Nearly continuous global coverage

The maximum revisit time for a point on the Earth represents the maximum time between accesses of that point by any satellite in a constellation. It is an important measure of the worst-case frequency of having geometric access to observe points on Earth. Figure 1a, b presents global contours of maximum revisit time for the discovered 24- and 48-h period constellations, respectively. The data contours account for station-keeping and drift over a period of slightly more than 8 years (3,000 days), with statistics calculated over a grid of ground target points with 1° spacing in latitude and longitude. The contour data indicate that 24- and 48-h-period constellations achieve continuous coverage over 86 and 95% of the globe, respectively. For those regions that experience outages, the maximum duration is on the order of 80 min once per day. The Supplemental Methods section provides additional background on the coverage metrics used in this study.

Fig. 1: Maximum revisit time and minimum elevation angle. a Maximum revisit time for the 24-h constellation. b Maximum revisit time for the 48-h constellation. c Minimum elevation angle for the 24-h constellation. d Minimum elevation angle for the 48-h constellation. The top color scale represents maximum revisit time from 0 to 75 min. The bottom color scale represents minimum elevation angle from 0 to \(2{0}^{\circ }\). The \(x\) and \(y\) axes are longitude and latitude, respectively. Full size image

Orbit phasing describes both the positions of individual spacecraft relative to one another, as well as the position of the spacecraft relative to the rotating Earth. The specific phasing of the constellation determines the longitudinal position of regions that experience outages (Fig. 1a, b). Thus, these outage regions can be placed over regions of less interest to the constellation operator. An operator of a global agricultural monitoring constellation might, for example, position the coverage gaps over open ocean areas. Furthermore, these outage regions can be easily modified during the lifetime of the constellation if the regions of interest change. Small true anomaly phase changes to the constellation will shift these regions longitudinally for very little propellant cost, and can be performed multiple times.

The minimum elevation angle is defined as the minimum allowable angle between the horizon and any viewable spacecraft at a ground point. The intent of this angle is to account for terrain obstructions, such as buildings and mountains. If the Earth were a perfect sphere, without any features, then a minimum elevation angle of \({0}^{\circ }\) would be sufficient (ignoring atmospheric effects). However, these assumptions do not hold, and thus it is common in constellation analysis to use a positive minimum elevation angle to account for most types of terrain. In practice, it is common to require minimum elevation angles of 5–10°14. This is sufficient for most ground points, but is not applicable in all cases: consider an observer in a city with tall skyscrapers nearby, or an observer at the base of Mount Everest. The observed minimum elevation angle provides another measure of the quality of coverage for the constellations.

Figure 1c, d shows the minimum elevation angle observed across the 3,000 day simulation of the 24- and 48-h constellations. For the 48-h constellation, most of the Earth has a satellite at an elevation angle >\({5}^{\circ }\) at all times; only the outage regions experience lower elevation angles. A vehicle at higher altitude has geometric access to a larger portion of the globe than the equivalent vehicle at lower altitude. One can see this demonstrated in the context of a commercial airline flight: at take-off one can see far less of the surrounding area than when at cruise altitude. This geometric effect extends to elevation angle as well: a satellite at higher altitude has, at any acceptable elevation angle, a larger field of view than a satellite at lower altitude. Thus, the lower altitude 24-h constellation (Fig. 1c) has the larger areas that experience elevation angles <\({5}^{\circ }\).

Minimizing propellant demands

Beyond initially attaining high-quality geometric coverage, another key aspect of a constellation design is the propellant required to actively manage the component satellites’ orbital configurations to maintain desired levels of coverage. The amount of propellant required is a function of the size of the maneuver(s) and the efficiency of the thrusters. The size of an orbit change maneuver is measured by the change in the velocity vector across the maneuver, generally referred to as the delta velocity (\(\Delta {{V}}\)). The thruster efficiency is characterized by a parameter called the thruster specific impulse. Given these two parameters, the propellant required for a maneuver or set of maneuvers can be computed using the rocket equation. In the field of orbit constellation design, it is common to use the \(\Delta {{V}}\) as a surrogate measure of the propellant required15. The reason for this is that there are many different spacecraft thrusters available, each of which has a different efficiency. The constellation design is generally performed far in advance of spacecraft construction or thruster selection. Therefore, the thruster efficiency is generally unknown at the time of the constellation design. The \(\Delta {{V}}\) measure can be easily translated into propellant requirements once the thruster efficiency is known. Minimizing the need for active station-keeping (\(\Delta {{V}}\)) by leveraging the energy from orbit perturbations implicitly mitigates the impact of thruster considerations on the constellation design by reducing the fraction of the vehicle mass that must be devoted to propellant. The Supplementary Methods section describes the station-keeping framework used in this study in more detail.

