As part of a study program started in 1993, members of the Japanese Rocket Society designed the passenger vehicle " Kankoh-maru" to carry 50 passengers to a 200 km altitude orbit with inclination of some 40 degrees (1, 2). Initial flights are to comprise two orbital revolutions, and the service is expected to grow progressively. Kankoh-maru operators will have considerable freedom to select orbital routes which give passengers interesting views of the Earth, and attractive flight paths have begun to be analyzed for this purpose (3). According to the economic analysis performed to date, the cost per passenger could fall as low as $20,000, provided that demand grew to a scale of several hundred thousand passengers per year (4). In market research performed in several countries to date, most people express a preference for staying in orbit for several days. In order to provide this service, there will be a need for orbital accommodation, growing eventually to a scale of several thousands of guests simultaneously, which will involve design, manufacture, launch, assembly and operation of these facilities. It will also require Kankoh-maru operators to operate return flights to and from orbital hotels, in addition to simple orbital flights.

In planning passenger services to and from orbiting hotels, Kankoh-maru operators will have to consider a range of additional factors, including physical constraints imposed by orbital mechanics; vehicle performance factors such as Kankoh-maru's propellant capacity; operations factors such as the launch sites being used, and the availability of propellant (particularly LOX) supplies at the orbital destination; and commercial factors such as flight schedules, and the price-elasticity of demand for passenger flights to different destinations (since more propellant could be used to carry fewer passengers on a particular flight, provided that sufficient passengers were prepared to pay a higher price for the service).

Of these factors, orbital considerations are the most fundamental since they determine the frequency of launch opportunities to reach a given hotel from a given airport, the time taken to rendezvous and dock with the hotel, and the quantity of propellant required for a given payload. These orbital factors are not particularly complex conceptually, although there are many subtle details. However, they are unfamiliar to the airline companies and hotel chains which are beginning to consider offering these services. These factors are described in some detail in this paper, though with some simplifications in order to make it approachable by non-specialists.

The viewpoint of a commercial operator planning orbital passenger flights aboard " Kankoh-maru" is different from that of a government space agency performing a research mission; in particular they will generally be trying to maintain or increase their profitability, which leads to a continuous interest in both increasing revenues and reducing costs. At the operational level this will lead to other objectives, of which two will be particularly important:

1. Minimizing propellant usage (and so propellant cost), thereby also maximizing each flight's revenue-earning payload capacity (whether passengers or cargo).

2. Minimizing the duration of rendezvous flights, thereby increasing the number of revenue-earning flights that each Kankoh-maru vehicle can perform (up to the design target of 300 flights per year).

Consequently, in drawing up plans for such services, companies will have these objectives in mind in selecting between possible alternatives.

Orbital mechanics imposes severe constraints on vehicles attempting to rendezvous in orbit. The most fundamental of these constraints　is based on the concept of the orbit plane. We consider the case in which Kankoh-maru is planning to take off to rendezvous with an already orbiting hotel (which will not maneuver). It is a fundamental property of orbital mechanics (5, 6) that the plane of the hotel's orbit is fixed (to a first approximation) relative to the distant stars (that is, it is "inertially" fixed). If Kankoh-maru was launched so that its orbit initially lay in a different plane from the hotel, then if their trajectories intersected at some point, their high speeds (typically 8 km/second for low Earth orbit), combined with the angle between their orbit planes, would make their relative speed extremely high. (This type of approach is known as "interception", and may be used for anti-satellite operations.)

Consequently, in such a case where the two spacecraft are initially launched into different orbital planes, the only way that a low final relative speed can be achieved is if Kankoh-maru makes a plane-change maneuver, using its thrusters to rotate its orbital plane to coincide with that of the hotel, sometime before its closest approach. However, such maneuvers are extremely expensive in propellant, the reason being that an orbiting spacecraft is essentially a mass circling the Earth at very high speed - as already noted, around 8 km/sec for low Earth orbit ( LEO) - on a "cord" of very long radius (about 6,600 km). Its angular momentum is thus also extremely large, and so a great deal of torque is required in order to change the direction of the angular velocity vector. This vector is perpendicular to the orbit plane: consequently, it is very difficult to alter the orientation of this plane. To give a numerical example, if the Space Shuttle used all its on-board propellant to perform a plane-change, the angle by which it could alter its orbital plane would be only about 1.8 degrees.

