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Apollo lunar landing launch window: The controlling factors and constraints

Robin Wheeler

Let's go to the moon. When shall we go? Right away. Where shall we go? Copernicus, Gassendi, Marius Hills? Let choose along the way.

If only it was that easy. When launching to land on the moon there are two fixed parameters. The location of the launch site (for Apollo this was launch complex 39 at KSC) and the landing site you are aiming for on the moon. To arrive at this landing site with the right lighting conditions for the descent and approach a journey must be planned that meets the various constraints that affected the Apollo lunar mission planning, primarily in the form of trajectory shaping and the limitation of launch opportunities, known as launch windows.

Trajectory geometry constraints and spacecraft performance capabilities combined to limit the accessible area on the moon.

These accessible landing area limitations combined with operational constraints to limit launch opportunities to certain specific periods. In order to fully understand the mission planning considerations and the effects of the various constraints, we need to look closely at the trajectory characteristics.

An understanding of the interrelation of operational constraints and trajectory shaping is essential to understand the limitations placed on the launch opportunities.

Each mission phase will be described in flight order commencing with the launch phase.

Launch phase

Earth parking orbit phase

Trans lunar injection

Trans lunar coast phase

Lunar orbit phase

Total launch window considerations

Launch phase

The mission planning considerations for the launch phase of the Apollo lunar mission were related primarily to launch 'windows', launch vehicle performance, and contingency planning.

Launch windows were defined for two different time intervals:

• Daily window which had a duration of a few hours during a given 24 hour period.
• Monthly window which consisted of a few days during a given month or lunar cycle.

The daily window was continuous from opening to close; but a monthly window may have had gaps. For example, a monthly launch window could cover a 7 day period, but a daily launch window may not exist for some of the intermediate days within this period. Only the effects on the launch phase, of providing a launch window will be described in this section..

It is obvious that for operational flexibility it was highly desirable to have as large a launch window as possible, both daily and monthly. A daily launch window allows for delays or holds that may occur during the countdown. The mission would not have to be rescheduled to another day if the daily launch window was larger than the cumulative delays or holds. A monthly launch window allowed the mission to be quickly rescheduled. If the daily launch window were missed, the mission would not necessarily have to be delayed for a month.

Studies in the early 1960's indicated that if the hold exceeded 2 hours, the launch would probably be scrubbed for that day. For the Apollo lunar missions, daily launch windows required a range of launch azimuths; the longer the daily launch window, the larger the required range of launch azimuths. The mechanism by which variable launch azimuths provides launch windows, will be described in the translunar injection phase. The range of launch azimuths available, were limited due to range safety considerations, launch vehicle performance and earth orbit insertion tracking requirements:

• Range Safety- The range safety limits were defined as between 72° and 108° (measured clockwise from due north). The primary reason for these range safety limits was to keep the space vehicle on the Eastern Test Range following any abort during launch.
• Booster Performance- A 90° launch azimuth takes maximum advantage of the earth's rotation in achieving orbital velocity. As the azimuth shifts away from 90°(in either direction), the launch vehicles performance requirements increase, or its payload capability is decreased as shown in figure 1. The Saturn V launch vehicle was capable of providing lunar mission payloads for launch azimuths beyond the 72° to 108° range; however, its flight performance reserves were constrained to these launch azimuth limits.

Figure 1

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As it was not possible to predict when during the launch window the launch would actually occur, it was not always possible to take advantage of the payload gain the launch azimuth may allow. Also if it was possible to utilise any payload gain at a particular azimuth at least 47% of this gain would have to be in SPS propellant.

• Insertion Tracking-There was an operational requirement to track the space vehicle for at least 3 minutes after earth orbit insertion in order to make a GO / NO-GO for orbit decision. Since the Apollo space vehicle was inserted into earth orbit some 1,400 n. miles downrange from KSC, a ship was required to provide this tracking and communications. This vessel was usually the 'Vanguard' see figure 2.

Apollo 11 AOC Chart-Atlantic area showing the Vanguards location

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Figure 2 Vanguard tracking ship

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Full Apollo 11 AEO Chart for orbit 1

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A 26° range in usable launch azimuths anywhere between the values of 72° and 108° provided for at least a 2.5 hour daily launch window. A 2.5 hour launch window was considered the minimum acceptable. Most missions planned a range of launch azimuths which provided up to 4.5 hour launch windows. The choice of where the 26° range is located within these maximum bounds is up to the mission planners, and is based on such things as maximising space vehicle fuel reserves, Manned Spaceflight Tracking Network (MSFN) coverage, launch window duration, and providing a daylight launch. The full 26° range of launch azimuths was seldom planned for due to other mission constraints.

As previously mentioned another constraint on the launch phase mission planning was the monthly launch window. A monthly launch window allowed the mission to be rescheduled as soon as possible following a launch scrub or a countdown hold that extends beyond the daily launch window. It also allowed some flexibility in the initial planning of the launch day, the effects of space vehicle recycle characteristics and limitations.

