Orbital Operations SP 210

Orbital Operations Orbiting spacecraft follow 2-body (Keplerian) orbits The orbit is centered on the exact center of the Earth because of the extremely small mass compared to Earth

Orbital Operations Accurate calculations are required for precise spacecraft maneuvers and precise trajectories. High accuracy is needed to compensate for: –Gravitational influence from other bodies including the Sun, Moon, and Jupiter –Non-spherical shape of the Earth (and other explored planets) –Slight pressure from sunlight –Gravitational anomalies at or near the Lagrange stability points

Orbital Operations 2-body orbits Orbit follows an elliptical path (described by an ellipse, or circle) Orbited body located at one of two focal points (other is empty) Major axis – longest axis Semi-major axis – ½ major axis = a –Measure of average separation Minor axis – shortest axis Semi-minor axis – ½ minor axis = b

Orbital Operations 2-body orbit features Apogee – longest distance between satellite and Earth Perigee – shortest distance between satellite and Earth Height or altitude – height above surface –Ha – apogee height –Hp – perigee height Semi-major axis = a a = (Ha + Hp)/2 + R Earth a = (apogee + perigee)/2

Orbital Operations 2-body orbit features Orbit period = p p = [4pi 2 a 3 /G(m1+m2)] 1/2 p proportional to a 3/2 a proportional to p 2/3 Larger semimajor axis orbits have longer periods and slower orbital velocities Rendezvous techniques generally use lower orbits to catch up to target spacecraft in higher orbits

Orbital Parameters Keplerian Cartesian

Orbital Operations Orbital parameters Orbital parameters are used to define an orbit and the position in that orbit with variables that are dependent on the reference frame and coordinates used Two different types of coordinate system are commonly used 1. Cartesian (X, Y, Z) system used for numerical computations of the orbital motion 2. Keplerian system that uses angles and lengths is better suited for calculation of planetary orbits and interplanetary flight

Orbital Operations Orbital parameters Each requires a minimum of seven parameters to define the orbit and satellite position at a specific time –Keplerian system Semimajor axis, eccentricity, right ascension (angle) of the nodes, inclination angle, argument (angle) of the perigee, true anomaly (angle), and time –Cartesian system X, Y, X, Vx, Vy, Vz, t

Orbital Parameters Orbital inclination Two orbit planes that are not coplanar (not in the same plane) define an angle difference called the inclination angle, or wedge angle The two planes include a spacecraft/satellite orbit and a second reference orbit plane, or a reference plane (Earth’s equatorial plane for example)

Orbital Parameters Orbital inclination The intersection of the two planed defines a line called the line of nodes –Ascending node – satellite orbit path passing upward through the reference plane –Descending node – satellite orbit path passing downward through the reference plane

Orbital Parameters Orbital inclination The expression for the orbital ∆V required for inclination change is ∆V = 2V sin(∆i/2) where V = orbital velocity, ∆i = inclination angle difference between current orbit plane and target orbit plane –Note the 2V in this expression V is the velocity at inclination change burn, generally allowed only at the line of nodes Ideally, the ∆V burn would occur at apogee since that is the lowest velocity in the orbit The line of nodes may be far from the apogee, making the fuel expenditure larger

Orbital Parameters Orbital inclination To conserve fuel, any plane change required for a mission segment is generally combined with any phase or orbital altitude change

Orbital Parameters Semi-major axis Lies along the line of apsides –Apsides are perigee and apogee The semi-major axis for an Earth orbit is the mean separation between the satellite and the center of the Earth Semi-major axis = a a = (Ha + Hp)/2 + R Earth a = (apogee + perigee)/2

Orbital Parameters Semi-major axis Any change in semi-major axis is relatively expensive in fuel –A limit of 1,000 ft/s for the Orbiter's ∆V fuel budget means that the 2 ft/s ∆V needed for a 1 nm orbit change places a limit of several hundred nautical miles, at most, on the orbital semi-major axis change –Roughly 220 ft/s ∆V is needed for deorbit

Orbital Parameters Eccentricity (e) Eccentricity describes the elongation of an orbit –Highly eccentric – flat –Low eccentricity – circular Range is from 0 (circular) to less than 1 (highly eccentric) Eccentricity changes in the orbit can be made with OMS burns. These produce: 1. Semi-major axis change 2. Constant semi-major axis with a purely radial burn