A fundamental rendezvous constraint is therefore that Kankoh-maru can be launched only at times when its launch site passes through the orbital plane of the hotel which it plans to visit. If orbit planes were truly inertially fixed, these "planar launch windows" would occur precisely twice per day, as the Earth rotates inside the fixed orbit plane. In reality, orbit planes rotate slowly, as a consequence of the Earth's "oblateness": this is a slight flattening at the poles due to the spinning of the planet which effectively creates a band of additional matter around the Equator. This massive band exerts a slight net torque on an orbiting satellite, so causing its orbit plane to rotate, or "precess", slowly.

For a typical LEO case, the resulting precession rate is around 6 deg/day, (that is about 180 deg/month or a full 360 degrees roughly every 2 months), towards the West. As a result of this slow precession, planar launch windows actually repeat with a period of around 23.6 hrs, i.e. drifting approximately 24 minutes/day, thereby returning "full circle" by drifting 24 hours roughly every two months. It should also be noted that the two launch opportunities per "day" are equally spaced only for launch sites near the Equator; for non-equatorial launch sites the higher the latitude the closer together are the two successive planar launch windows. The limiting case is when the orbital inclination is the same as the launch site latitude, giving only one opportunity per "day".

The latitude of the launch site not only determines the spacing during the day of the two planar launch windows, but it is also important in orbital analysis for another reason. As already described, a rendezvous launch opportunity occurs only when the hotel's orbit plane passes through Kankoh-maru's launch site. The hotel orbit must therefore reach at least as far North as the launch site; that is, it must have an inclination, or angle to the Equator, at least equal to the launch site latitude.

Equivalently, a Kankoh-maru taking off from a launch site with latitude of, say, 50 deg, will enter an orbit with inclination of at least 50 deg: this inclination is obtained by launching due East. Since this launch direction (or "azimuth") takes maximum advantage of the rotation of the Earth (around 0.5 km/s at the Equator), a due East launch requires the minimum amount of propellant, and so gives the greatest possible payload for any launch vehicle and launch site. Launching either North or South of due East will, contrary to what might initially be expected, lead to a lesser performance.

Since most of the large centers of population tend to be at the middle and high latitudes, it appears likely that the orbital inclination of hotels and so the launch sites of interest will be similar. Consequently, the orbits of most space hotels will have fairly high inclination: for instance, a value of 50 deg would allow launches from most of the United States, Japan and Europe. An inclination as great as this would have the additional advantage that a great deal of the Earth's surface would be overflown, so providing a wide range of views for passengers. The disadvantage is that it requires more propellant to reach this inclination than a lower one. It is interesting to note that the International Space Station, and the Russian/Kazakh Salyut and Mir space stations fly at a very similar inclination to this (51.6 deg). The reason for this is the high latitude (45.6 deg North) of the Russian launch site, Tyuratam, used for manned spacecraft.

Summarizing, the orbit plane of a hotel defines two launch opportunities per 23.6 hr "day", with these opportunities typically being fairly close together. In principle, these launch windows are instantaneous, occurring as the hotel's orbit plane passes exactly through the launch site. In practice, Kankoh-maru could make a small "dogleg" maneuver during its ascent in order to compensate for launching when the hotel plane is not exactly through the launch site. This flexibility gives the planar launch windows a finite duration: in practice, it has been found (7) that a dogleg of up to 0.5 deg is feasible, giving rise to planar launch windows that are typically on the order of 4-7 min long. The exception to this is if the hotel orbit inclination is only around 0.5 deg greater than Kankoh-maru's launch latitude: in this case, the portion of the hotel orbit farthest from the Equator remains close to the launch site for an extended period and the two daily launch opportunities merge, giving a single launch window of as long as one hour. These calculations are highly dependent on the details of each case in question, and so more detailed analyses of particular cases, including especially propellant requirements under different conditions, is desirable. In particular these calculations are dependent on the parameters of the orbit used by the target hotel, which we consider next.

The altitude and inclination of a hotel's orbit have major implications for the cost of both the hotel's initial construction and its operations; for the performance required of Kankoh-maru to reach the hotel with its planned complement of 50 passengers; and for the selection of airports from which it will be convenient for both passenger and cargo flights to take-off in order to rendezvous and dock with the hotel.