Further details of the operations carried out during a holds and a scrub turnaround can be found here

The maximum turnaround time was a major factor in defining the minimum acceptable duration of the monthly launch window. Studies in the mid 1960's for NASA by Bellcomm Labs, provided some significant data that was used to develop the minimum launch window philosophy. The most important characteristic was the minimum recycle time for the space vehicle, as shown in figure 3.

Figure 3

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As the graph above shows, if the mission was scrubbed after the countdown had reached T-6 hours, the minimum time to recycle was in excess of 24 hours, and was as long as 40 hours at T=0. Thus, a minimum launch window required to guarantee a recycle capability is 3 days. This did not allow any additional time for repairs or replacing components. If this activity could not be carried out in parallel with the recycling, 3 days would not be sufficient. Therefore, a window of only 3 days duration was not desirable, but was considered a workable minimum in some situations. In order to provide time for repairs to be carried out and still make the monthly launch window, it had to be as long as possible. Another Bellcomm Labs study from the mid 1960's, indicated that the probability of a successful launch was between 85% and 90% if a 3 day launch window was available, and that this probability increases to about 95% if the launch window is of 5 days duration. Based on this data, the early lunar landing missions were planned only for those periods when at least a 3 day launch window existed, and every effort was made to provide a 5 day launch window.

One final consideration in the launch phase was the desirability of a daylight launch. There are three reasons which made a daylight launch highly desirable, all three concerned contingencies.

Aborts off the launch pad. The recovery of the crew in the KSC, Merritt Island area would be complicated and hazardous if it had to be performed under conditions of darkness.

Aborts later in the launch phase require attitude maneuvering of the spacecraft, so it was desirable to have a sunlit horizon as a backup manual attitude reference.

Finally, it was desirable to have photographic coverage of the boost phase for post-flight analysis, if a catastrophic failure occurred.

Based on these considerations, every effort was made to provide for a daylight launch, although the missions were not constrained to daylight only launches as demonstrated by the final lunar mission, Apollo 17.

Apollo Lunar Launch statistics

Source post mission reports

[1] Launch delayed 40 min : 02 sec due to launch site weather constraints.

[2] Launch window opened 6/12/72

[3] Hold called at T-30 seconds due to problems with the terminal countdown sequencer. The launch was recycled to the T-22 minutes (see article on hold porcedures), held there and once the fix had been approved the count was picked up again, counted down to T-8 minutes where it was held again and finally proceeded to a satisfactory launch 2 hours and 40 minutes after the planned time.

Earth parking orbit phase

Earth parking orbits helped to facilitate launch windows of a reasonable duration. They acted as a time buffer.

The only major consideration in the earth parking orbit phase is it's duration, i.e. the number of earth orbits. The parking orbit duration was defined by space vehicle system considerations. The minimum was set at 1.4 hours with a maximum duration is 4.5 hours from earth orbit insertion to the beginning of the trans lunar injection (TLI) and was limited by the launch vehicle capability to provide attitude control and by the launch vehicles battery lifetime (approximately 13 hours). This allows up to three earth parking orbits prior to the second S-IVB burn with a margin for the continued use of the S-IVB APS and batteries through injection of the S-IVB on its post transposition and docking trajectory, be it either into solar orbit or on a course that lead to an impact on the lunar surface.

There are other considerations in limiting the parking orbit duration, although they were not considered 'hard' constraints. The S-IVB propellant boil-off and IU inertial platform drift made it desirable to inject as soon as possible. The minimum duration of the earth parking orbits was limited by the time required to perform system checks, both onboard and from the ground, and also to realign the spacecrafts guidance platform. Crew timeline plans dictated that this would take in the order of 1.5 to 2 hours, or approximately 1 to 1.25 orbits.

There was also a minimum network coverage requirement that stated that two tracking stations and a command station must be passed over before the GO decision for the second S-IVB burn (TLI), however this was always accomplished during the first earth parking orbit during the first 'stateside' pass.

Thus, there was a 3 hour period from 1.5 to 4.5 hours after earth orbit insertion in which the trans lunar injection (TLI) could occur. This meant that the injection (TLI) must occur on the second or third earth orbit. Figure 4 illustrates the ground track for three earth parking orbits for a 90 deg launch azimuth.

Figure 4

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Trans lunar injection (TLI)

The trans lunar injection (TLI) position was rigidly constrained by performance considerations. The geometry of the moons orbit, the energy requirements of the trans lunar transfer trajectory, and the necessity of efficiently burning the S-IVB propellant all combine to place very tight restrictions on the location of this maneuver.

Transfer energy considerations. In order to arrive in the vicinity of the moon the spacecraft was 'aimed' (targeted) at a position where the moon would be at the time of its arrival as illustrated in figure 5.

Figure 5

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In order to accomplish this 'rendezvous' with a minimum expenditure of propellant, the injection (TLI) must occur very close to the extension of the earth-moon line at the time of the spacecrafts lunar arrival. This is termed the negative of the unit vector of the moons position (the position on the opposite side of the earth from the sub-lunar point), which is called the moons antipode. The optimum trajectory is very similar to a Hohmann transfer.

