ASEN 5050 SPACEFLIGHT DYNAMICS Interplanetary

Transcription

1 ASEN 5050 SPACEFLIGHT DYNAMICS Interplanetary Prof. Jeffrey S. Parker University of Colorado Boulder Lecture 29: Interplanetary 1

2 HW 8 is out Due Wednesday, Nov 12. J2 effect Using VOPs Announcements Reading: Chapter 12 Lecture 29: Interplanetary 2

3 11/7: Interplanetary 2 Schedule from here out 11/10: Entry, Descent, and Landing 11/12: Low-Energy Mission Design 11/14: STK Lab 3 11/17: Low-Thrust Mission Design (Jon Herman) 11/19: Finite Burn Design 11/21: STK Lab 4 Fall Break 12/1: Constellation Design, GPS 12/3: Spacecraft Navigation 12/5: TBD 12/8: TBD 12/10: TBD 12/12: Final Review Lecture 29: Interplanetary 3

4 Orion s EFT-1 Space News Lecture 29: Interplanetary 4

5 Quiz #14 Lecture 29: Interplanetary 5

6 Quiz #14 V ~ 8 km/s V atm ~ 0.48 km/s theta ~ 3.1 deg Perigee Point Lecture 29: Interplanetary 6 θ N Atm motion S S/C motion (inertial)

7 Quiz #14 Problem 2 Sun Lecture 19: Perturbations 7

8 Quiz #14 Problem 3 Sun Lecture 19: Perturbations 8

9 Quiz #14 Lecture 29: Interplanetary 9

10 Quiz #14 Lecture 29: Interplanetary 10

11 ASEN 5050 SPACEFLIGHT DYNAMICS Interplanetary Prof. Jeffrey S. Parker University of Colorado Boulder Lecture 29: Interplanetary 11

12 Interplanetary History Planets Moons Today: tools, methods, algorithms! Small bodies Lecture 29: Interplanetary 12

13 Building an Interplanetary Transfer Simple: Step 1. Build the transfer from Earth to the planet. Step 2. Build the departure from the Earth onto the interplanetary transfer. Step 3. Build the arrival at the destination. Added complexity: Gravity assists Solar sailing and/or electric propulsion Low-energy transfers Lecture 29: Interplanetary 13

14 Use two-body orbits Patched Conics Lecture 29: Interplanetary 14

15 Patched Conics Gravitational forces during an Earth-Mars transfer Lecture 29: Interplanetary 15

16 Sphere of Influence Measured differently by different astrodynamicists. Hill Sphere Laplace derived an expression that matches real trajectories in the solar system very well. Laplace s SOI: Consider the acceleration of a spacecraft in the presence of the Earth and the Sun: Lecture 29: Interplanetary 16

17 Sphere of Influence Motion of the spacecraft relative to the Earth with the Sun as a 3 rd body: Motion of the spacecraft relative to the Sun with the Earth as a 3 rd body: Lecture 29: Interplanetary 17

18 Sphere of Influence Laplace suggested that the Sphere of Influence (SOI) be the surface where the ratio of the 3 rd body s perturbation to the primary body s acceleration is equal. Lecture 29: Interplanetary 18

19 Sphere of Influence Laplace suggested that the Sphere of Influence (SOI) be the surface where the ratio of the 3 rd body s perturbation to the primary body s acceleration is equal. Primary Earth Accel 3 rd Body Sun Accel Primary Sun Accel 3 rd Body Earth Accel Lecture 29: Interplanetary 19

20 Sphere of Influence Laplace suggested that the Sphere of Influence (SOI) be the surface where the ratio of the 3 rd body s perturbation to the primary body s acceleration is equal. Primary Earth Accel 3 rd Body Sun Accel = Primary Sun Accel 3 rd Body Earth Accel Lecture 29: Interplanetary 20

21 Sphere of Influence Find the surface that sets these ratios equal. After simplifications: Lecture 29: Interplanetary 21

22 Sphere of Influence Find the surface that sets these ratios equal. Earth s SOI: ~925,000 km Moon s SOI: ~66,000 km Lecture 29: Interplanetary 22

23 Use two-body orbits Patched Conics Lecture 29: Interplanetary 23

24 Interplanetary Transfer Use Lambert s Problem Earth Mars in 2018 Lecture 29: Interplanetary 24

25 Interplanetary Transfer Lambert s Problem gives you: the heliocentric velocity you require at the Earth departure the heliocentric velocity you will have at Mars arrival Build hyperbolic orbits at Earth and Mars to connect to those. V-infinity is the hyperbolic excess velocity at a planet. Lecture 29: Interplanetary 25

