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ELQ Q %B B`LQ ȢG !F$GGP}$GGLQG$ B`Q8GRRQLR8GQQQ$GQQI LRQGGRGRQLbRQmQ$GQGQQ}L6xo~{>>888>f<\}c6>8pp8?]}w><~~~<`x`~<~~<^}0~0~<~~<~~f~``~~f~~~``~~~f~~f~`~~~~f~~``~~ff8888<>>``ff88<<w_}wk~~fff~~ff~~~f~``~~f~~~```~`~~~~fff~~ff~<ckwf~<~fff~~~~~0~<~~<`}~xngTTTTTTfff~~`~~fl0fF>6xo~{>>888>f<}ck. Press the trigger to start the orbiter section of the simulation or "SELECT" to go to the lander simulation. If the simul?}ation ends while you are in the lander section, you may press "SYSTEM RESET" to return to the start of the orbiter section or@} "START" to run the lander simulation again.Scoring.When the simulation ends, a score will be displayed. Points are awardA}ed for destroying the target drone, docking with the Space Station, reaching lunar orbit and landing within Daedalus Crater oB}n the Moon. In addition, you are awarded bonus points for the amount of fuel and life support you have left when you accompliC}sh these various goals. Every low altitude beep in the lander section signals the addition of two points to your score. TheD}re are penalties for running out of life support, crashing or destroying the Space Station. A few points are also deducted evE}ery time you fire your engine, use Navigation Mode or fire the laser. Points will also be deducted for every mile per hour ofF} either horizontal or vertical speed when you land on the Moon. If either your horizontal or vertical speed is greater than 2G}2 mph when you land, it is considered a crash.Finally, points are deducted for every minute of time it takes you to complete H}the simulation. This includes time in Nav. Mode.The Author has found that he can run through the entire simulation in underI} twenty minutes. If you go directly to the Moon without first intercepting the drone or docking with the Space Station, the sJ}imulation takes about ten minutes. Twenty thousand points is an excellent score for the full simulation. This requires some lK}uck as well as skill. The starting orbits are chosen randomly. Some orbits will be easier and faster to match than others. GeL}nerally lower orbits are easier to match.Orbiter Navigation Tips.There are two easy ways to make an elliptical orbit intoM} a circular orbit. You can speed up when you are at the high point on your orbit, or you can slow down when you are at the loN}w point. To practice this first trace your ship's orbit (the "S" in the circle in the stick diagram). Find the low point on tO}he orbit, and turn your ship so that it points against its direction of travel at that place. For instance, if the low point P}in your orbit is at 3 o'clock with respect to the Earth, your motion at that place will be straight up on the screen. Thus, tQ}o point your ship against its (counterclockwise) direction of travel, set the direction dial to 6 o'clock (straight down). AfR}ter you've set the direction, set the throttle (try 1,000 m.p.h.), and when your ship is at its low point, fire the engine. TS}race your new orbit. You will see that the opposite side of the orbit is lower than it was. Your orbit will be circular if yoT}u have lowered the high point to the same altitude as the low point. The alternative is to turn your ship so it points in tU}he direction of travel at the high point on the orbit and fire your engine to speed up. You will see that the opposite side oV}f your new orbit is higher than it was. Use a similar method to make a circular orbit elliptical or egg shaped. If you speeW}d up, you will raise the opposite side of your orbit. If you slow down in a circular orbit you will lower the opposite side oX}f the orbit. Remember that the high point and low point are always on opposite sides of the orbit.You can rendezvous with tY}he target using only the maneuvers described above. When the simulation starts, trace the orbits of both the target and your Z}ship. First, make your orbit approximately circular. Second, raise or lower one side of your orbit so that it touches the low[} point of the target orbit. To do this you will need to speed up or slow down at the opposite side of your orbit. Third, spee\}d up or slow down at the point where your orbit touches the target orbit to nearly match the shape of the target orbit.Even]} when you match orbits with the target, the target may not be at the same place in its orbit as you are. If your orbit is sl^}ightly higher than the target's, you will move slightly slower. The higher you are the slower you go. Thus, if you are ahead_} of the target, raise your orbit slightly and wait for the target to catch up. This could take several orbits. (Remember to s`}peed up the program to reduce the wait.) In the same manner if the target is ahead of you, slow down! Remember that by slowina}g down you will lower your orbit and thereby go faster. Try it and see.When you get within 1,800 miles of the target, turn b}on the radar. (Remember that 1,800 miles is about one quarter of the diameter of the Earth. You can judge the distance againsc}t the image of the Earth in the center of the screen.) The target will appear as a blip on the radar screen. Move the stick ld}eft or right to aim the laser. There is a viewscreen at the lower right of the screen which shows what