1. ASEN 5050 SPACEFLIGHT DYNAMICS Orbit Transfers
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 11: Orbit Transfers

2. Announcements Homework #4 is due Friday 9/26 at 9:00 am
You’ll have to turn in your code for this one.
Again, write this code yourself, but you can use other code to validate it.
Concept Quiz #9 is active after this lecture; due before Friday’s lecture.
Mid-term Exam will be handed out Friday, 10/17 and will be due Wed 10/22. (CAETE 10/29)
Take-home. Open book, open notes.
Once you start the exam you have to be finished within 24 hours.
It should take 2-3 hours.
Reading: Chapter 6
Lecture 11: Orbit Transfers

3. Space News Last night: MOM arrived at Mars!
Lecture 11: Orbit Transfers

4. Space News SpaceX’s Dragon berthed with the ISS
Lecture 11: Orbit Transfers

5. Quiz #8
Lecture 8: Orbital Maneuvers

6. Quiz #8
Lecture 8: Orbital Maneuvers

7. Quiz #8
Lecture 8: Orbital Maneuvers

8. Quiz #8
Lecture 8: Orbital Maneuvers

9. ASEN 5050 SPACEFLIGHT DYNAMICS Orbital Maneuvers
Prof. Jeffrey S. Parker
University of Colorado - Boulder
Lecture 11: Orbit Transfers

10. Changing Orbital Elements
Δa  Hohmann Transfer
Δe  Hohmann Transfer
Δi  Plane Change
ΔΩ  Plane Change
Δω  Coplanar Transfer
Δν  Phasing/Rendezvous
Lecture 11: Orbit Transfers

11. Circular Rendezvous (coplanar)
Target spacecraft; interceptor spacecraft
Lecture 11: Orbit Transfers

12. Circular Rendezvous (coplanar)
Lecture 11: Orbit Transfers

13. How do we build these?
Lecture 11: Orbit Transfers

14. How do we build these?
Lecture 11: Orbit Transfers

15. How do we build these? Determine your phase angle, φ
Determine how long you want to spend performing the transfer
How many revolutions?
Build the transfer
Compute the ΔV
Lecture 11: Orbit Transfers

16. How do we build these?
Compute the ΔV
Lecture 11: Orbit Transfers

17. Example 6-8
Lecture 11: Orbit Transfers

18. Example 6-8 Should be positive
This should really be an absolute value (one maneuver is in-track, one is anti-velocity)
This should really be an absolute value (one maneuver is in-track, one is anti-velocity)
Lecture 11: Orbit Transfers

19. Conclusions
Better to use as many revolutions as possible to save fuel.
Trade-off is transfer duration
If you perform the transfer quickly, be sure to check your periapse altitude.
Lecture 11: Orbit Transfers

20. Circular Coplanar Rendezvous (Different Orbits)
Lecture 11: Orbit Transfers

21. Circular Coplanar Rendezvous (Different Orbits)
Use Hohmann Transfer
The “wait time”, or time until the interceptor and target are in the correct positions:
π – αL - +
Synodic Period:
Lecture 11: Orbit Transfers

22. Example Circular Coplanar Rendezvous
Build me a transfer from one circular equatorial orbit to another.
Orbit 1: radius = 15,000 km, longitude = 10 deg
Orbit 2: radius = 30,000 km, longitude = 45 deg
Lecture 11: Orbit Transfers

23. Example Circular Coplanar Rendezvous
Step 1: draw a picture. ? x
Orbit 1
Lecture 11: Orbit Transfers
Orbit 2

24. Example Circular Coplanar Rendezvous
Step 2: Hohmann. ? x
Orbit 1
Lecture 11: Orbit Transfers
Orbit 2

25. Example Circular Coplanar Rendezvous
Step 3: Phasing.
How far will the target move during the transfer? x
Orbit 1
Lecture 11: Orbit Transfers
Orbit 2

26. Example Circular Coplanar Rendezvous
Step 3: Phasing. α x
Orbit 1
Lecture 11: Orbit Transfers
Orbit 2

27. Example Circular Coplanar Rendezvous
Step 3: Phasing. The target will advance deg during the transfer. x
Orbit 1
Lecture 11: Orbit Transfers
Orbit 2

