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

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

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

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

Quiz #8 Lecture 8: Orbital Maneuvers

Quiz #8 Lecture 8: Orbital Maneuvers

Quiz #8 Lecture 8: Orbital Maneuvers

Quiz #8 Lecture 8: Orbital Maneuvers

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

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

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

Circular Rendezvous (coplanar) Lecture 11: Orbit Transfers

How do we build these? Lecture 11: Orbit Transfers

How do we build these? Lecture 11: Orbit Transfers

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

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

Example 6-8 Lecture 11: Orbit Transfers

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

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

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

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

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

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

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

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

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

Example Circular Coplanar Rendezvous Step 3: Phasing. The target will advance 116.9 deg during the transfer. x Orbit 1 Lecture 11: Orbit Transfers Orbit 2

Example Circular Coplanar Rendezvous Step 3: Phasing. The vehicles start 35 deg apart. They need to be 63.1 deg apart (180-116.9 deg) x ϑ Orbit 1 Lecture 11: Orbit Transfers Orbit 2

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

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

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

Example 6-9 Lecture 11: Orbit Transfers

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

Circular Non-Coplanar Phasing Lecture 8: Orbital Maneuvers

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

Circular Non-Coplanar Phasing Lecture 8: Orbital Maneuvers

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

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

Right Spherical Triangle Lecture 8: Orbital Maneuvers

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

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 = 0.465 km/s. Westward launches must make this up, so difference is 0.93 km/s. Lecture 8: Orbital Maneuvers

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

Launch Sites Lecture 8: Orbital Maneuvers

Noncoplanar Transfers Lecture 8: Orbital Maneuvers

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

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

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