In addition to the orbit plane factors already mentioned above, a major consideration in selecting a hotel orbit is the rate at which the orbital altitude will "decay" due to air resistance in the Earth's outer atmosphere. Although reentry from orbital missions is usually defined to begin at an "Entry Interface" (EI) altitude of 122 km, the Earth's atmosphere does not end abruptly at this height. Rather, this is the altitude at which significant heating typically occurs on a returning vehicle. A very rarefied but measurable atmosphere extends well above this height, reaching as far as 1,000 km above the surface of the Earth. The entire low Earth orbit ( LEO) altitude range therefore actually lies within the very tenuous upper atmosphere of the Earth. One way in which this can be observed is by the faint glow that surrounds the leading face of the Space Shuttle during orbital night, caused by an interaction with oxygen in the atmosphere.

However, the most significant effect of the upper atmosphere on LEO spacecraft is that it exerts a small drag force, causing them to gradually lose energy, and so slowly spiral in towards the Earth, eventually reentering the atmosphere. This process, known as orbital decay, is somewhat unpredictable, since the density of the upper atmosphere can vary significantly as a result of changes in solar activity. This variability of the orbital decay process was well illustrated by the difficulty that was encountered in predicting the reentry location of the Skylab space station in 1979.

The rate of a spacecraft's orbital decay also depends on the mass-to-surface-area ratio of the spacecraft, and on its orientation relative to its velocity vector; low-mass spacecraft with large solar panels, for example, decay faster than smaller, heavier spacecraft. In this respect hotels will be rather different from other spacecraft: they will have a variety of configurations, and will be larger, but with a proportionately smaller area of solar panels, and generally changing orientation, although such details are not predictable in detail today. However, some general observations can be made, the fundamental one being that spacecraft flying at altitudes of around 200 km or less only remain in orbit for on the order of a day. (Consequently such low altitudes have been used only for spacecraft such as manned vehicles on short missions or as temporary "parking orbits".)

The main effect of atmospheric drag on an orbiting spacecraft is to reduce its orbital altitude gradually but continuously, causing it to spiral in towards the Earth, slowly at first but at a gradually accelerating rate. In the final phase, once an altitude of around 180 to 200 km has been reached, it takes only a few hours to reenter and (usually) burn up. Figure 1 illustrates this behavior for the particular case of a spacecraft initially orbiting at an altitude of 300 km.

A consequence of the gradual nature of orbital decay in higher orbits is that thrusters on board the spacecraft can maintain its altitude at the desired value by performing quite small reboost maneuvers (8). The frequency of these maneuvers needs to be increased as the selected orbital altitude decreases. There is therefore a basic tradeoff involved in selecting the nominal orbital altitude for a hotel: if the altitude is increased, fewer reboost maneuvers will be required, and consequently less reboost propellant will be used per year, reducing hotel operating costs. But on the other hand, increasing the hotel's altitude reduces the mass that a given launch vehicle can carry to it, due to propellant limitations. This increases the cost/kg of delivering supplies to the hotel, and the cost of return-flights to the hotel by both passengers and hotel staff.

Figures 2 and 3 illustrate the effects of atmospheric drag in two different ways. Figure 2 shows the estimated orbital lifetime, i.e. time until reentry if no thrusting is performed, as a function of initial altitude for a typical spacecraft. This figure is based on the orbital model used in (9), and so the case of a real hotel may differ to some extent. Figure 3 estimates the annual amount of reboost propellant (expressed as a percentage of the total spacecraft mass) required to maintain the spacecraft's orbital altitude at the original, nominal value. This figure also may be different for orbital hotels.

From the above figures it can be seen that an orbital hotel should be placed in an orbit with altitude at least 350 km, and preferably 400 km or greater. In practice, small periodic reboost maneuvers will not keep the altitude at precisely the nominal value; rather, it will be maintained in a "saw-tooth" pattern within an altitude range that is considered acceptable. Selecting the optimal depth of this band (for example, up to 5 km or up to 10 km) will involve a number of considerations, including the cost of propellant storage and transportation, integration of reboosting with hotel operations, and traffic regulations. However, it is clearly a major requirement that the hotel orbit must remain convenient for rendezvous purposes, as we examine next.

The "Planar Launch Windows" specify the times at which Kankoh-maru can be launched into the same orbit plane as the hotel. However, in order for a rendezvous to be accomplished, the two spacecraft must not only orbit in the same plane, but must actually reach the same point in this plane at some instant with the same velocity: this is known as the "Rendezvous Phasing Problem".