This minimum energy transfer trajectory would have placed the earth parking orbit perigee at the moons antipode if the moons mass did not perturb the trans lunar trajectory. However the moon does perturb the spacecrafts trans lunar trajectory, as shown in figure 5 above, and therefore the earth parking orbit perigee must lead the moons antipode by approximately 8 degrees to compensate. The apogee altitude of the osculating conic trans lunar trajectory was determined by the trans lunar flight time which defined the trajectory energy requirements at trans lunar injection (TLI).

To inject the spacecraft to the moon in the most efficient manner, an impulsive velocity (acceleration) would be added along the orbital velocity vector (direction), giving an injection at the perigee of the trans lunar conic. Since an impulsive (instant) addition of velocity is not possible, a finite burn time is required, and the actual injection position is on the order of 20° ahead on the antipode. The thrust from the S-IVB is directed approximately along the velocity vector, and as the velocity increases above orbital, the altitude and flight-path angle increase. For the Apollo lunar orbit rendezvous flight mode, by the time sufficient energy has been gained, the altitude has increased by 60 to 75 n. miles above that of the earth parking orbit and a positive flight-path angle of 6° had been attained. Since the conic trajectory is very nearly parabolic (eccentricity 0.97) the true anomaly is approximately equal to twice the flight-path angle, so perigee is approximately 12° to 14° behind the burn cut-off position. The TLI burn arc itself is 25°, so that ignition always occurs within a few degrees of the moons antipode.

The preceding details have shown that the injection (TLI) position is very closely tied to the moons antipode. To go to the moon efficiently the spacecraft must inject near it, so we must now look at the issue of getting to the moons antipode from the launch pad at Cape Kennedy (now Cape Canaveral).

The moons antipode, being a unit vector from the centre of the earth in the direction opposite to the moons position, moves as the moon travels in its orbit around the earth. The launch pad is rotating with the earth, and both of these motions must be compensated for in order to rendezvous with the moons antipode. It is best to divide the description of the moons antipode movements into two categories-a long period cycle and a short period cycle.

The long period cycle is due to the moons orbital travel about the earth. Figure 6 below illustrates this effect. Assume that the earth is a fixed motionless sphere and is not rotating about its axis. The moons orbital plane cuts this sphere as shown. As the moon revolves around the earth, its antipode would trace a great circle in this plane around the earths surface. Note that the direction of travel is from West to East. The orbital period is some 28 days, and thus at the end of this time the antipode would be back where it began (relative to the earths surface), traveling eastward at the rate of about 0.54° per hour. The latitude of the moons antipode would have a time history similar to that shown in figure 6.

Figure 6

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The short period cycle motion of the moons antipode across the earths surface is due to the earths rotation about its axis. To illustrate this it is assumed that the moon is now fixed at point in its orbit, and the earth is now rotating about its polar axis. The moons antipode travel is illustrated in figure 7.

Figure 7

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In this case the latitude is constant and the longitude changes from East to West at 15° per hour.

The complete picture of the moons antipode travel across the earths surface is obtained by combining the long and short period cycle motions. The latitude varies sinusoidally with time with an amplitude of 28.5° (in 1968) and a period of 28 days. The longitude variation is at a nearly constant rate of 14.5° per hour.

The launch must occur at a certain time for each launch azimuth in order to intercept the moons antipode. This correct launch time was defined by the antipodes position, the time interval from launch to arrival at the antipodes position, and the moons antipode travel during this time interval. Figure 8 illustrates this issue. Consider an inertial sphere of radius equal to the earth.

Figure 8

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A trace of the launch pad travel as a function of time on this sphere is represented by a fixed latitude completely encircling the sphere. The launch pad completes one revolution of the sphere per day. The trace of the moons antipode is given by the intersection of the moons orbit plane and the sphere. The moons antipode completes a revolution every 28 days. The launch at any given azimuth must be timed so that the inertial plane of the resulting earth parking orbit contains the moons antipode at the time the space vehicle crosses the moons orbit plane. Later launch times require greater launch azimuths. If additional parking orbits are required, the launch must occur later to account for the additional antipode travel. For each 360° travel of the launch pad, there are two launch times for each azimuth which allow interception of the moons antipode. This is best illustrated in figure 9, which shows the same situation in earth fixed co-ordinates.

In this figure, the launch pad is now fixed, and the moons antipode travels rapidly over the surface of the earth. The moons antipode is shown at four different times during the day, corresponding to the positions in intercept for 72° and 108° launch azimuths. The launch must be timed so that the space vehicle intercepts the moving moon antipode. The time required for the moons antipode to travel from the interception of the 72° launch azimuth trajectory, defines the duration of the launch window. The interception of the moon orbit plane is shown for each position. This figure shows how two different launch times for one azimuth can provide intercept with the moons antipode. One provides injections going south over the Atlantic or Indian Oceans and the other provides injections going north over the Pacific Ocean. For the day illustrated in this figure, the Atlantic injection gives a trajectory that is nearly in the moons orbit plane, and the Pacific injection results in a trajectory that is highly inclined to the moons orbit plane.

Figure 9

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Half a lunar cycle later, the Pacific injection would be highly inclined. The magnitude of this relative inclination depends on the lunar declination and is at a maximum when the moon is near the equator. When the moon is near maximum declination, both windows provide trajectories with low relative inclinations.