26 Earth Departure We have v-infinity at departure Compute specific energy of departure wrt Earth: Compute the velocity you need at some parking orbit: Lecture 29: Interplanetary 26

27 Earth Departure Departing from a circular orbit, say, 185 km: Lecture 29: Interplanetary 27

28 Launch Target Lecture 29: Interplanetary 28

29 Launch Target Outgoing V Vector Locus of all possible interplanetary injection points Lecture 29: Interplanetary 29

30 C 3, RLA, DLA Launch Targets (In the frame of the V-inf vector!) Lecture 29: Interplanetary 30

31 Launch Targets Lecture 29: Interplanetary 31

32 Mars Arrival Same as Earth departure, except you can arrive in several ways: Enter orbit, usually a very elliptical orbit Enter the atmosphere directly Aerobraking. Aerocapture? E = V = V 2 2 µ R V = r 2µ R Lecture 29: Interplanetary 32 µ a

33 Aerobraking Lecture 29: Interplanetary 33

34 Comparing Patched Conics to High- Fidelity Lecture 29: Interplanetary 34

35 Gravity Assists A mission designer can harness the gravity of other planets to reduce the energy needed to get somewhere. Galileo launched with just enough energy to get to Venus, but flew to Jupiter. Cassini launched with just enough energy to get to Venus (also), but flew to Saturn. New Horizons launched with a ridiculous amount of energy and used a Jupiter gravity assist to get to Pluto even faster. Lecture 29: Interplanetary 35

36 Gravity Assists Gravity assist, like pretty much everything else, must obey the laws of physics. Conservation of energy, conservation of angular momentum, etc. So how did Pioneer 10 get such a huge kick of energy, passing by Jupiter? Lecture 29: Interplanetary 36

37 Designing Gravity Assists Rule: Unless a spacecraft performs a maneuver or flies through the atmosphere, it departs the planet with the same amount of energy that it arrived with. Guideline: Make sure the spacecraft doesn t impact the planet (or rings/moons) during the flyby, unless by design. Turning Angle ~V out 1 ~V 1 in r p = µ planet V 2 1 E = ~ V ~ V out 1 = ~ V in Lecture 29: Interplanetary 37 cos A

38 How do they work? Use Pioneer 10 as an example: OUT OF FLYBY INTO FLYBY ~V sun sc = ~ V 1 + ~ V sun jup V sun sc V sun jup V sun jup ~V 1 ~ V out 1 = ~ V in 1 ~V 1 = ~ V sun sc ~V sun jup Lecture 29: Interplanetary 38

39 Gravity Assists We assume that the planet doesn t move during the flyby (pretty fair assumption for initial designs). The planet s velocity doesn t change. The gravity assist rotates the V-infinity vector to any orientation. Check that you don t hit the planet V sun jup V sun jup V sun sc ~V 1 ~V 1 = ~ V sun sc ~V jup sun ~V 1 Lecture 29: Interplanetary 39

40 Gravity Assists We assume that the planet doesn t move during the flyby (pretty fair assumption for initial designs). The planet s velocity doesn t change. The gravity assist rotates the V-infinity vector to any orientation. Check that you don t hit the planet V sun jup V sun sc V sun jup ~V 1 ~V 1 = ~ V sun sc ~V jup sun Lecture 29: Interplanetary 40 ~V 1

41 Designing a Gravity Assist Build a transfer from Earth to Mars (for example) ~V 1 in Defines at Mars Build a transfer from Mars to Jupiter (for example) ~V 1 out Defines at Mars Check to make sure you don t break any laws of physics: r p = µ planet V 2 1 ~ V out 1 = ~ V in cos A Lecture 29: Interplanetary 41 1

42 Designing a Gravity Assist Another strategy: Build a viable gravity assist that doesn t necessarily connect with either the arrival or departure planets. Adjust timing and geometry until the trajectory becomes continuous and feasible. Lecture 29: Interplanetary 42

43 Gravity Assists Please note! This illustration is a compact, beautiful representation of gravity assists. But know that the incoming and outgoing velocities do NOT need to be symmetric about the planet s velocity! This is just for illustration. Lecture 29: Interplanetary 43

44 Gravity Assists We can use them to increase or decrease a spacecraft s energy. We can use them to add/remove out-of-plane components Ulysses! We can use them for science Lecture 29: Interplanetary 44

45 HW 8 is out Due Wednesday, Nov 12. J2 effect Using VOPs Announcements Reading: Chapter 12 Lecture 29: Interplanetary 45