The fundamental orbital property that is used to achieve correct phasing for rendezvous is that lower orbits have shorter periods: for instance, a 300 km orbit has a period of 90.5 min, whereas one at 250 km has a period 1 min shorter. Consequently, if Kankoh-maru is in the lower of these orbits and the hotel is in the higher, Kankoh-maru will complete one revolution of the Earth approximately 60 sec before the hotel does. At the orbital speeds involved, this implies that Kankoh-maru will move forward relative to the hotel by approximately 480km each revolution. This leads to what is usually referred to as the "Ten-to-One Rule": the distance by which the lower of two spacecraft will pull ahead of the higher, per orbital revolution, is approximately ten times their average vertical separation.

Kankoh-maru could also be launched into an initial orbit higher than that of the hotel with which it is to rendezvous, whereby the hotel would "overtake" Kankoh-maru. However this would be inefficient in using more propellant than necessary. Kankoh-maru will therefore usually approach orbiting hotels from below - and so from the Ten-to-One Rule, will be overtaking them. Consequently, if the correct phasing to permit rendezvous is to be achieved, Kankoh-maru's launch will have to be timed to occur when the hotel is an appropriate distance ahead of it. In addition, of course, the planar launch window condition must also be satisfied, i.e. launch must occur when the target orbit plane passes within 0.5 deg or less of the launch site. As already noted, this condition is generally satisfied twice every 23.6 hrs. Suppose now that, on one particular day, one of the planar launch opportunities also satisfies the phasing constraint for a particular launch site, and so Kankoh-maru can take-off and reach the hotel. An important question is then: how long will it be before both the planar and the phasing conditions are again simultaneously satisfied for that site? The solution is that the two conditions are satisfied when 23.6 hrs or a multiple of it is equal to an integral number of hotel orbit periods. In this case the hotel will return to the same position relative to the launch site after the appropriate number of full orbital revolutions.

As already seen, the period of an orbit depends on its altitude. Consequently, if we are to achieve the desired "resonance" between the planar and phasing launch windows (i.e. whole numbers of each coincide periodically), only certain precise orbital altitudes will be acceptable for the hotel. Figure 4 plots the altitudes that are required in order to obtain rendezvous launch windows repeating at intervals of one, two, three or four days.

The dependence on inclination results from the fact that the rate of precession of the hotel orbital plane (i.e. its slow rotation towards the west) is not fixed but is a function of its eccentricity. Hence the planar launch window repeat interval will not be exactly 23.6 hrs, but will vary slightly with the orbit's inclination. (It is interesting to note that the Russian/Kazakh Salyut and Mir space stations made extensive use (10) of two-day and three-day repeat-cycle orbit altitudes, in order to provide conveniently frequent launch opportunities for Soyuz and Progress rendezvous missions.)

In practice, there are additional constraints on how long the total rendezvous procedure can be allowed to take. These constraints are likely to be quite severe for commercial flights to orbiting hotels, whether passenger flights or cargo flights, since Kankoh-maru operators will need to achieve high utilization rates. In current missions to Mir, rendezvous often takes up to two days, a duration that would probably be unacceptably long for most commercial operations.

The main consequence of requiring a short rendezvous procedure is a reduction in the size of the initial phase difference between the two vehicles that is acceptable. This reduces the number and duration of phasing launch windows. For example, if a rendez-vous procedure lasting more than 12 hours were judged to be unacceptable, then the number of usable launch windows would be reduced. This requirement would therefore increase the importance of having the hotel in a repeating orbit as described above, in which case the planar and phasing windows overlap more frequently.

In order to quantify this effect, we consider a hotel in a 350 km altitude orbit, and suppose that Kankoh-maru launches to rendezvous with it during the planar launch window but with a significant phase difference. In order to catch up with the hotel as quickly as possible, Kankoh-maru will have to spend time in the lowest orbit practicable, i.e. about 200 km altitude, which is Kankoh-maru's nominal launch altitude. By the Ten-to-One Rule, each orbital revolution which Kankoh-maru makes at this altitude allows it to advance relative to the hotel by about 1,500 km. This seems a considerable distance; however, 1,500 km is covered by Kankoh-maru in its orbit in just over 3 minutes. Consequently, each revolution spent by Kankoh-maru at 200 km allows it to correct for an initial phasing error of 3 minutes (or 1500 km). If the hotel were actually halfway around its orbit (i.e. 45 minutes) from the desired point during the planar launch window, this phasing error would require about 15 low orbits by Kankoh-maru in order to compensate - or about 22 hours.

