Институт прикладной математики им. М.В.Келдыша РАН
Download
1 / 31

???????? ?????????? ?????????? ??. ?.?.??????? ??? - PowerPoint PPT Presentation


  • 157 Views
  • Uploaded on

Институт прикладной математики им. М.В.Келдыша РАН. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences. Mathematical Model of the Spacecraft Landing on Ganymede’s Surface. Alexey Golikov, Andrey Tuchin. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about '???????? ?????????? ?????????? ??. ?.?.??????? ???' - sal


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
2896057

Институт прикладной математики им. М.В.Келдыша РАН

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences


Alexey golikov andrey tuchin

Mathematical Model им. М.В.Келдыша РАН

of the Spacecraft Landing

on Ganymede’s Surface

Alexey Golikov, Andrey Tuchin

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

“Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


Essential goals
Essential goals им. М.В.Келдыша РАН

  • Orbit measurements: interpretation, information processing, ballistic and navigational mission support, etc.

    • ground supported trajectory measurements (GSTM):

    • range

    • range rate

    • measurements by the strup down

  • Orbit determination: determination of all orbital parameters taken into account essential orbit perturbations

  • Maneuver optimization:planning the scheme of maneuvers, error estimation of maneuver realization

  • Landing on the surface of Ganimede: optimal scheme of descent session by using the thruster

  • “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Ganymede lander mission stages
    Ganymede Lander: им. М.В.Келдыша РАНMission Stages

    • Launching of the spacecraft (SC)

    • Interplanetary flight Earth→Jupiter

    • gravitational maneuvers about Earth & Venus

    • Artificial satellite of Jupiter

    • gravitational maneuvers around Ganymede & Callisto

    • Artificial satellite of Ganymede (ASG)

    • preliminary elliptical orbit

    • circular polar orbit at the height of 100 km

    • prelanding orbit with low pericenter

    • session on Ganymede’s surface

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Scheme of the stage asg
    Scheme of the stage ASG им. М.В.Келдыша РАН

    Preliminary orbit

    Orbital corrections

    GSTM

    Orbit period

    Inclination

    Eccentricity

    _________

    _____

    Descent

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Scheme of the stage asg1
    Scheme of the stage ASG им. М.В.Келдыша РАН

    Transition to preliminary elliptical orbit after braking at approach to Ganymede

    Series of GSTM for orbit determination

    Orbital corrections of orbit period & inclination to form circular polar orbit at the height of 100 km

    Series of GSTM within 2 days for orbit determination

    Bound orbital corrections (consisting of 2 corrections of the orbit period) to precise circular polar orbit

    Circular polar orbit with science experiments

    Orbital maneuver to form a landing orbit

    Series of GSTM on 2-3 adjacent circuits of a landing orbit

    Descent maneuver into given point on the surface of Ganymede

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Perturbing forces
    Perturbing forces им. М.В.Келдыша РАН

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Essential perturbating factors
    Essential им. М.В.Келдыша РАНperturbating factors

    • Gravitational field of Ganymede (2×2):

      2nd zonal harmonics

      2ndsectorial harmonics

    • Jupiter’s gravity attraction:

      circular equatorial orbit

    • Rotation of Ganymede is synchronized with its orbit around Jupiter ,

      there are resonance effects

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Preliminary orbit
    Preliminary orbit им. М.В.Келдыша РАН

    Near equatorial and high eccentric orbit

    Take into account the orbit evolution (perturbations)

    Preliminary orbit with high eccentricity is very unstable: for e=0.5 it will destroy in 2 hours

    For eccentricity e<0.3 equatorial elliptical orbits are stable

    Polar elliptical orbits are unstable for e>0.01

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Evaluation of preliminary orbit e 0 5
    Evaluation of preliminary orbit им. М.В.Келдыша РАН(e=0.5)

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Evaluation of preliminary orbit e 0 51
    Evaluation of preliminary orbit им. М.В.Келдыша РАН(e=0.5)

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Evaluation of preliminary orbit e 0 52
    Evaluation of preliminary orbit им. М.В.Келдыша РАН(e=0.5)

