errors: 20 m by range, 0.2 mm/sec by range rate.

8. Flight trajectory measurement program On the path part prior to the first correction the measurements are carried on daily, four tracking stations being on duty up to distances 2 Mkm, two ones being on service after this threshold. On the path part after the first correction the measurements are carried on every four days, two tracking stations in the Bear Lakes and Ussuriisk being at work. The measurements are carried on by two tracking stations daily during two weeks prior to the second correction fulfillment. And after second correction two tracking stations do measurements one time weekly.

9. The scheme of the Descent Module (DM) delivery One should provide with the prescript Venus atmosphere enter angle, illumination constraints and radio vision conditions from the on-ground tracking stations as well. These circumstances are ensured by two corrections on the flight trajectory: namely on the seventh day of flight and the four days prior to entering Venus atmosphere. The DM escapes the main SC and does autonomous flight after the second correction. The Orbital Apparatus (OA) performs the withdrawal maneuver and then the trim maneuver to transfer at the outgoing hyperbola with given inclination (90º) and given pericenter height (250 km) where it get the braking impulse to go on the elliptical orbit around Venus. With all that the ОА should reach the minimum distance up to Venus the four hours earlier than the DM would reach its atmosphere. In entering the Venus atmosphere the DM has to connect with the OA which would retransmit the telemetrical flow to the Earth.

10. The scheme of the Descent Module (DM) delivery

11. Ballistics destination areas on the Venus surface in 2020 – 2026 years 2020 г2021 г2023 г 2024 г 2026 г

12. Dependence of angles the Earth-Decent Module-Venus (E-L-V) and the Sun-Decent Module-Venus (S-L-V) from landing longitudes for 2020 year

13. The period options for the main SC orbits and for the subsattellite orbits № The subsattellite orbit period, (hours) The main SC orbit period (hours) 14824 2 48 324 412

14. Option 1. The main SC orbit elements after setting in the Venus orbit ParameterValue Semiaxis ( tkm)62.633609 Eccentricities0.899 Inclination ( degrees)90.0 Longitude of the ascending node (degrees)240.2 Argument of the pericenter (degrees)334.4 Mean motion (n) rad/tsec0.03636 Period (hours)48.0 Distance at the pericenter (tkm)6.301876 Height at the pericenter (km)249.983 Distance at apocenter (tkm)118.965344 Height at apocenter (km)112913.450640 Latitude of the under-satellite point (degrees)–25.578 Longitude of the under-satellite point (degrees)240.258

15. Energy costs of the SC to maneuver on the Venus satellite orbits (VSO) The transition impulse module to the VSO is equal to 648 m/sec. The transition impulse module from the two days orbit period to the one day orbit period is equal to 158 m/sec.

16. The SC orbit motion determination on the VSO Range and range rate measurements The Earth Tracking station Line of sight Possible change of the SC apocenter

17. Enumeration of error sources for the SC motion and the count model Insufficient accuracy for the Venus gravity field taken into account for fast operative work ; the NASA RS-SHTJV360 gravity model has order 360x360; Availability of the unaccounted micro-accelerations because of attitude engine burns; Inaccurate accounting of the solar radiation pressure influence Inexactness in the relative motion of Venus to the Earth

18. Conclusions 1. With optimizing mission energy costs we get that the Decent Module area location on Venus turned out to be off direct radiovision from the Earth and isn’t illuminated by the Sun. Hence telemetry from Decent Module has to communicate through the Orbital Craft and the Decent Module performance capacity has to maintain by inner source. 2. Changing in the ballistics scheme to ensure the sharp navigation calls for additional energy costs. 3. It is advisable to construct the task of joint determination for motion parameters of the SC, Venus and the Earth within a single dynamical model.