Orbital Parameters Eccentricity (e) Changes in eccentricity are made most often to establish the desired orbit from the initial orbit –Usually a transition from an eccentric orbit to a circular orbit The ∆e type of burn can also be used for: –Proximity maneuver with a relative velocity change –Rendezvous maneuver with lower/higher orbit spacecraft targets

Orbital Parameters Orbit phase Orbital phase is the orbital position of the spacecraft with respect to a specified position in the orbit at a specified time Refers to the angle difference between the orbiting spacecraft and either the orbit perigee, or the target

Orbital Parameters Orbit phase Phase change can be made either with a semi- major axis change, or with a ∆V burn while in the same orbit –For a small distance closure, an acceleration burn can be made while staying in or near the desired orbit, followed by an opposing burn executed at arrival

Orbital Parameters Orbit phase If the distance is more than tens of kilometers, the Orbiter must first decrease its semi-major axis with a retrograde OMS burn to speed up relative to the target –This is followed by a prograde burn to return to the original orbit in the proximity of the target For a retarded phase (leading the target), a prograde burn would be executed to increase the semi-major axis to slow the Orbiter relative to the velocity of the target position –Followed with a retrograde burn to return to the original orbit in the proximity of the target

Orbital Parameters ∆V An orbit parameter change, whether semi-major axis, eccentricity, inclination, or phase, requires a change in relative velocity –Executed as a ∆V burn OMS for large translational ∆V burns RCS for small translational ∆V burns The velocity in orbit must be changed in order to alter any of the orbit parameters

Orbital Parameters ∆ V Total ∆ V budget for a typical Orbiter mission is approximately 1,000 ft/s for both RCS and OMS operations –This limitation is carefully monitored during the various mission flight segments to ensure that the Orbiter can return safely to Earth with sufficient reserve for deorbit, entry, and landing

Coordinate Systems Body Axis Coordinate System (BACS) Geocentric Celestial Local-Vertical Local-Horizontal (LVLH) Inertial XPOP

Orbital Operations Coordinate systems Coordinate systems are used to define and/or calculate positions within a specific reference frame More than one coordinate system is required for space operations due to: –Continual changes in the spacecraft position –Changing Earth's orientation due to rotation –Changes in the spacecraft orientation with respect to the background sky, and the Earth-based or space-based communications sites

Orbital Operations Coordinate systems Coordinate transformations (moving from one coordinate system to another) are continually calculated for specified points within the wide collection of flight reference coordinate systems Navigation star positions, communications sites, the Sun's relative position, and a host of other relevant, although ever-changing, positions are used by the guidance and navigation system Position and relative reference data are also available for the vehicle's data management systems, and for crew operations, and for the sensors and payloads

Orbital Operations Coordinate systems The Orbiter has a Cartesian primary reference coordinate system called the Body Axis Coordinate System (BACS) BACS is centered on the Orbiter's structural center- of-mass –Longitudinal (roll) X-axis points forward –Lateral (pitch) Y-axis points to the right (looking forward) –Vertical (yaw) Z-axis points downward towards the ET

Orbital Operations Coordinate systems Coordinate system for the External Tank, the SRBs, and the STS are all similar in orientation, but displaced Although separated, the Orbiter, the ET, and the STS system center X, Z planes coincide

Orbital Operations Geocentric Coordinates Geocentric reference coordinates are practical and used for: –Surface and nautical navigation –Astronomy –Space Shuttle and spacecraft navigation Primary advantage for these coordinates is the fixed star positions with respect to this coordinate reference frame

Orbital Operations Geocentric & Celestial Coordinates Geocentric and celestial coordinates correspond to the Earth's equator and poles, resulting in the fixed stars appearing to simply rotate with respect to the Earth –Sun and planets rotate in the sky like the stars, but they also change path in the sky through the seasons because of the 23 1/2 o tilt of the Earth's rotational axis

M50 Geocentric Coordinate System Precessed from 1950 Primary (X) axis –Lies in equatorial plane –Points at the vernal equinox Z axis points along the Earth's north rotational axis (north celestial pole)

Orbital Operations Geocentric Coordinates Because the Earth's tilt axis is fixed in angle but rotates in a circle, the stars appear to rotate slowly with a precession (rotation) period of 26,000 years –Precession period is long, however accurate star positions require correction of the star and planet positions to the time of observation if the position calculations are to be exact