It should be noted that the Pacific injection always results in a trajectory above the moon orbit plane, regardless of the moons declination or whether it is ascending or descending. This effects the relative location of the available lunar landing areas from these two injection windows. This effect will be described later on.

You can see that when the launch azimuth bounds are defined, the proper launch time can be found, taking into account the planned number of earth parking orbits.

If the trans lunar injection opportunity was missed, it could be attempted one earth parking orbit later when the space vehicle again approached the moons antipode. However, since the moons antipode is traveling in a plane that is not necessarily the same as the space vehicles orbit, a plane change would be required. This is illustrated in figure 10.

Figure 10

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It can be seen that the moons antipode has traveled out of the space vehicles earth parking orbit when the vehicle returns to the position of injection. The magnitude of the out-of-plane travel is dependent on the relative inclination between the earth parking orbit and the moon orbit plane. This second injection would require a greater propellant expenditure by the S-IVB because of the plane change involved. If two injection opportunities are to be provided, the launch would be timed so that both would require a plane change, because this minimised the propellant required. The launch would occur a little bit later so that the first time the space vehicle crosses the moons orbit plane, the moons antipode has not reached the plane of the earth parking orbit. The second time the space vehicle crosses the moons orbit plane, the moons antipode has now passed through the plane of the earth parking orbit. If three injection opportunities are to be provided, the launch would be timed so that the moons antipode was in the earth parking orbit plane for the second one.

Figure 11 illustrates the effects of different targeting methods on the characteristic velocity required to provide additional injection opportunities.

Figure 11

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Three cases are shown above. The first shows the additional ∆V required when the launch is timed for the first injection to be coplaner (shown in blue). The second and third opportunities have large additional ∆V requirements. In the second case, the launch is timed to split the ∆ azimuth between the first and second injection opportunities (shown in green). In the third case, launch is timed so that the second injection is coplaner (shown in red). This method would provide three injection opportunities.

The penalties shown are only illustrative; the actual values strongly depend on the relative inclination between the two planes.

Because injection is limited to the second or third earth parking orbit, only two injection (TLI) opportunities are planned for, and the second technique (shown in green) is used.

The combination of launch azimuth limits, earth parking orbit duration constraints, and the geometry of the moons orbit confine the location of the injection (TLI) positions to two geographical areas. These areas are generally centred over the South Atlantic Ocean and the Pacific Ocean, and for this reason are distinguished by these names. The bounds, as illustrated in figure 12, are defined by the first orbit for a 72° launch azimuth, the third orbit of a 108° launch azimuth, and the extremes of lunar declination. All of the possible injection positions are illustrated in figure 12. Figure 12a & 12b show Apollo Earth Orbit chart for the 2nd & 3rd revolutions respectively, for various launch inclinations for the Apollo 11 mission.

Figure 12

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Fig 12a Full Apollo 11 AEO Chart for orbit 2

Fig 12b Full Apollo 11 AEO Chart for orbit 3

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Apollo TLI statistics

Source post mission reports

Trans lunar coast phase

The important elements of the trans lunar coast phase are: the effects of the trajectory inclination relative to the moons orbit plane; the effects of the "free-return" flight plan, and its relationship to the lunar orbit insertion (LOI) maneuver; and finally some alternatives to the free-return flight plan.

Firstly we must look at the trans lunar coast trajectory relative to the trajectory to the moons orbit plane. It was mentioned previously that the Pacific injections always result in trans lunar trajectories above the moons orbit plane, whilst Atlantic injections in the main are below it as shown in figure 13. To what extent the trans lunar trajectory is out of plane is a function of the moons declination and whether or not it is ascending or descending in its orbit. These parameters influence the magnitude of the effects, however they do not change the general conclusions.

Figure 13

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Following a Pacific injection, the spacecraft approaches the moon from above the moons orbit plane. This takes the trajectory below this plane on the far side of the moon, where the lunar orbit insertion (LOI) maneuver is performed. The resulting lunar orbit therefore is constrained to be approximately as illustrated in figure 14. A plane change during the lunar orbit insertion (LOI) can modify the resultant orientation somewhat, but the basic conclusion remains that to land at northern latitudes on the near side on the moon, a Pacific injection will result in lower propellant expenditure (for most months of the year). Conversely, Atlantic injections favour the southern latitudes (for most months of the year). This will be demonstrated later when the accessible lunar areas are defined.

Figure 14

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Free return trajectory

One of the most constraining requirements of the Apollo lunar landing mission was the free-return trajectory. It severely limited the area on the moon that Apollo missions could reach. Although it was costly in terms of spacecraft performance requirements, the inherent safety feature of a free return trajectory made it a highly desirable method of getting to the moon.

A circumlunar free-return trajectory, by definition, is one which circumnavigates the moon and returns to the vicinity of the earth as shown in figure 15.

Figure 15

The perigee altitude of the return trajectory takes the spacecraft into the earths atmosphere where by using negative lift the command module re-entry can be controlled and avoid skipping out of the atmosphere again, and aerodynamic deceleration can be kept below 10 g's. Thus should the spacecraft suffer a complete failure of both the SPS & DPS propulsion systems, it would still return safely to a splashdown on earth.

