1. ARO309 - Astronautics and Spacecraft Design
Winter 2014
Try Lam
CalPoly Pomona Aerospace Engineering

2. Orbital Maneuvers
Chapter 6

3. Maneuvers We assume our maneuvers are “instantaneous”
ΔV changes can be applied by changing the magnitude “pump” or by changing the direction “crank”
Rocket equation: relating ΔV and change in mass
where g0 = m/s2 or

4. Isp
Isp is the specific impulse (units of seconds) and measures the performance of the rocket

5. V
V (“delta”-V) represents the instantaneous change in velocity (from current velocity to the desired velocity).
Circular Orbit Velocity
Elliptical Orbit Velocity

6. Tangent Burns Your Initial Orbit R1 Your Spacecraft
Initially you are in a circular orbit with radius R1 around Earth
Your Initial Orbit R1
Your Spacecraft

7. Tangent Burns R1 R2 V Your new orbit after the V burn
Initially you are in a circular orbit with radius R1 around Earth
You perform a burn now which puts in into the red-dotted orbit. So you perform a V. R1 R2 V
Your new orbit after the V burn

8. Tangent Burns
Initially you are in a circular orbit with radius R1 around Earth
You perform a burn now which puts in into the red-dotted orbit. So you perform a V. R1 R2

9. Hohmann Transfer V2 R1 R2 V1
The most efficient 2-burnmaneuver to transfer between 2 co-planar circular orbit
V2 R1 R2
V1

10. Hohmann Transfer (non-circular)
Another way to view it is using angular momentum

11. Hohmann Transfer (non-circular)

12. Bi-Elliptic Transfer

13. Bi-Elliptic Transfer
If rc/ra < then Hohmann is more efficient
If rc/ra > then Bi-Elliptic is more efficient

14. Non-Hohmann Transfers w/Common Line of Aspides

15. Non-Hohmann Transfers w/Common Line of Aspides

16. Non-Hohmann Transfers w/Common Line of Aspides

17. Apse Line Rotation Apse Line Rotation Angle NOTE:
Opportunity to transfer from one orbit to another using a single maneuver occurs at intersection points of the orbits
Apse Line Rotation Angle
NOTE:

18. Apse Line Rotation Setting and using the following identity
Opportunity to transfer from one orbit to another using a single maneuver occurs at intersection points of the orbits
Setting and using the following identity
Then has two solution corresponding to point I and J

19. Apse Line Rotation Given the orbit information of the two orbits
Opportunity to transfer from one orbit to another using a single maneuver occurs at intersection points of the orbits
Given the orbit information of the two orbits
Next, compute

20. Apse Line Rotation If you want to find the effect of a If
Opportunity to transfer from one orbit to another using a single maneuver occurs at intersection points of the orbits
If you want to find the effect of a If
(at periapsis)

21. Apse Line Rotation Another useful equation:
Opportunity to transfer from one orbit to another using a single maneuver occurs at intersection points of the orbits
Another useful equation:

22. Plane Change Maneuvers
In general a plane change maneuver changes the orbit plane or
where

23. Plane Change Maneuvers
In general a plane change maneuver changes the orbit plane
If there is no plane change, then
No plane change
and we get the same equation as from slide 130.
If then
Pure plane change (common line of apisdes)

24. Plane Change
Pure plane change (circular to circular)

25. Rendezvous target TIME = 0 V 0 spacecraft
Catching a moving target: Hohmann transfer assume the target will be there independent of time, but for rendezvousing the target body is always moving.
target
TIME = 0 V 0
spacecraft

26. Rendezvous TIME = TOF V 0 target spacecraft
Catching a moving target: Hohmann transfer assume the target will be there independent of time, but for rendezvousing the target body is always moving.
TIME = TOF V 0
target
spacecraft

27. Wait Time (WT) TIME = -WT 0 target V  spacecraft
How long do you wait before you can perform (or initiate) the transfer?
TIME = -WT 0
target V 
spacecraft

28. Co-orbital Rendezvous
Chasing your tail
Forward thrust to slow down
Phasing orbit size
target 0 V
spacecraft
Reverse thrust to speed up

29. Patched-Conic Sphere of Influence
An approximation breaks the interplanetary trajectory into regions where conic approximation is applicable
Sphere of Influence

30. Patched-Conic Computational Steps PATCH 1
An approximation breaks the interplanetary trajectory into regions where conic approximation is applicable
Computational Steps
PATCH 1: Compute the Hohmann transfer Vs
PATCH 2: Compute the Launch portion
PATCH 3: Compute the Arrival portion
PATCH 1
The V1 from the interplanetary Hohmann is V at Earth
The V2 from the interplanetary Hohmann is V at target body arrival

31. Patched-Conic RSOI V @Earth VEarth RC@DEP VDEP
An approximation breaks the interplanetary trajectory into regions where conic approximation is applicable
RSOI
Earth Departure
(assume circular orbit)
VEarth
VDEP

32. Patched-Conic VCAP RC@CAP RSOI VMars V @Mars
An approximation breaks the interplanetary trajectory into regions where conic approximation is applicable
VCAP
Target Body Capture
(assume circular orbit)
RSOI
VMars

33. Patched-Conic Total Mission V for a simple 2 burn transfer VDEP
An approximation breaks the interplanetary trajectory into regions where conic approximation is applicable
Total Mission V for a simple 2 burn transfer
VDEP
VCAP

34. Planetary Flyby Gravity-assists or flybys are used to Getting a boost
Reduce or increase the heliocentric (wrt. Sun) energy of the spacecraft (orbit pumping), or
Change the heliocentric orbit plane of the spacecraft (orbit cranking), or both

35. Planetary Flyby
Getting a boost

36. Planetary Flyby
Getting a boost

37. Planetary Flyby Getting a boost Stationary Jupiter Moving Jupiter
Planet’s velocity adds to the spacecraft’s velocity (like a fast moving runner grabbing you and running) 37

38. Planetary Flyby Getting a boost Fg Fg Vplanet Decrease energy wrt. Sun
Planet’s velocity adds to the spacecraft’s velocity (like a fast moving runner grabbing you and running)
Vplanet
Decrease energy wrt. Sun
Increases energy wrt. Sun 38

39. Planetary Flyby Getting a boost V
V leveraging is the use of deep space maneuvers to modify the V at a body. A typical example is an Earth launch, V maneuver (usually near apoapsis), followed by an Earth gravity assist (V-EGA).
post maneuver
If no maneuver