Orbital Operations Geocentric Coordinates This apparent motion to the stars is corrected by extrapolating or "precessing" the stars from a catalog of positions at a specified time period called an epoch Current star catalogs use the 1950 or 2000 epoch, meaning that a measurement in the year 2012 would have to have the star positions precessed 12 years from the 2000 epoch catalog For the Orbiter and other spacecraft, their position is calculated from the mean epoch coordinates called M50 (the mean 1950 reference) or the J2K (the mean 2000 reference)

Local-Vertical Local- Horizontal (LVLH) coordinates The constant horizon reference requires a constant angle between the flight reference angle and the Earth Presents a continual local horizon to the Orbiter and the crew LVLH establishes a continually rotating flight path angle to maintain a constant reference angle to the Earth's horizon Also used for the International Space Station

Inertial coordinates Inertial coordinates are fixed in space and fixed with respect to the stars Used for operations requiring a fixed position or reference –Telescope observations Spacecraft Instruments in Orbiter's payload bay Three inertial reference examples for specific Orbiter mission –Target identity (Target ID) values are selected in the Orbiter's Digital Auto Pilot

XPOP coordinates X-axis Perpendicular to Orbit Plane (XPOP) coordinates are similar to LVLH but have the X-axis rotated out of the orbital plane by 90 o Used for solar heating reference (Z axis is at solar noon), and for early ISS assembly

Orbital Maneuvers Orbit Insertion Posigrade Burns Retrograde Burns Radial Burns Orbit Transfer

Orbital Maneuvers Orbit insertion Orbital entry is completed following SSME shutdown (MECO) with an OMS boost OMS burn makes up the rest of the orbital ∆V generated by the first two stages (SRBs and SSMEs) –Total is approximately 7,780 m/s or 17,500 mi/hr Earlier launch-to-orbit operational procedures spelled out two burns to (1) enter and to (2) circularize the orbit –OMS-1 –OMS-2

Orbital Maneuvers Orbit insertion Replaced with a more efficient single boost from the boost-to-orbit apogee –Single OMS boost establishes the Orbiter in a circular, or nearly circular, low-Earth orbit –Non-OMS orbit entry is possible directly from the SSME burn to MECO for smaller payloads with greater efficiency

Orbital Maneuvers Orbit insertion Ascent and completion of the orbit entry is monitored carefully to make any corrections for the launch and ascent-to-orbit thrust variables that include: –Variations in thrust from one or both SRBs –Wind shear –Accumulated upper-level wind drift –Trajectory error –SSME performance variation

Orbital Maneuvers Posigrade (forward thrust) burn A posigrade thrust (exhaust rearward, thrust forward) adds forward velocity and energy to the spacecraft which alters the orbit by increasing the semi- major axis Can change orbit eccentricity –Addition of velocity or energy will normally increase the orbital semi-major axis –Retrograde burn that decreases orbital velocity or energy will normally decrease the semi- major axis

Orbital Maneuvers Posigrade burn Posigrade burn will create a higher apogee if executed at perigee, or increase the perigee if executed at apogee It may also be used to circularize an orbit if executed correctly at the orbit apogee

Orbital Maneuvers Posigrade burn – off axis Results in the rotation of the final orbit apsides (line between apogee/apoapsis and perigee/periapsis)

Orbital Maneuvers Retrograde (rearward thrust) burn In contrast to the posigrade burn, the retrograde burn (exhaust forward, thrust rearward) will decrease forward velocity and the spacecraft's orbital energy –Decreases the semi- major axis

Orbital Maneuvers Retrograde burn Retrograde burn creates a lower apogee if executed at perigee, or a lower perigee if executed at apogee Can also be used to circularize an orbit if executed correctly at the orbit perigee

Orbital Maneuvers Retrograde burn

Orbital Maneuvers Retrograde burn – off axis

Orbital Maneuvers Radial (inward/outward) thrust An inward or outward thrust that is perpendicular to the direction of travel will not increase the orbital energy, or the semi-major axis, or the orbit period In a circular orbit, a radial burn will increase the orbital eccentricity

Orbital Maneuvers Radial (inward/outward) thrust A radial burn can also –Decrease the eccentricity –Circularize an orbit if executed 90 o from the apsides

Orbital Maneuvers Orbit transfer Transfer from one orbit to another in the same plane is made with simple prograde or retrograde burns –Increases or decreases orbital semi-major axis respectively –Increases or decreases orbital energy respectively For a circular-to-circular orbit change, a second burn is required at the arrival position to circularize the orbit

