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

Orbital Maneuvers Chapter 6

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 = 9.806 m/s2 or

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

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

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

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

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

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

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

Hohmann Transfer (non-circular)

Bi-Elliptic Transfer

Bi-Elliptic Transfer If rc/ra < 11.94 then Hohmann is more efficient If rc/ra > 15.58 then Bi-Elliptic is more efficient

Non-Hohmann Transfers w/Common Line of Aspides

Non-Hohmann Transfers w/Common Line of Aspides

Non-Hohmann Transfers w/Common Line of Aspides

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:

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

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

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)

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:

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

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)

Plane Change Pure plane change (circular to circular)

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

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

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

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

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

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

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

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) RC@CAP RSOI VMars V @Mars

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

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

Planetary Flyby Getting a boost

Planetary Flyby Getting a boost

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

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

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