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Appendix to 1 Elements of a Space Mission - Supplement Direct Ascent and Hohmann Transfer Ascent to a satellite orbit Hohmann Transfer Ellipse. Note that direction of thrust is opposite the direction propellant is expelled. Elements of a Space Mission - Supplement LAUNCH PROCEDURE PARKING ORBIT, TRANSFER ORBIT: The launch vehicle, after ascent, either injects its payload into a GEOSTATIONARY TRANSFER ORBIT (GTO) (elliptic orbit the apogee of which is at the altitude of the GEO), or settles itself on a PARKING ORBIT (low altitude circular orbit (LEO)) prior to injection of its payload in GTO. At an apogee of the GTO, injection of the satellite in the final GEOSTATIONARY ORBIT (GEO) occurs. Transfer from one orbit to another is achieved by modifying the velocity of the body with a THRUST applied to it. The required change in velocity assumed to be impulsive is called VELOCITY INCREMENT Elements of a Space Mission - Supplement LAUNCH SITES Elements of a Space Mission - Supplement MINIMUM INCLINATION of the TRANSFER ORBIT a: launch angle relative to EAST l: latitude of the launch pad P: launch pad The INCLINATION i of the ORBIT PLANE of the launch vehicle is given by: cos i = (cos a)(cos l) For the launch of a geostationary satellite (non-retrograde orbit), MINIMUM INCLINATION is obtained for a = 0°, i.e. a launch towards the EAST. Moreover, the launch vehicle benefits from the VELOCITY INDUCED on the trajectory by the rotation of the Earth. GTO inclination is greater or equal than the latitude of the launch pad. An ORBIT INCLINATION CORRECTION MANOEUVER (dog-leg manoeuvre) is to be carried out to obtain a final orbit in the equatorial plane. Elements of a Space Mission - Supplement Plane Change Relationship is the angle through which the orbit plane is rotated, and V is the incremental velocity necessary to effect this change. The required velocity change, V, for plane change angles less than 5 degrees may be approximated as being equal to 2 x Vi x sin (/2). For example for an object in a 100 nm circular orbit with Vi = 25,570 ft/s, a plane change of only 5 degrees imposes a major penalty of 2,230 ft/s. This can be avoided or minimized by selecting a proper launch site and launching directly into that inclined plane. Elements of a Space Mission - Supplement ORBIT INCLINATION CORRECTION STRATEGY Correction of the transfer orbit inclination is performed by a velocity increment applied at ONE OF THE NODES of the orbit, such as the resultant velocity vector lies in the equatorial plane The lower the satellite velocity, the smaller the velocity increment maneuver is carried out at the apogee altogether with circularization. This implies: apogee of transfer orbit at GEO altitude, perigee-apogee line of the GTO in the line of nodes, therefore perigee is in the equatorial plane (injection onto GTO at equatorial plane crossing) orientation of the thrust with an angle relative to satellite velocity = arcsin (Vs sin i / VA), where VA is the total velocity increment to be applied for inclination correction and circularization (see next) Elements of a Space Mission - Supplement VELOCITY REQUIREMENTS: PROBLEM Consider the launch of a satellite using a conventional expendable launch vehicle (ARIANE): Determine: velocity Vp to be provided by the launch vehicle for direct injection at perigee (altitude hp = 200 km) of the geostationary transfer orbit (GTO) velocity increment V to be applied to the satellite for circularization assuming GTO inclination equal to 0° (transfer from GTO to GEO) velocity increment VA to be applied to satellite for transfer from GTO to GEO with correction of inclination i. Calculate VA with i = 7° Elements of a Space Mission - Supplement VELOCITY REQUIREMENTS DIRECT- INJECTION INTO GTO: Injection velocity = velocity Vp at perigee of GTO 1/2 Vp = ((2/(Re +hp) -(/a)) where: hp = perigee altitude hA = apogee altitude a = semimajor axis = (hp+hA)/2 + Re Re = Earths radius = 3.986 1014 m3/s2 = 6378 km PARKING ORBIT TO GTO (ORBITS IN THE SAME PLANE): Velocity increment Vp = Vp -VI 1/2 where: VI = parking orbit velocity = (/(Re+hp)) GTO TO GEO (CIRCULARIZATION ONLY): Velocity increment V =Vs -VA 1/2 where: VS = velocity on GEO = (/(Re+hA)) = 3075 m/s VA = velocity at. apogee of GTO . 