Orbital Maneuvers Orbit transfer For the simple case of circular orbits in a single plane (coplanar), the most energy efficient (lowest ∆V) is the Hohmann transfer Homann transfer includes: –Burn at the periapsis/perihelion of the transfer orbit (position A in the figure) –Second burn at the apoapsis/aphelion of the transfer orbit at a position 180 o from the first burn (B)

Orbital Maneuvers Orbit transfer Other transfer methods involve an increased thrust/propellant at both burn points, but result in a shorter time of flight and less than a 180 o trajectory between the departure and arrival burns –Type I transfer (<180 o ) A slower orbit transfer can be made with lower thrust and greater transfer time, but again at the expense of increased energy/delta V –Type II transfer (>180 o but <360 o )

Orbital Maneuvers Orbit transfer - direct

Rendezvous Maneuvers Launch Phase and Catch up Sequence Operations Docking Closure Example Relative Motion and Relative Motion Plots Rendezvous maneuver burns

Rendezvous Operations Rendezvous operations are used to orbit two spacecraft in proximity to one another and are/were commonly used in Space Shuttle missions –Satellite deployment and retrieval –Docking with the Mir –Docking with the ISS space station A typical rendezvous mission begins with the target spacecraft launched into a specified orbit The chase spacecraft is later launched into a trailing orbit in the same orbital plane –Delay between launches can be hours to years

Rendezvous Operations For STS missions, the Orbiter would be the chase craft, and would be launched into the same plane as the target vehicle just as the launch site passes through the orbit plane as the Earth rotates beneath –The orbit plane of the launch must be the same plane as the target vehicle (coplanar), hence the launch window is only a few minutes wide

Rendezvous Operations The phase angle between the two spacecraft positions in orbit also has to be correct to allow one or two days for the catch-up and rendezvous –Larger phase angles that would result in longer catch-up periods are unnecessary and resource expensive since these rendezvous flights are almost always manned missions

Rendezvous Operations Orbiter's docking maneuvers are done in daylight hours, so planning for the rendezvous must also take into account the position with respect to the Earth-Sun line at the actual rendezvous –This further limits the launch window

Rendezvous Operations For STS missions, the Orbiter would be the chase craft, and would be launched into the same plane as the target vehicle just as the launch site passes through the orbit plane as the Earth rotates beneath –The orbit plane of the launch must be the same plane as the target vehicle (coplanar), hence the launch window is only a few minutes wide The phase angle between the two spacecraft positions in orbit also has to be correct to allow one or two days for the catch-up and rendezvous –Larger phase angles that would result in longer catch-up periods are unnecessary and resource expensive since these rendezvous flights are almost always manned missions

Rendezvous Operations Orbiter's docking maneuvers are done in daylight hours, so planning for the rendezvous must also take into account the position with respect to the Earth-Sun line at the actual rendezvous –This further limits the launch window

Rendezvous Operations Rendezvous sequence The Orbiter is launched into a lower orbit to catch up with the leading target spacecraft since a lower orbit has a faster rotation –Closure rate of the angle between the two spacecraft is proportional to the altitude difference (actually the semi- major axis difference) of the two spacecraft As the Orbiter reaches the target vehicle and the phase angle approaches zero, the Orbiter is boosted to higher orbit to reach the target's circular orbit with the Orbiter closing on the target

Rendezvous Operations Rendezvous sequence To boost the Orbiter to the target in its circular orbit, a posigrade burn is first made to increase the semi-major axis of the Orbiter and decrease the orbit period –Followed by another posigrade burn to match the target's orbital velocity as the Orbiter reaches the target Since the Orbiter's approach to the target for docking must be gradual and very slow for the actual docking, the two burn rendezvous maneuver actually entails a number of burns in a sequence of slower approach speeds

Rendezvous Operations Rendezvous operations To speed up to catch a leading target in orbit, the chase vehicle must first be slowed with a retrograde thrust –This drops the chase spacecraft into a lower, faster orbit –Retrograde burn used to increase relative velocity To slow with respect to the target vehicle in orbit, the chase vehicle must be accelerated with a posigrade burn –This raises the chase spacecraft into a higher, slower orbit –Posigrade burn used to decrease relative velocity

Rendezvous Operations – Vehicle Convergence Orbits for both chaser and target spacecraft must be coplanar, and at altitudes that have minimal atmospheric drag For a catch-up phase that takes one to two days, the rate of convergence requires a separation angle dependent on the semi-major axis difference between the two spacecraft, typically 30 o - 70 o