The range in return perigee altitudes that provide this feature is called the re-entry corridor and is defined primarily as a function of the lift-to drag ratio of the Apollo command module. For Apollo this corridor was approximately 40 n.miles wide, centred around an altitude of 25 n.miles.The accuracy of the trans lunar injection (TLI) ∆V required for a free return trajectory is < 0.1 fps. This degree of accuracy could not be achieved by the Saturn V I.U's guidance system, as you are dealing with a TLI ∆V of approximately 10,000 fps. The contingency for an SPS failure would be to use the lunar modules DPS (as employed during Apollo 13) or the SM RCS to provide the necessary ∆V correction to compensate for injection errors.

The free-return trajectory severely limits the accessible area of the moon because of the very small variation in allowable lunar approach conditions and because the energy of the lunar approach trajectory is relatively high. The high approach energy causes the orbit insertion ∆V to be relatively high. However, the main limitations to the accessible area are a result of the small range in the flight times for trans lunar coast. Figure 16 illustrates the effect of flight time on the location of the perilune. All free-return trajectories have trans lunar transit times between 60 and 80 hours, and it can be seen in this illustration that perilune is limited to a region within 10° of the earth-moon line projected through to the lunar far side or approximately 180° longitude. For non free-return trajectories, the transit time can be anything from 50 to 110 hours.

Figure 16

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Perilune could be adjusted from 140° W longitude to 140° E longitude merely by selecting the appropriate trans lunar flight time. The narrow region of the perilune position for free-return trajectories combined with a small range of approach inclinations is what limits the accessible area.

The relative inclination between the free-return trajectory and the moon orbit plane is less than 11°. Any trajectory with a greater inclination than this, simply does not return to the entry corridor at earth, regardless of the perilune position. The range of free-return trajectory conditions near the moon is illustrated in figure 17. A relatively small cone is formed by the locus of perilune positions.

Figure 17

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The braking maneuver to decelerate the spacecraft from the hyperbolic approach trajectory into a lunar orbit is performed out of sight of the earth above the moons far side at or near perilune. For illustrative purposes, lets assumed that it occurs at perilune. In order to land at a site that was not contained by the approach trajectory plane, a plane change had to be undertaken. It was generally more propellant efficient to combine this plane change with the deceleration at lunar orbit insertion. When the landing site is near the node, however, an excessively large plane change is required to bring the trajectory over the site. Since the approach trajectories have low inclinations and orbit insertion occurs near the 180° longitude, to bring the lunar orbit over landing sites at high latitudes in the region near 0° longitude, large plane changes were required. The propellant capacity of the spacecraft limited the magnitude of the plane change that could be made.

There is a locus of perilune positions; although it is not that there is not one focal point through which all of the trajectories must pass; there is an area. This tends to relieve the limitations slightly, but the fact remains that a plane change at LOI is relatively ineffective in achieving higher latitudes near the zero longitude region. Also as the landing site is moved away from the zero longitude, the plane change requirements become greatly reduced.

If the lunar orbit insertion (LOI) were not made at perilune, the magnitude of the plane change could be reduced in many cases as shown in figure 18. In this figure, two orbits resulting from lunar orbit insertion at two different positions along the approach hyperbola illustrated. Both pass over the landing site, and both could be acceptable.

Figure 18

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If the insertion was performed at perilune, a much larger plane change would be required, so it appears that if the insertion burn were made prior to perilune, the ∆V required would be much less. However, there is an additional penalty associated with this pre-perilune braking due to the fact that a flight-path angle change must also be included. Figure 19 shows the in-plane geometry. If the LOI is performed at any position other than perilune, the velocity vector must not only be reduced, but its direction also needs to be changed to achieve a circular lunar orbit. A flight-path angle change, is just as expensive as an azimuth change. It is much more propellant efficient to make a small plane change. This trade-off was made in the mission trajectory design to obtain the optimum combination.

Figure 19

Another feature of the non-perilune retrograde manoeuvre (LOI) is that the resultant lunar orbit altitude is above the perilune altitude. The perilune must be reduced a certain amount in order to obtain the desired orbital altitude. The exact amount of reduction depends on the true anomaly of the LOI manoeuvre, but in no case was a perilune of less than 40 n.miles employed.

LOI SPS burn ground tracks

Figure 20 The figures in brackets show the spacecraft altitude at LOI ignition and cut-off in miles.

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It can be seen in the chart above, figure 20, that none of the LOI burn ground tracks pass directly over the pericynthion location. This is due to the plane change element of the LOI burn to place the spacecraft in to the desired lunar orbit.

Hybrid trajectory

Since the free-return flight plan was so constraining on the accessible lunar area, parallel investigations of other techniques were conducted. The primary goal of these investigations was to develop techniques that retained most of the safety features of the free-return, but did not suffer from the performance penalties. An example of this type of mission plan is termed a Hybrid Flight Plan illustrated below in figure 21.

