1 / 18

Orbital Mechanics Overview 3

Orbital Mechanics Overview 3. MAE 155 G. Nacouzi. Orbital Mechanics Overview 2. Interplanetary Travel Overview Coordinate system Simplifications Patched Conic Approximation Simplified Example General Approach Gravity Assist: Brief Overview Project Workshop.

serena
Télécharger la présentation

Orbital Mechanics Overview 3

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Orbital Mechanics Overview 3 MAE 155 G. Nacouzi GN/MAE155

  2. Orbital Mechanics Overview 2 • Interplanetary Travel Overview • Coordinate system • Simplifications • Patched Conic Approximation • Simplified Example • General Approach • Gravity Assist: Brief Overview • Project Workshop GN/MAE155

  3. Interplanetary Travel: Coordinate System • Use Heliocentric coordinate system,i.e., Sun centered • Use plane of earth’s orbit around sun as fundamental plane, called ecliptic plane • Principal direction, I, is in vernal equinox • Define 1 Astronomical Unit (AU) = semimajor axis of earth orbit (a) = 149.6 E6 km (Pluto, a ~ 39.6 AU) Heliocentric-ecliptic coordinate system for interplanetary transfer: Origin- center of Sun; fundamental plane- ecliptic plane, principal direction - vernal equinox GN/MAE155

  4. Principal Forces in Interplanetary Travel • In addition to forces previously discussed, we now need to account for Sun & target planet gravity • Simplify to account only for gravity forces, ignore solar pressure & other perturbances in mission planning => forces considered - Gravity effects of Sun, Earth, Target Planet on S/C GN/MAE155

  5. Principal Forces in Interplanetary Travel • A very useful approach in solving the interplanetary trajectory problem is to consider the influence on the S/C of one central body at a time => Familiar 2 body problem • Consider departure from earth: • 1) Earth influence on vehicle during departure • 2) Sun influence=> Sun centered transfer orbit • 3) Target planet gravity influence, arrival orbit GN/MAE155

  6. Interplanetary Trajectory Model: Patched Conic • Divide interplanetary trajectory into 3 different regions => basis of the patched-conic approximation • Region 1: Sun centered transfer (Sun gravity dominates) - solved first • Region 2: Earth departure (Earth gravity dominates) - solved second (direct or from parking orbit) • Region 3: Arrival at target planet (planet gravity dominates) - solved third GN/MAE155

  7. Interplanetary Trajectory Model: Patched Conic Sphere of Influence • Two body assumption requires calculating the gravitational sphere of influence, Rsoi, of each planet involvedRsoi (radius) = a(planet) x (Mplanet/Msun)^0.4 Earth Rsoi = 1E6 km gravity Rsoi GN/MAE155

  8. Interplanetary Trajectory Model: Patched Conic • Sun centered transfer solved first since solution provides information to solve other 2 regions • Consider simplified example of Earth to Venus • Assume circular, coplanar orbits (constant velocity and no plane change needed) • Hohmann transfer used: • Apoapsis of transfer ellipse = radius of Earth Orbit • Periapsis of transfer ellipse = radius of Venus Orbit GN/MAE155

  9. Simple Example • Required velocities calculated using fundamental orbital equations discussed earlier • ra= 149.6 km; Va = 27.3 km/s • rp= 108.2 km; Vp = 37.7 km/s • Time of transfer ~146 days Earth @ Launch Venus @ arrival GN/MAE155

  10. Simple Example • Example calculations: Hyperbolic Excess Velocity, VHE ,S/C velocity wrt Earth VHE = VS/S - VE/S where, VS/S ~ vel of S/C wrt Sun, VE/S ~ Vel Earth wrt Sun VHE = 27.29 - 29.77 = -2.48 km/s Similarly, @ target planet, hyperbolic excess vel, VHP needs to be accounted for VHP = VS/S - VP/S = 37.7 - 35 = 2.7 km/s; VP/S ~ Vplanet wrt Sun Note: C3 = VHE2, Capability measure of LV GN/MAE155

  11. Patched Conic Procedure • 1) Select a launch date based on launch opportunity analysis • 2) Design transfer ellipse from earth to tgt planet • 3) Design departure trajectory (hyperbolic) • 4) Design approach trajectory (hyperbolic) Reference: C. Brown, ‘Elements of SC Design’ GN/MAE155

  12. Patched Conic Procedure Mars • 1) Launch opportunityTo minimize required launch energy, Earth is placed (@ launch) directly opposed to tgt planet @ arrival • Calc. TOF, ~ 1/2 period of transfer orbit • Calculate lead angle = Earth angular Vel (e)x TOF • Phase angle, r = 2 pi - lead angle Wait time = r- current/(target - e) r Earth Synodic period~ period between launch opport., S = 2pi/(e - target) S = 2yrs for Mars GN/MAE155

  13. Patched Conic Procedure • 2) Develop transfer ellipse from Earth to Target Planet (heliocentric) accounting for plane change as necessary • Note that the transfer ellipse is on a plane that intersects the Sun & Earth at launch, & the target planet at arrival. • Plane change usually made at • departure to combine with injection • and use LV energy instead of S/C GN/MAE155

  14. Patched Conic Procedure • 3) Design Departure trajectory to escape Earth SOI, the departure must be hyperbolicwhere, Rpark~ parking orbit, VHE~hyperbolic excess velocity • 4) Design approach trajectory to target planetwhere Vpark is the orbital velocity in the parking orbit and V is the SC velocity at arrival. Vretro is the delta V to get into orbit GN/MAE155

  15. Patched Conic Procedure GN/MAE155

  16. Gravity Assist Description • Use of planet gravity field to rotate S/C velocity vector and change the magnitude of the velocity wrt Sun. No SC energy is expended Reference: Elements of SC Design, Brown GN/MAE155

  17. Gravity Assist Description • The relative velocity of the SC can be increased or decreased depending on the approach trajectory GN/MAE155

  18. Examples and Discussion GN/MAE155

More Related