Rendezvous Operations – Vehicle Convergence Example: A target orbit of 250 km and a chase orbit altitude of 200 km, results in a closing rate of o /sec Target vehicle 250 km orbit km Earth radius = 6628 km semi-major axis = sec orbit period Chase vehicle 200 km orbit km Earth radius = 6578 km semi-major axis = sec orbit period

Rendezvous Operations – vehicle convergence Example (cont.) For a target vehicle orbit of sec, the closure rate per orbit is the closure rate per second times the period in seconds Closure rate per orbit = orbit period difference = o /sec x sec orbit period = 4.12 o /orbit –With 86,400 sec/day, the convergence of the two spacecraft would occur in 24 hours if separated initially by 66.4 o Another way to calculate the same problem is to use orbits per day for the target vehicle and 4.12 o /orbit –4.12 o /orbit times orbits/day = 66.4 o per day closure

Rendezvous Operations – Vehicle Convergence

Rendezvous Operations Satellite/spacecraft relative motion A convenient representation of the target and chase vehicles is to use a relative motion plot of the spacecraft that follows the target spacecraft The relative motion plot will fix the motion of the target vehicle which makes the relative motion much simpler to follow –This also makes the representation of the thrust effects and orbit relationship between the two spacecraft easier to visualize

Rendezvous Operations Satellite/spacecraft relative motion Although the true center of the plot is at the Earth's center, the center of the relative motion frame is moved up and placed on the target –The orbit of the target vehicle is assumed to be circular

Rendezvous Operations – Relative Motion With the chase vehicle in a lower orbit than the target vehicle, its relative motion is from right to left because of the faster orbit speed A chase vehicle in a higher orbit (larger semi-major axis) would have relative motion from left to right with respect to the target (centered) vehicle

Rendezvous Operations Thrust effects on relative motion Posigrade thrust will increase the semi-major axis of a spacecraft in orbit but decrease the orbital speed Displayed on a relative motion plot, a posigrade burn on a vehicle located at the center position would move the vehicle upward (higher energy and semi-major axis) and to the right (slower orbital speed)

Rendezvous Operations Thrust effects on relative motion A periodic motion upward and downward above the horizontal centerline is created by elliptical orbit produced by a posigrade burn Retrograde burns will have the opposite affects, pushing the chaser generally downwards and resulting in oscillatory motion upward and downward, with a path running from right to left

Rendezvous Operations Rendezvous and phase change burns The rendezvous procedures for STS missions evolved from earlier Gemini and Apollo manned missions, and have been refined over more than 25 years of orbital operations A list of the basic maneuvers used for the Orbiter's rendezvous and proximity operations are described in the following list (from STS-93 press kit) OMS-1 (Orbit insertion) - A little-used ascent abort burn OMS-2 (Orbit insertion) - Typically used to circularize the initial orbit following ascent to complete orbital insertion. For ground- up rendezvous flights, this is also considered a rendezvous phasing burn.

Rendezvous Operations Rendezvous and phase change burns NC (Rendezvous phasing) - Executed to hit a range relative to the target at a future time. This is used for a preliminary phase adjustment that beings the Shuttle to the Terminal initiation point (Ti) and subsequent Mid-Course maneuvers (MCs). NH (Rendezvous Height adjust) - Executed to hit a delta-height relative to the target at a future time

Rendezvous Operations Rendezvous and phase change burns NPC (Rendezvous Plane Change) - Executed to remove orbit plane difference errors relative to the target at a future time. This maneuver is expensive in fuel and is limited to approximately 5 o for the Orbiter. NCC (Rendezvous Corrective Combination) - First targeted burn in the rendezvous sequence –Using accurate GPS or star tracker data, it is performed to remove phasing and height errors relative to the target at Ti –This technique can be applied in any orbit transfer, including interplanetary trajectories

Rendezvous Operations Rendezvous and phase change burns Ti (Rendezvous Terminal initiation) –Second on-board targeted burn in the rendezvous sequence –Uses rendezvous radar and other data to place the Orbiter on a trajectory to intercept the target in one orbit –Ti burn is timed for the rendezvous to be made during midday of the next orbit Timing of the Ti burn is near noon (usually three minutes before) in the preceding orbit

Rendezvous Operations Rendezvous and phase change burns MC-1, MC-2, MC-3, MC-4 (Rendezvous midcourse burns) Corrective mid-course burns use GPS or star tracker and rendezvous radar data to correct the post-Ti trajectory in preparation for the final, manual proximity operations