28. Example Circular Coplanar Rendezvous
Step 3: Phasing. The vehicles start 35 deg apart. They need to be 63.1 deg apart ( deg) x ϑ
Orbit 1
Lecture 11: Orbit Transfers
Orbit 2

29. Example Circular Coplanar Rendezvous
Step 3: Phasing. They need to be 63.1 deg apart. x
Orbit 1
Lecture 11: Orbit Transfers
Orbit 2

30. Example Circular Coplanar Rendezvous
Step 3: Phasing. They need to be 63.1 deg apart.
Orbit 2
Orbit 1 x
Lecture 11: Orbit Transfers

31. Circular Coplanar Rendezvous (Different Orbits)
Use Hohmann Transfer
The “wait time”, or time until the interceptor and target are in the correct positions:
π – αL - +
Synodic Period:
Lecture 11: Orbit Transfers

32. Example 6-9
Lecture 11: Orbit Transfers

33. Example 6-9
I think this should be pi – alpha, not alpha – pi (see Fig 6-17)
Lecture 11: Orbit Transfers

34. Circular Non-Coplanar Phasing
Lecture 8: Orbital Maneuvers

35. Circular Non-Coplanar Phasing
Requires proper nodal alignment as well as proper phasing. Because of the long wait times, an intermediate phasing orbit is usually used to set up the proper phasing
Must determine time to reach node:
(Movement of target during Dt)
(360 - n)
Lecture 8: Orbital Maneuvers

36. Circular Non-Coplanar Phasing
Lecture 8: Orbital Maneuvers

37. ASEN 5050 SPACEFLIGHT DYNAMICS Launch
Prof. Jeffrey S. Parker
University of Colorado - Boulder
Lecture 11: Orbit Transfers

38. Launch Launching a satellite:
For a direct launch, the launch site latitude must be less than or equal to the desired inclination, otherwise we must change the inclination of the orbit.
Lecture 8: Orbital Maneuvers

39. Right Spherical Triangle
Lecture 8: Orbital Maneuvers

40. Cannot direct launch into orbit with inclination < fgc
We can show this using spherical trigonometry for a right spherical triangle (eq. C-23):
Thus,
Because |sin b | ≤ 1, the launch latitude fgc ≤ i
Another useful relation: sin fgc = sin(i) sin(w+n)
Cannot direct launch into orbit with inclination < fgc
Lecture 8: Orbital Maneuvers

41. Launch The launch site velocity is:
Note all the velocity is Eastward in the SEZ system, so launching from the equator on a 90 azimuth may be best.
The velocity at the equator is vL = km/s. Westward launches must make this up, so difference is 0.93 km/s.
Lecture 8: Orbital Maneuvers

42. Launch Azimuths Launch sites and allowable azimuths
Lecture 8: Orbital Maneuvers

43. Launch Sites
Lecture 8: Orbital Maneuvers

44. Noncoplanar Transfers
Lecture 8: Orbital Maneuvers

45. Noncoplanar Transfers
Launch window – select UT to achieve orbit’s desired initial nodal location (determine qgst)
First determine launch azimuth b (inverse sine gives two possible answers: b and 180-b, for ascending (-90 < u < 90) and descending (90 < u < 270) passes.)
Now, determine the auxiliary angle from:
The values lu and 360-lu represent prograde and retrograde orbits respectively.
Lecture 8: Orbital Maneuvers

46. Noncoplanar Transfers
Tolerance on ascending node (±DW) creates “launch window”, or range of values of qGST. Once qGST is chosen:
Substitution of qGST0 for each day (GST at 0 hrs on that day) gives the launch time on each day.
Dv is more complicated.
Lecture 8: Orbital Maneuvers

47. Announcements Homework #4 is due Friday 9/26 at 9:00 am
You’ll have to turn in your code for this one.
Again, write this code yourself, but you can use other code to validate it.
Concept Quiz #9 is active after this lecture; due before Friday’s lecture.
Mid-term Exam will be handed out Friday, 10/17 and will be due Wed 10/22. (CAETE 10/29)
Take-home. Open book, open notes.
Once you start the exam you have to be finished within 24 hours.
It should take 2-3 hours.
Reading: Chapter 6
Lecture 11: Orbit Transfers