the laser is pointed ae}t. The laser's direction is shown by the red pointer in the direction dial. In all of the navigation described above you haf}ve been called on to fire your engine only at either the high or low points of your orbit and then only in the direction of mg}otion or against it. You can do all you need in this manner but more complex maneuvers are possible. Your engine can be firedq} `?B%DOS SYSB+AUTORUN SYSB XFONT SETBnaDOC 000BDOC 001B6DOC 002 at any time and in any direction. When you learn to use the Navigation Mode to test course changes, you can shortcut the ster}ps I've described above.Lander Navigation Tips. The object is to make a soft landing in the center of Daedalus Crater on s}the far side of the Moon. This is marked with a "+" on the large map on the screen. As you approach Daedalus Crater, set the t}throttle as high as it will go and aim your ship backwards against its direction of travel. When you get near to the landing u}area, lower your horizontal speed to zero. This should be done in stages so that you reach zero over the center of the Daedalv}us Crater. Then rotate the lander so that it points straight up. Let the lander fall until it is 50 miles from the surface thw}en fire your engine to stop its vertical motion. Lower the throttle to about .5 G. This is about three times the force of thex} lunar gravity. Let the lander drift lower firing the engine enough to keep the speed under control. Finally, reduce the throy}ttle to about .17 G. This will balance gravity. Hold the trigger down all the time and only move the throttle. Open the throtz}tle a little to slow your rate of descent or decrease the throttle to fall faster. Watch the VERT speed as well as your fuel {}supply.ttle to slow your rate of descent or decrease the throttle to fall faster. Watch the VERT speed as well as your fuel Technical Details.This program consists of about 55 K bytes of object code and was written entirely in Assembler. The follo}}wing section contains a technical description of the program. This may interest you if you enjoy math and physics. If not, do~}n't bother to wade through all this. The rest of the manual tells you all you need to know to operate the program.Orbits in} a gravitational field take the shapes of conic sections: circles, ellipses, parabolas and hyperbolas. This program simplifie}s the real world by confining all motion to the plane of the Moon's orbit. Since all orbits shown on the screen are in the sa}me plane, there is no need to match orbit inclinations as part of the rendezvous. Using radial coordinates the formula for }the shape of an orbit is: R=(H*H)/(K*(1E*cos(Th+Phi))) R=Radius (distance to the center of the Earth) } H=Angular momentum K=Gravitational Constant E=Eccentricity Th=Angular position } Phi=Orientation of the orbit major axisThe angular momentum ("H") of an orbiting body is the product of its tangential v}elocity ( VT ) and its radius ( R ): H=VT*R. H is constant, or, in other words, angular momentum is conserved. This also mean}s that VT is inversely proportional to R: The satellite will speed up as it nears the Earth and slow down as it moves away. T}his is apparent as you watch the simulation.The major axis of an orbit is the greatest width of the orbit measured through }the center of the planet. This equals the perigee plus the apogee. The period of an orbit (the time the satellite takes to co}mplete one trip around the orbit) is proportional to the length of the major axis taken to the 3/2 power. When you go to the }Moon, you will start from a fairly low orbit and fire your engine to enter a highly elliptical transfer orbit with an apogee }of about 230,000 miles (the radius of the Moon's orbit). The length of the major axis of the transfer orbit will be just over} 230,000 miles. The length of the major axis of the Moon's orbit is 460,000 miles. You can calculate the ratio of the periods} of the two orbits: Ratio=(460,000/230,000)^(3/2) =2*sqrt(2)= 2.828This shows that the Moon's period is abo}ut 2.8 times as long as the period of the transfer orbit. Since it takes one half of the period to move from perigee to apoge}e (the orbit is symmetric around the major axis), it will take about 1/5.6 of the Moon's period to reach apogee in your trans}fer orbit. This means you must set up your transfer orbit so that its apogee is at least 64 degrees ahead of the Moon's posit}ion. ( 360 degrees/5.6=64 degrees.) In this way your ship and the Moon will reach the same point at the same time. To be safe} you should lead the Moon by more than 64 degrees. As you near apogee in your transfer orbit, your VT will be quite low, perh}aps 400 mph. The Moon will have a constant VT of about 2,300 mph and will catch you rapidly. Since you spend a comparatively }long time at the apogee of your orbit, you can afford to get there early and wait for the Moon to catch up.The paragraph ab}ove described a transfer orbit which was tangent to the starting orbit and tangent to the Moon's orbit. Such a transfer orbit} is called a "Hohmann Transfer". A Hohmann Transfer is a minimum energy transfer orbit, but it is not very fast. To save time} at the expense of fuel you can use a transfer orbit which has an apogee higher