1/2 = ((2/(Re +hA) - (/a)) GTO TO GEO WITH A PLANE CHANGE i AT APOGEE: 2 2 1/2 VA = (VS + VS -2 VA VS cos i) Park GTO Vp VI VP VA VA (Km) (Km) (m/s) (m/s) (m/s) (m/s) (m/s) ARIANE - 200-35766 10239 - - 1597 i = ° STS 290 290-35786 10160 7732 2430 1607 1820 i = 28° Elements of a Space Mission - Supplement INFLUENCE OF ORBIT INCLINATION CORRECTION ON THE SATELLITE MASS The given velocity increment at apogee is provided by the so-called APOGEE MOTOR which creates a thrust by expelling gases generated by combustion of propellant, then accelerated by a nozzle. The required mass of propellant is related to the velocity increment by Mp = Ms [1 - (exp(-V /g.lsp)], Where : Isp, specific impulse is a propellant characteristic (s) 2 : g is the Earth's gravitational constant (9.807 m/s ) : Mp is the propellant mass, Ms the initial satellite mass For a given initial satellite mass at launch, the larger the velocity increment to be provided, the smaller the mass on final geostationary orbit. Elements of a Space Mission - Supplement ORBITAL INJECTION SEQUENCE WITH AN EXPENDABLE LAUNCH VEHICLE The sequence is divided into three phases: LAUNCH PHASE, from take-off to injection in GTO, where the upper stage (plus satellite) of the launcher reaches the altitude of the GTO perigee on a trajectory which ends parallel to the Earth surface with the required velocity, TRANSFER PHASE, from GTO injection to GEO injection, on which the orbit is monitored and the orientation of the satellite required for inclination correction is provided, POSITIONING PHASE, from GEO injection to positioning the satellite at its nominal station. Elements of a Space Mission - Supplement ORBITAL INJECTION SEQUENCE WITH STS With the Space Transportation System (STS), the procedure from its nominal orbit (circular, 290 km, 28° inclination) comprises: DEPLOYMENT of the satellite from the cargo bay. GTO INJECTION by firing the perigee motor which provides the required velocity increment, TRANSFER PHASE and POSITIONING PHASE Deployment is achieved using spring ejection, the attitude of the satellite being spin stabilized. GTO injection occurs at equatorial plane crossing, so the transfer orbit has its perigee (and hence apogee) in the equatorial plane. No inclination correction is performed (as a result of the high satellite velocity, this maneuver would be very propellant consuming). Elements of a Space Mission - Supplement POSITIONING: DRIFT ORBIT AND STATION ACQUISITION GEO INJECTION is performed at a specific transfer orbit apogee number, to allow for: accurate determination of the transfer orbit, visibility of the satellite from at least two control stations, circularization near the nominal station longitude. Due to dispersions, after apogee maneuver, the achieved orbit is not exactly that of a geostationary satellite: residual eccentricity and inclination causes the satellite to drift. This DRIFT ORBIT must be adjusted using satellite thrusters. STATION ACQUISITION operations consist of: orbit refinements, sun acquisition and solar panels deployment, earth capture and station acquisition. Elements of a Space Mission - Supplement SATELLITE TRACK DURING TRANSFER ORBIT (ARIANE LAUNCH) Elements of a Space Mission - Supplement OPERATIONS DURING DRIFT ORBIT Elements of a Space Mission - Supplement LAUNCH WINDOW The LAUNCH WINDOW is the set of time periods during the year within which the satellite can be launch taking into account various constraints: adequate power supply and thermal control in GTO (satellite/Sun position, eclipses), accurate determination of the satellite attitude at apogee (angle Sun-satellite and satellite-Earth) EXAMPLE OF LAUNCH WINDOW WITH ARIANE Elements of a Space Mission - Supplement ORBITAL INJECTION SEQUENCE WITH PERIGEE VELOCITY AUGMENTATION Elements of a Space Mission - Supplement ORBITAL INJECTION SEQUENCE WITH SUPERSYNCHRONOUS TRANSFER ORBIT .
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