Figure 21

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The spacecraft was injected into a highly eccentric elliptical orbit which had the free-return characteristics; that is, a return to the entry corridor without any further manoeuvre's. The launch vehicle energy requirements were reduced, and a greater payload (more SPS propellant) could be carried. Some three to five hours after injection (TLI), after the SPS has been checked out, a mid-course manoeuvre would be performed by the spacecraft to place it on a lunar approach trajectory. This lunar approach trajectory would not be free-return, and hence would not be subject to the same limitations in trajectory geometry. This would therefore open the opportunity to reach landing sites at higher latitudes, with little or no plane change, by approaching the moon on a highly inclined trajectory. This Hybrid Flight Plan offered large improvements in performance over the free-return plan, but still retained most of its safety features. The spacecraft did not venture away from the free-return ellipse until the transposition and docking sequence had been completed and the spacecraft had separated from the spent S-IVB. The attached LM therefore provided a second propulsion system for returning to earth in the event of a contingency. The manoeuvre on to a hybrid trajectory would only occur after a full checkout of the SPS. Typical parameters defining the ability to return to a free-return trajectory from an hybrid course are listed below:

Using the SPS or DPS until pericynthion + 2 hours

Using the SM RCS for the CSM / LM combination until approximately GET 57hours

Using the SM RCS for CSM only until approximately GET 69 hours

One of the difficulties in flight planning the hybrid mission was that the initial trajectory was not amendable to conic approximations. So much time was spent milling around out near the moon that conics or patched conics do not provide accurate simulations. It was extremely important that rapid calculation procedures be available (in the Real Time Computer Complex-RTCC) because of the large number of iterations required to "search in" or design a mission trajectory. This was in the early days of high speed computing, so these calculations required resources which are hard to comprehend today. And if all of this must be done with precision integrating trajectory programs, the time required became excessively large.

Apollo LOI statistics

Source post mission reports

[1] Apollo's 10,11,12,13,16,17 only employed one MCC during the trans lunar coast. Apollo's 8, 14, 15 employed two.

A comparison of accessible areas available for Hybrid and free-return flight plans is shown in figure 22. Only the areas between 45° E and 45° W longitude is shown as this was the primary Apollo zone of interest. The area available with free-return trajectories is limited to the region near the lunar equator. While the area attainable with the Hybrid mission, which is essentially the same as that for a non-free-return mission, is much larger. It includes all of the area available to free-return missions, and extends to much higher latitudes in the low longitude regions.

Figure 22

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Lunar orbit phase

Two parameters are of interest in the lunar orbit phase, the orientation of the lunar orbit and the number of lunar parking orbits required. The orientation of the plane of the lunar orbit was selected to minimise the ∆V requirements. There were three maneuvers that must be considered to optimise the required ∆V.

The three maneuvers are:

Lunar Orbit Insertion (LOI)

Trans-Earth Injection (TEI)

Lunar Orbit Plane Change

The moon's relatively slow rotation rate, combined with the reasonably low lunar orbit inclinations, result in a small out-of-plane motion of the lunar landing site. The LOI maneuver is planned so that the resulting lunar orbit plane contains the planned landing site at the nominal landing time, as illustrated in figure 23. Position 1 represents the location of the landing site at the time of lunar orbit insertion. When the LM makes the landing, the landing site has rotated to position 2.

During the lunar surface stay, the landing site continues to rotate out-of-plane of the CSM to position 3. An orbital plane change maneuver was carried out by the CSM using the SPS, prior the the LM ascent from the lunar surface.This puts the CSM in a new orbit plane which will pass over the landing site at the nominal lunar launch time.

Figure 23

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The trans-earth injection (TEI) maneuver was performed to take the CSM out of this final lunar parking orbit and usually a plane change was required. The SPS performance requirements were optimised by choosing the best inclination of the lunar parking orbit, consistent with the landing site location and the planned lunar surface stay time.

The number of lunar orbits both prior to the LM descent and following ascent and rendezvous are dictated by the crew procedures timelines and MSFN tracking considerations. At least three orbits were required for the crew to activate and checkout the LM. Following, rendezvous and docking, a minimum of two orbits were required to prepare the CSM for trans-earth injection (TEI). This allowed the crew to transfer themselves and their spoils from the lunar surface, from the LM and stow them in the CSM. This also allows sufficient time for MSFN tracking to precisely determine the CSM orbit.The lunar landing missions stayed in lunar orbit for at least 7 1/2 hours following rendezvous and docking between the LM ascent stage and the CSM and often remained for over 24 hours to complete studies from lunar orbit.

Total launch window considerations

So far we have considered each phase of the Apollo lunar missions from launch to lunar orbit. We must now consider all of the factors in these phases of flight that constrain the launch window in concert.

There were at least six major considerations that in one way or another limited the times at which the Apollo lunar landing mission could be launched. These constraining factors are due to either the characteristics of the moon's orbit about the earth, mission operational requirements, or spacecraft / launch vehicle performance capability.

These constraints are:

1. Launch azimuth
2. Lighting conditions at the planned landing site
3. Lunar landing site location
4. Spacecraft / launch vehicle performance
5. Daylight launch
6. Minimum number of launch opportunities during a month

Launch azimuth

The way the launch azimuth effects the launch time was described earlier. We saw that for a specific launch azimuth and s specified number of earth orbits defined the required launch time that provided a rendezvous in earth parking orbit with the moon's antipode. The fact that either of two distinct launch times could provide this antipode rendezvous was illustrated. It also became apparent that one of these times resulted in a trans-lunar injections (TLI) approximately over the Atlantic Ocean, whist the other resulted in injections approximately over the Pacific Ocean.