Rendezvous Operations Example: STS-121 orbital operations - major event list 7/4/2006 Tue 2:37 PM 0d 0h 0m STS-121 Launch 7/4/2006 Tue 3:15 PM OMS-2 orbit circularization burn 7/4/2006 Tue 7:38 PM NC-1 rendezvous OMS burn 7/5/2006 Wed 6:43 AM NC-2 rendezvous OMS burn 7/5/2006 Wed 11:13 AM NPC rendezvous OMS burn 7/5/2006 Wed 5:43 PM NC-3 rendezvous OMS burn 7/6/2006 Thu 5:38 AM NH rendezvous OMS burn 7/6/2006 Thu 6:33 AM NC-4 rendezvous OMS burn 7/6/2006 Thu 8:05 AM Ti OMS burn (ISS distance: 8 nm) 7/6/2006 Thu 9:21 AM MC-4 course correction burn 7/6/2006 Thu 10:52 AM Docking NC = Rendezvous phasing NH = Rendezvous Height adjust NPC = Rendezvous Plane Change NCC = Rendezvous Corrective Combination Ti = Rendezvous Terminal initiation MC-1, MC-2, MC-3, MC-4 = Rendezvous midcourse burns

Rendezvous Operations Example: STS-121 orbital operations - major event list 7/4/2006 Tue 2:37 PM 0d 0h 0m STS-121 Launch 7/4/2006 Tue 3:15 PM OMS-2 orbit circularization burn 7/4/2006 Tue 7:38 PM NC-1 rendezvous OMS burn 7/5/2006 Wed 6:43 AM NC-2 rendezvous OMS burn 7/5/2006 Wed 11:13 AM NPC rendezvous OMS burn 7/5/2006 Wed 5:43 PM NC-3 rendezvous OMS burn 7/6/2006 Thu 5:38 AM NH rendezvous OMS burn 7/6/2006 Thu 6:33 AM NC-4 rendezvous OMS burn 7/6/2006 Thu 8:05 AM Ti OMS burn (ISS distance: 8 nm) 7/6/2006 Thu 9:21 AM MC-4 course correction burn 7/6/2006 Thu 10:52 AM Docking NC = Rendezvous phasing NH = Rendezvous Height adjust NPC = Rendezvous Plane Change NCC = Rendezvous Corrective Combination Ti = Rendezvous Terminal initiation MC-1, MC-2, MC-3, MC-4 = Rendezvous midcourse burns

Rendezvous and Proximity Operations Rendezvous Maneuver Burns R-bar Approach V-bar Approach

Rendezvous & Proximity Operations Rendezvous and proximity approaches As the Orbiter nears the target vehicle, the closure velocity from a slightly elliptical catch-up orbit will bring the Orbiter through or near the target vehicle's position Mid-course correction burns are then used to refine the closure trajectory and velocity after the initial Ti intercept burn executed one orbit earlier This places the chase vehicle near the target for rendezvous from below and from the right (lower orbit and higher velocity)

Rendezvous & Proximity Operations Rendezvous and proximity approaches To allow for a controlled approach for docking or satellite retrieval, the Orbiter must slow its relative velocity to a closure speed as small as several cm/s –The low relative speed is necessary for a contact docking or a vehicle capture During the final stages of the Orbiter's approach to the target vehicle it will transition from closure in a slightly eccentric orbit to a slower, more precise approach for docking or capture

Rendezvous & Proximity Operations Rendezvous and proximity approaches The two proximity approach paths are 1.Vertically from below Called the R-bar approach since its along the radial line between the Earth and the target 2. Horizontally along the velocity vector of the target vehicle Called the V-bar approach since its along the velocity vector (bar refers to the vector notation)

Rendezvous & Proximity Operations Rendezvous and proximity approaches R-bar on the left V-bar on the right

Rendezvous & Proximity Operations Rendezvous and proximity approaches Orbital maneuvers for the rendezvous/proximity approach begin with the phasing and Ti burns Mid-course corrections are then used to establish the Orbiter on the approach path for one of two primary approach techniques, although other techniques are available

Rendezvous & Proximity Operations Rendezvous and proximity approaches The upward R-bar approach to the target vehicle allows convergence along the radial (R) direction The V-bar approach in the flight path direction, or in the opposite direction along the flight path –Both begin with an approach from below since the final eccentric orbit brings the chase vehicle to the target vehicle at the chase’s apogee point

Rendezvous & Proximity Operations Rendezvous and proximity approaches R-bar on the left V-bar on the right