than the Moon's orbit. You can even use a ver}y high energy hyperbolic transfer. This will cause your ship to shoot past the Moon's orbit at high speed rather than lingeri}ng there to be gathered in by the lunar gravity. Such a high speed transfer requires great accuracy and probably one or more }midcourse corrections. Remember also that the Moon cannot capture you if you move by it at too high a speed. You must be rea}dy to slow down. This whole process can consume a lot of fuel so plan carefully.This program computes orbital constants fro}m the position (Th and R) and the velocity (VT and VR) of the satellite. The following formulae apply: H=VT*R Angular} momentum PE=VR^2 + VT^2  2*K/R Energy The PE represents the total energy of the satellite. It is the sum of the} kinetic energy of the satellite's motion (VT^2 + VR^2) less the strength of the gravitational attraction holding it to its p}lanet (2*K/R). If PE is negative, the satellite is bound to the planet it orbits. If the PE is zero or positive the satellite} is not bound to the Earth. Such an orbit is either parabolic or hyperbolic. This ties into the next equation: E=sqrt((}H^2 * PE/(K^2))+1) EccentricityAn ellipse has two foci both located on the major axis. The center of mass of the planet b}eing orbited is at one of the foci. The eccentricity is defined as the ratio of the distance between the foci to the length o}f the major axis. This can also be calculated by the size of the apogee ("A") and perigee ("P"): E=(AP)/(A+P)For a }circular orbit A=P so E=0. To compute the constants for an orbit the computer first finds the VT and VR: VT=H/R VR}=((K * E)/H) * sin(Th + Phi)Changes in the velocity whether by engine burn or gravitational perturbation are added to give }new values of VT and VR. Orbit constants are calculated from these new values. Note that engine burns have an instantaneous e}ffect. Though the engine appears to burn for a period of time the course change actually occurs in the first instant.Becaus}e of the manner in which the computer simulates orbital motion, the simulation quality decays for orbits with very low tangen}tial velocities. Indeed, the program prevents you from cancelling all the VT. You cannot simply fall straight to the Earth. I}f you try this you will see that the orbital motion becomes jerky. This does not impare normal orbits, however.The lander s}ection of the program simulates orbital motion in a different manner. No orbit constants are computed. Instead the computer k}eeps track of the position and velocity of the lander. The program calculates the effect of gravity and corrects the altitude} to take account of the curvature of the Moon's surface. Thus, if the speed is right, the lander will hold a constant altitud}e. In other words, the lander will orbit the Moon. Use your knowledge of orbital mechanics to navigate. Note that the lander'}s orbit is inclined 10 degrees to the lunar equator. Since the lunar equator runs across the middle of the lunar map, the lan}der's position moves in a sine curve over the lunar surface with an amplitude of 10 degrees. I hope you enjoy the program. }If you have any comments or questions, write me: John Reagh, P.O. 2286, Seattle, WA 98111.I hope you enjoy the program. ]et being orbited is at one of the foci. The eccentricity is defined as the ratio of the distance between the foci to the leng}th of the major axis. This can also be calculated by the size of the apogee ("A") and perigee ("P"): E=(AP)/(A+P)Fo}r a circular orbit A=P so E=0. To compute the constants for an orbit the computer first finds the VT and VR: VT=H/R } VR=((K * E)/H) * sin(Th + Phi)Changes in the velocity whether by engine burn or gravitational perturbation are added to g}ive new values of VT and VR. Orbit constants are calculated from these new values. Note that engine burns have an instantaneo}us effect. Though the engine appears to burn for a period of time the course change actually occurs in the first instant.Be}cause of the manner in which the computer simulates orbital motion, the simulation quality decays for orbits with very low ta}ngential velocities. Indeed, the program prevents you from cancelling all the VT. You cannot simply fall straight to the Eart}h. If you try this you will see that the orbital motion becomes jerky. This does not impare normal orbits, however.The land}er section of the program simulates orbital motion in a different manner. No orbit constants are computed. Instead the comput}er keeps track of the position and velocity of the lander. The program calculates the effect of gravity and corrects the alti}tude to take account of the curvature of the Moon's surface. Thus, if the speed is right, the lander will hold a constant alt}itude. In other words, the lander will orbit the Moon. Use your knowledge of orbital mechanics to navigate. Note that the lan}der's orbit is inclined 10 degrees to the lunar equator. Since the lunar equator runs across the middle of the lunar map, the} lander's position moves in a sine curve over the lunar surface with an amplitude of 10 degrees. I hope you enjoy the progr}am. If you have any comments or questions, write me: John Reagh, P.O. 2286, Seattle, WA 98111.entirely in Assembler. The fa