This characteristic of discrete launch azimuths defining particular launch times can be expanded to show that a range of launch azimuths define a range of launch times. And for the limited range of the Eastern Test Range, 72° to 18°, the launch times for each injection window can be calculated. These daily launch windows, as limited by launch azimuth, are shown for 1968 in figure 24. This this illustration, the unshaded areas represent allowable launch times. The letters "P" and "A" denote the Pacific and Atlantic Ocean injection windows. Each windows is opened for a 72° launch azimuth and closed at 108°.

Figure 24

(click on above diagram for larger version)

The difference in launch time for the two windows varies throughout each month. In some periods the closing of one launch window was followed immediately by the opening of another. On other occasions there could be as much as 14 hours between the closing of one launch window and the opening of the next.

It should be noted that the opening time of each succeeding launch window was later than the previous one. The rate of this change was quite rapid at times and almost negligible at others. The relatively flat period as illustrated in the figure above for each launch window, corresponds to the part of each lunar month when the translunar injection (TLI) is in the moon orbital plane.

Lunar landing site lighting and location

The required landing lighting and landing site location were inseparable in their effects on the Apollo launch windows. The effects of the operational landing site lighting constraints have to be evaluated along with the sites longitude.

To provide to LM crew with the optimum visibility during the final phase of the descent and landing, the local sun angle had to be within 5 and 14 degrees above the eastern horizon (behind the LM). These lighting conditions allowed the LM crew to visually evaluate the landing area they were headed into and select the most appropriate location for touchdown.

This range of allowable sun elevations at landing had a major effect on the determination of a lunar landing launch window. Figure 25 illustrates the required lighting geometry.

Figure 25

(click above image for larger version)

This figure shows the sunrise terminator at 0° longitude. The lunar landing could only be achieved in a location within the 5° and 14° longitude lines shown above. The region of acceptable lighting moves across the face of the moon as it rotates, following the sunrise terminator from east to west at approximately 13° per day. The effects of latitude can be ignored in the region close to the lunar equator. Figure 26 illustrates the fact that for approximately 60% of each month there was no acceptable lighting conditions anywhere within the Apollo zone of interest ( 45° E to 45° W).

Figure 26

(click on above diagram for larger version)

The restrictions incurred if only one landing site was targeted can also be illustrated in this figure. If for example the chosen landing site was at 25° E longitude, it can be deduced from figure 26 that only two days are available in which the landing could be attempted. Only one day is available within each 28 day lunar cycle. Therefore for the early Apollo lunar landing missions, to provide multiple launch opportunities during a single lunar cycle, several landing sites had to be planned for.

The number of lunar landing opportunities was directly related to the number of launch opportunities. For lunar landing missions that employed the free-return type of trajectory, this relationship between the launch time and the lunar landing time is quite closely fixed, with only a slight variation. It is therefore possible to plot the available launch and landing times in one graph. Figure 27 shows the landing periods when the lighting conditions were acceptable for February 1969. The opportunities shown in this figure are for Pacific ejections only.

Figure 27

(click on above diagram for larger version)

The launch periods are displayed for each of these landing opportunities. The time span available for each landing opportunity was approximately 10 hours and was due to: the variations in launch time between the launch azimuths of 72° and 108°; the possibility of injecting (TLI) on either the first or second opportunity (although all lunar bound Apollo missions injected on the second opportunity); and the differing translunar coast time for the different energy trajectories available to the free-return trajectory type. The shaded areas represent the range of lunar landing site longitudes that had acceptable lighting conditions for each launch day. It should be noted that on each launch day, the region of available longitudes for landing differed. This region moves westward at about 13 degrees per day, with virtually no overlap. No single longitude is available for more than a single launch day, when taking in to consideration the 2.5 hour launch window constraint. This clearly illustrates the combined effects of the appropriate lighting conditions and the location of the lunar landing site on the Apollo-Saturn lunar launch window.

It can also be seen in figure 26, that to avoid duplication or gaps in the launch window, the longitudinal spacing of the planned lunar landing sites must be in increments of approximately 8° to 13°. By having this longitudinal spacing it was possible to minimise the probability of having 2 lunar landing sites available on a single day, or even worse, having no landing sites available at all on a particular day.

This illustration shows the landing site distribution that was required to provide monthly launch windows. To guarantee that a launch opportunity existed on consecutive days the landing sites had to be located between 8° and 13° of longitude apart. One landing site to each launch opportunity. To provide launch windows on alternate days, landing sites located 20° to 26° apart had to be chosen.

The details above describe the effects of the lighting on the lunar landing site longitude location and how this effects the launch date. The lunar landing site latitude also effects the available launch dates, due to limitations of the SPS performance. Even if the lighting is acceptable, if the landing site is situated outside the bounds of the SPS, then this rules out these launch windows. The accessible latitudes are defined by the following factors:

SPS propellant available as a function of longitude.