A delay of 22 hours may be acceptable for a Space Shuttle mission in which the rendezvous procedure can be permitted to take more than one day. However, it will probably be considered longer than desirable for a commercial passenger flight. Like an airline, the commercial operator of a Kankoh-maru will wish to maximize the vehicle's use by minimizing the length of each round-trip to a hotel. In addition, keeping passengers within Kankoh-maru for one day is likely to be considered undesirable. It is worth noting, however, that this might be less of a problem than a flight in an airliner of similar duration, since passengers in weightlessness will not get uncomfortable from sitting in their seats. Thus it may be that for operational convenience some flights of this length will be operated, suitable entertainment and services being provided. This might be roughly analogous to non-direct long-distance airline flights today, which are longer and less convenient but usually less expensive than direct flights.

It should be noted that in practice it is efficient to use elliptical orbits, in which the apogee (the maximum altitude) and the perigee (the minimum altitude) are significantly different, as well as circular orbits, in rendezvous operations. This adds considerably to the range of possibilities and so to the complexity of the analysis, but for simplicity we do not discuss this topic in detail here.

A further important point related to orbit phasing is that atmospheric drag will reduce the altitude of a hotel in a nominally 350 km orbit by approximately 1 km every 2 days. This will lead to a cumulative phasing error of about 25 seconds after 2 days, or about 1.5 minutes per week, which would add 45 minutes to the length of the rendezvous procedure in the previous case. This suggests that small (less than 1 m/s) reboost maneuvers should be performed on roughly a weekly basis in order to preserve the repeat cycle of the hotel orbit. Increasing the hotel orbital altitude somewhat would allow these maneuvers to be performed slightly less frequently without corrupting the repeating nature of the orbit, but at the cost of increasing launch cost to the hotel. It will be interesting to analyze a number of particular cases in more detail.

The preceding discussion is used in the following section as the basis for a possible rendezvous sequence between Kankoh-Maru and an orbiting hotel. For definiteness, a hotel orbit inclination of 60 deg is assumed; 　such an orbit would permit launches from Japan, the United States and most of Europe, and provide views of most of the Earth's surface. The hotel should be in a repeating orbit, and so　an altitude of 355 km is chosen here, giving a repeat cycle of two days.

A variant of the four-revolution (i.e. 6 hours) rendezvous sequence employed on the Gemini 6, 8 and 10 missions (7) is proposed here. This procedure was the basis for the rendezvous procedures used for the Apollo missions in lunar orbit, and some parts of it are employed in the Space Shuttle program (11). The Gemini program also tested a three-revolution rendezvous (on missions 9 and 12) that was quite similar to the four-revolution version, and a one-revolution rendezvous on Gemini 11; the latter was successful, but it entailed a very short launch window, due to tight phasing constraints.

In outline, the maneuvers required in the proposed rendezvous procedure are as follows. The resulting launch window is roughly 160 seconds long, due to the phasing constraint. The on-orbit maneuvering required to achieve rendezvous is approximately 100 m/s, which corresponds to about 1.3 tons of Kankoh-Maru propellant (1). It should be noted that this propellant consumption does not vary through the launch window: the amount consumed in steps [2] and [4] combined is a constant - that is, it is not dependent on the time at which Kankoh-maru is launched within the window.

1. Launch of Kankoh-Maru into a low (200 km) circular orbit nominally coplanar with the hotel. That is it is launched during the planar launch window as well as the phasing launch window.

2. Half an orbit (i.e. 45 minutes) after launch, Kankoh-maru fires its engines to accelerate (a "posigrade" or "speed-up" maneuver) so as to raise the apogee of its orbit, while leaving the perigee at 200 km. The new apogee altitude will be 25 km below the hotel, i.e. at an altitude of 330 km. If Kankoh-Maru's launch is delayed somewhat, it will need to achieve a greater phase-angle catch-up to reach the hotel, which can be achieved by raising its apogee to some intermediate value between 200 and 330 km.