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Evaluation of preliminary orbit e 0 3
    Evaluation of preliminary orbit им. М.В.Келдыша РАН(e=0.3)

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Evaluation of the polar orbit e 0 3
    Evaluation of the polar orbit им. М.В.Келдыша РАН(e=0.3)

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Evaluation of preliminary orbit e 0 1
    Evaluation of preliminary orbit им. М.В.Келдыша РАН(e=0.1)

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Transfer to circular polar orbit
    Transfer to circular polar orbit им. М.В.Келдыша РАН

    • Series of maneuvers to change the orbit period & inclination

    • Maneuver optimization by using the Lambert problem with unfixed finite constraints

    • Solution of this problem is achieved by iterative procedure

    • Take into consideration an essential condition: the polar orbit at high altitudes is unstable!

    • Supplementary constraint: to form the polar orbit only on low heights & using “quasiequilibrium points”

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Circular polar orbit
    Circular polar orbit им. М.В.Келдыша РАН

    Altitude 100 km

    Series of GSTM within 2 days for orbit determination

    Bound orbital corrections (consisting 2 corrections of the orbit period) to precise circular polar orbit

    Science experiments (with orbit keeping corrections)

    It needs to take into account the orbit evolution (perturbations)

    Orbital maneuvers to form a prelanding orbit with low pericenter

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Circular polar orbit1
    Circular polar orbit им. М.В.Келдыша РАН

    Long-periodic perturbations of the orbit:

    where

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Evaluation of polar circular orbit
    Evaluation of polar circular orbit им. М.В.Келдыша РАН

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Evaluation of polar circular orbit1
    Evaluation of polar circular orbit им. М.В.Келдыша РАН

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Prelanding orbit
    Prelanding им. М.В.Келдыша РАН orbit

    Altitude of the pericenter 15 km

    Altitude of the apocenter 100 km

    Eccentricity 0.0158

    Series of GSTM on 2-3 adjacent circuits of a landing orbit to precise orbital parameters

    Limit errors of GSTM are non greater than 0.2 mm/s and 20 m

    Preliminary estimated errors of orbit prediction at the start of descent are non greater 2.5 m/s and 5 km

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Evaluation of prelanding orbit
    Evaluation of им. М.В.Келдыша РАНprelanding orbit

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Descent session
    Descent Session им. М.В.Келдыша РАН

    • 2 variants depending on the start time of descent:

    • 24 hours => 16 hours of measurements GSTM

    • 12 hours => 6 hours of measurements GSTM

    • Nominal program of the thrust direction corresponds to the solution of the problem optimization

    • Using Pontryagin’s principle of maximum

    • Constraints depend on the problem definition

    • Navigation is provided by the strup down

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Ganymede lander module
    Ganymede Lander module им. М.В.Келдыша РАН

    • Mass before descent maneuver 900 kg

    • Propulsion system 215 kg

    • Total burn 4200 N

    • Specific thrust 319 s

    • Dry mass 385 kg

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Example of solution
    Example of solution им. М.В.Келдыша РАН

    • Solution by Pontryagin’s principle of maximum

    • First stage of the descent session: from 15 km to 2 km

    • Results of solution:

    • vertical velocity: 10 m/s forward to center of Ganymede

    • descent duration: 320 sec

    • fuel expenses: 422 kg

    • angle distance of descent: 7.4 deg

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Direction of the thrust
    Direction of the Thrust им. М.В.Келдыша РАН

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Altitude vs distance
    Altitude vs. Distance им. М.В.Келдыша РАН

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Velocity vs time
    Velocity vs. Time им. М.В.Келдыша РАН

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Radial velocity
    Radial velocity им. М.В.Келдыша РАН

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Transversal velocity
    Transversal velocity им. М.В.Келдыша РАН

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    Thank you
    Thank you! им. М.В.Келдыша РАН

    Alexei R. Golikov

    golikov@keldysh.ru

    Andrey G. Tuchin

    tag@keldysh.ru

    Keldysh Institute of Applied Mathematics,

    Russian Academy of Sciences

    “Ganymede Lander: scientific goal and experiments”, 5-7 March 2013


    ad