Lunar declination and libration.

Trans lunar injection window.

The accessible area for a typical day can be seen in figure 28. This illustration shows that the area available from the Pacific injection window is offset to the north of that available from the Atlantic window. These areas shift to the south as the moon travels to northern declinations and then vise versa. This latitude shift in the accessible area boundaries is cyclic, with a period approximately equal to the lunar orbit period. The following illustrations show the accesssible lunar landing areas following LOI from a free return trajectory, on the early Apollo lunar landing missions.

Figure 28

(click on above diagram for larger version)

If a location on the lunar surface lies within the accessible area throughout a month, regardless of the daily shift of these areas, it was classed to be 100% accessible. The 100% accessible areas were significant in selecting the lunar areas to examine for possible landing sites. It was necessary to pick the early Apollo lunar landing sites in the area that was 100% accessible as the mission planners would no longer need to factor in the lunar declination or libration. Only lighting constraints would remain.

This 100% accessible area presents a worse case picture, as no consideration was given to the fact that only 8 days per month were really usable, during the early Apollo lunar landing missions to multiple landing sites, due to the lighting constraints. More appropriate would be to plot the 100% accessible area on those days of each month when the lighting conditions were acceptable at one of multiple planned lunar landing sites.This would be for sun illumination between 7° and 20° and between 45°E and 45°W longitude, plotting the latitude limits only for the longitude region in which the lighting is acceptable. Figure 29 illustrates this type of plot. for February 1969. The accessible area varies from month to month because the lighting cycle period differs from the declination and libration cycles

Figure 29

(click on above diagram for larger version)

The accessible areas for each month during a year can be combined to show the area which remains accessible for the entire year. This is illustrated in figure 30.

Figure 30

(click on above diagram for larger version)

It has been shown above that the landing site location has a major effect on the timing of the Apollo lunar landing launch window, not only due to lighting conditions and longitude interactions, but also through latitude and spacecraft performance interactions.

In summary, given a particular planned lunar landing site, a launch was only possible on the day the lighting was acceptable and then only if this landing site was within the latitude bounds that were attainable for that longitude on that particular day.

Spacecraft / launch vehicle performance

If it had been possible to design both the Apollo CSM and LM with large enough fuel and oxidiser tanks, it would have allowed them to perform trajectory shaping manouvres to access virtually all of the lunar surface. However the Saturn V's payload capacity was limited so there was a constant battle during the spacecraft design phase to control the overall hardware weight, leaving as much margin as possible to maximise the quantity of propellant that could be carried. Mission planners had to ensure that the mission trajectories required for a particular lunar mission, did not exceed the total ∆V available. The available ∆V changed as the mission phases progressed as detailed below.

During trans lunar coast following TP&D.

* RCS burn time limited to 1000 sec maximum, this value assumes 4 jet operation.

During LOI

* RCS burn time limited to 1000 sec maximum, this value assumes 4 jet operation.

During lunar orbit

* RCS burn time limited to 1000 sec maximum, this value assumes 4 jet operation.

During TEI

During trans earth coast

A safety margin had to be provided above and beyond the optimum ∆V requirements for the various phases of the mission. Examples are shown below for the flight propellant weights carried on Apollo 11 and 17.

SM - SPS propellant

SM - RCS propellant

LM -DPS propellant

LM - APS propellant

LM - RCS propellant

It can be seen from the propellant margins detailed above that only small margins could be accomodated due to the severe pressures on the overall payload weights. It can also be seen how greater propellant quantities were carried aboard Apollo 17 (a 'J' mission) by virtue of developments of the Saturn V, increasing engine performance and reducing launch vehicle weight. This enabled the 'J' Apollo missions to be targeted at more challenging landing sites and carry larger payloads in the form of on orbit experiments, the Lunar Roving Vehicle, a larger suite of surface experiments and more consumables on both the CSM and LM for extended mission duration.

Daylight launches

When targeting some landing sites which may be accessible when performance considerations are taken into account, a daylight launch may not be possible for the entire year for Alantic injections. Also winter launches for Pacific injections were greatly limited due to the length of available daylight each day. In some years a combination of performance limitations and the daylight launch constraint combine to eliminate virtually all available launch windows. For the early Apollo lunar landing missions which had the scope to land a more than one site, which therefore would require up to a five day launch window, if these sites were south of the lunar equator, only the spring and early summer months would provide daylight only launch window opportunities. For sites located north of the lunar equator a five day daylight launch window would normally be available throughout the year if the Pacific injection was employed.

So you can now see that a variety of constraints come together to limit both the times at which a lunar landing launch can occur and the area of the moon that was accessable to the Apollo spacecraft. Careful analysis of the mission requirements coupled with detailed flight planning and real time analysis, combined to allow the mission planners to extract the maximum performance out of the Apollo Saturn space vehicle. This planning paid dividends when preflight and inflight anomalies occurred allowing the flight teams to delay flight events, trouble shoot the anomalies and make plans to correct or bypass the faults and continue using new procedures and an amended flight plan, normally to a successful landing (with the exception of Apollo 13).

Robin Wheeler 2009