3. If there is any (small) residual error in the inclination of its orbit, Kankoh-maru fires its engines to make a small plane change the next time that it crosses the equator (i.e. at the next "nodal crossing").

4. If required, two revolutions after the first apogee-raising maneuver, Kankoh-maru fires its engines again to raise its apogee again to achieve the desired 330 km altitude.

5. Half an orbit later, Kankoh-maru circularizes its orbit at 330 km altitude by firing its engines again to raise its perigee. It is now orbiting 25 km below the orbit of the hotel, and so is catching up with it at a rate of approximately 250 km/orbit.

6. Kankoh-maru makes a final engine burn (known as the Terminal Phase Initiation (TPI (7), or just TI (11) maneuver) in order to put it on a trajectory that will reach the hotel after traversing another 130 deg of the orbit, that is, after approximately 32 minutes. (This value of 130 deg was selected for the Gemini program so that the line-of-sight between the two vehicles was as nearly as possible inertially fixed (7). This allowed the crew-members to confirm that their rendezvous procedure was correct by observing the target visually, and checking that it remained in a fixed position relative to the stars. Despite great advances in computer technology since the Gemini and Apollo programs, and the current availability of the Global Positioning System (GPS) navigation aid, such manual backup procedures are still of value for ensuring safety. They are somewhat analogous to airline pilots carrying maps on board modern, highly-automated airliners.)

7. Once Kankoh-maru is close to the hotel, the "Proximity Operations Phase" begins. This consists of a slow approach by Kankoh-maru towards the hotel, typically followed by station-keeping (where the two spacecraft maintain a constant relative position), and finally by docking.

Hotel Proximity Operations

The overall process of rendez-vous and docking with a hotel will be governed by the traffic control rules used in the vicinity of the hotel. These have not been finalized yet; they will be decided by hotel operators. However, possible systems have been conceptualized that involve a series of nested zones in the same orbital plane as the hotel, such as in (12). As air traffic control rules cover aircraft approach and departure routes to and from airports, so these rules will cover the routes which Kankoh-maru may take in approaching and leaving the hotel. In addition, a staff member on board the hotel is likely to have the role of Traffic Controller, giving instructions directly to the pilot of Kankoh-maru. At a time when several orbital hotels are in operation, some may decide to use the same orbit, although there are technical and legal complexities in achieving this, including even defining the "same" orbit for practical purposes (13).

An important question in the proximity operations phase is the choice of the direction in which Kankoh-maru's final approach occurs. In the Gemini, Apollo and early Space Shuttle operations, the final approach was made horizontally, that is along the orbital velocity vector, or "VBAR". Advantages of using this type of approach are that it can be halted at any point if problems arise, and the two vehicles remain in the same relative positions without the need for additional thruster firings. However, a difficulty with the VBAR approach is that Kankoh-maru would have to make a final braking burn just before docking. As this burn would use thrusters that face towards the hotel, there is the potential problem of the thruster exhaust gases impinging on vulnerable parts of the hotel, such as windows, solar arrays, or other equipment.

This problem is avoided if Kankoh-maru makes its final approach vertically, that is along the orbital radius vector, or "RBAR". In such an approach, orbital mechanics actually provides a form of passive braking, as Kankoh-maru's upward velocity falls as its altitude increases. As a result, the only thruster firing that Kankoh-maru is required to perform is horizontal (in order to keep from drifting ahead of the hotel due to its lower orbit), together with an occasional burn to accelerate towards the hotel (since "orbital braking" continually reduces the speed of approach). In this way no thruster firings are needed that are aimed towards the hotel, and so exhaust gas impingement ("pluming") is no longer a problem. The RBAR approach has been used for all of the rendezvous missions between the Space Shuttle and the Mir space station, and pluming of the delicate Mir solar arrays by the Space Shuttle's large thrusters has thereby been avoided.

Space Shuttle missions to Mir also usually involve a "fly-around" of Mir after separation, allowing inspection of the station for external damage, etc. Figure 5 shows a typical example of such a path around the Space Shuttle. A similar fly-around of the hotel by Kankoh-maru would probably be popular with guests, since it would give them a range of interesting views of the hotel against the backgrounds of both the Earth and the stars. Consequently, when the flight schedule permits, a fly-around of the hotel may be performed on first approach to the hotel and/or on departure.

IMPLICATIONS FOR KANKOH-MARU

In the preceding sections we have described some of the basic features of rendezvous and docking operations for Kankoh-maru visiting a hotel in low Earth orbit. From the point of view of an airline planning such services, the return-flight including reentry and landing is equally important, and we intend to extend this discussion to cover also return-flight operations. In principle, similar conditions apply: that is, it is necessary to schedule de-orbit operations for a time when Kankoh-maru's orbit plane and phasing within its orbit have the correct positions relative to the landing site. Combining both rendezvous and return-flight analyses will give useful inputs concerning the performance required of Kankoh-maru, its propellant requirements for different services, attractive take-off sites, and other matters.

Even from the limited analysis performed so far there are some useful insights. For example, Kankoh-maru is designed to reach a circular orbit of 200 km altitude at 40 deg inclination; consequently to reach higher orbits and/or higher inclinations will require more propellant and/or a reduction in payload on those flights. This has implications for the economics of these services: in round figures Kankoh-maru is being designed to carry 50 passengers, equivalent to some 5 tons of payload, to 200 km altitude. If, as in the case discussed above, 1.3 tons of additional propellant is required to reach the hotel, this represents 1/4 of the payload. Other things being equal this might be paid for by charging passengers a 33% premium, which in turn has implications for commercial issues such as the price-elasticity of demand for the service.

Another matter which the above discussion shows is the potential value to Kankoh-maru operators of propellant supplies in orbit. By reducing the amount of propellant that Kankoh-maru must carry to its orbital destination (for its return-flight), the ability to refuel on arrival would greatly increase its flexibility, its payload capacity, and so its revenue-earning capacity per flight. Furthermore, Kankoh-maru uses liquid hydrogen ( LH2) as fuel and liquid oxygen ( LOX) as oxidizer, and these can be generated from water by solar-powered electrolysis - a technology particularly suitable for use in orbit. This therefore leads to the question: can LOX (or water) delivery costs to LEO be reduced sufficiently, perhaps through dedicated "tanker" supply launches, that, after paying the cost of storing on orbit (&/or the cost of electrolysis) propellant can be supplied to Kankoh-maru in orbit at a price less than carrying it itself? If so, this will be an attractive direction for business investment when hotels start operating in orbit.

This paper has discussed some of the implications for Kankoh-maru operations of planning to rendezvous with an orbital hotel. In particular, the orbit selected for a hotel has major implications for Kankoh-maru's propellant requirements, and hence for its design, and also for the selection of airports for launch sites. Among other results, the requirement to be able to view much of the Earth favors the use of high latitude launch sites. However, the above discussion has presented only the fundamentals for one or two simple cases, and there is great scope for more detailed analysis of more, and more complex cases.

Although detailed orbital calculations can be performed easily using standard software on personal computers, the particular viewpoint of commercial travel service operators is new, and adds a range of novel constraints and complicating factors to the analysis. There is therefore a wide range of new issues for consideration, all of which require more detailed analysis. As examples:

1. After re-entry Kankoh-maru is designed to have a 200 km "cross-range" capability (that is, it is able to move up to 200 km to the right or left of its re-entry path), which has implications for its return "windows". Returning to a different airport than its take-off site may permit more efficient flight schedules, leading to the "pairing" of airports that can cooperate well for a given orbital hotel and/or hotel orbit.

2. Having almost empty propellant tanks on its return flight, Kankohmaru will be much lighter than on take-off and could make a larger plane change by carrying more propellant than the minimum, thereby effectively increasing its cross-range above 200 km, but at additional cost.

3. On occasions it will be possible to reduce the rendezvous time by launching earlier during the window, but at the cost of requiring a larger "dogleg" maneuver, which would use more propellant, and so cost more.

These and many other such possibilities need detailed analysis, combining sophisticated orbital mechanics, advanced spacecraft design, business analysis, and market data.

As a step in that direction, we have started to perform this analysis in a way that we hope makes it approachable by non-specialists. The ultimate objective of this work is that concepts such as apogee, orbital phasing error, RBAR, "dog-leg" and the "Ten-to-One Rule" should become as familiar to airline flight dispatchers as terms such as "great circle", "jet-stream" and "go-around" are today. Likewise, commercially important terms such as "passenger load factor", "block time", "spacecraft utilization" and "ticketing costs" should become equally familiar to spacecraft designers and operators.

Pilot Procedures for Kankoh-Maru Operations

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