Figure 2 plots the maximum single-satellite \(\Delta {V}\) station-keeping requirement as a function of time for the 24- and 48-h constellations, as well as for the 27- and 48-h Draim constellations and the widely employed geostationary equatorial orbit (GEO). A \(2.{5}^{\circ }\) inclination control threshold is used. The constellations substantially outperform the Draim and GEO configurations in \(\Delta {V}\) performance at all durations considered. The required station-keeping propellant is reduced in both cases by ~60%. To provide a sense of the different propellant requirements, a specific illustrative example is provided in Table 1, which lists a sample propellant budget for a notional spacecraft. These data demonstrate the impact of using the constellation configurations reported here rather than the equivalent GEO or Draim configurations on the mass budget for a vehicle. The constellations reduce the overall vehicle mass budget by ~60–65% for either chemical or electric propulsion systems. By harnessing the energy from the perturbing forces, the constellations considerably reduce the propellant required to operate in these orbit regimes. By reducing the example constellation’s propellant mass (Table 1) without adversely impacting its design life, this constellation design can potentially realize major mission-level benefits. This example reflects a 1,000-kg vehicle over a 6,000-day lifetime (\(2.{5}^{\circ }\) inclination tolerance, \({5}^{\circ }\) argument of perigee tolerance), where values in parentheses represent the percent reduction in propellant mass for the 24- and 48-h constellations relative to GEO. Table 1 shows that the reduction in propellant mass is large enough to potentially accommodate another instrument, include another mission focus, double the design life, or some combination of these mission-level benefits. The reported constellation designs thus represent an alternative for propellant-averse missions, which can tolerate space vehicle motion relative to the ground which is fixed in a geostationary orbit.

Fig. 2: Maximum single-satellite station-keeping \(\Delta {V}\) requirement. Mission duration varies from 3000 to 6000 days to capture a broad cross section of typical geostationary satellite lifetimes. Both constellations (light and dark blue circles) perform better than the GEO (gray circles) or benchmark Draim configurations (light green and dark green circles). While both 24- and 48-h constellations outperform the GEO configuration in terms of station-keeping propellant requirements by ~60%, the 24-h constellation retains the same orbit altitude, permitting similar conditions for payloads. Full size image

Table 1 Comparison of propellant requirements. Full size table

Using perturbations to sustain coverage

The individual spacecraft in constellations often occupy different orbital planes. The location of these planes relative to each other is specified by the right ascension of the ascending node (RAAN). Maintaining this relative spacing allows the constellation coverage to remain at nominal performance levels. There are many inertial configurations of a constellation that result in the same relative positions. Consider the simple example of three spacecraft whose RAANs are 0, 120, and \(24{0}^{\circ }\); the relative planar spacing is \(12{0}^{\circ }\). A constellation also might have RAAN values of 30, 150, and \(27{0}^{\circ }\); these inertial values are different, but the relative spacing is the same. There is a subtlety regarding the RAAN: because the spacecraft planes are different, they will each experience slight differences in perturbative effects (e.g., nonlinear forces due to the gravity of the sun and the moon). Therefore it is good practice to ensure that these perturbative effects do not adversely affect the constellation, regardless of what the inertial RAANs might be. The Supplementary Methods section details the specific perturbations that are considered in this analysis.

The station-keeping performance of the 24- and 48-h-period constellations is fairly independent of the position of the constellation in RAAN. To demonstrate, Fig. 3 plots the total and maximum single-satellite station-keeping \(\Delta {V}\) for both constellations as a function of a shift in inertial RAAN position while maintaining relative RAAN spacing. The reported data consider a mission duration of 6,000 days and an inclination control threshold of \(0.{1}^{\circ }\), providing an aggressive station-keeping environment for study. The standard deviation of the maximum single-satellite \(\Delta {V}\) for the 24- and 48-h cases is 35 and 23 m \({{\rm{s}}}^{-1}\), respectively. This demonstrates that the identified coverage gap locations from Fig. 1 can be shifted in epoch (or equivalently longitude) without dramatically impacting active station-keeping requirements. Constellation designers can thus select and control the location of the coverage gaps, providing crucial flexibility to how the reported designs can be used for specific missions.

Fig. 3: Station-keeping \(\Delta {V}\) requirement. Total constellation (red) and maximum single satellite (blue) reported as a function of constellation and shift in RAAN applied uniformly to all satellites. The relatively flat curves indicate that constellations are not constrained to the reported gap locations, and can be adjusted with a limited impact to lifetime propellant needs. Full size image

Figure 4a, b plots the position of the satellites in each constellation on annual station-keeping requirement contours in RAAN and inclination space for 24- and 48-h orbit periods, respectively. The contours in the plot show the \(\Delta {V}\) required to maintain a given inclination using semiannual station-keeping maneuvers. The shape of the contours results primarily from third-body interactions with the sun and the moon. Effectively, dark purple regions on the map show where satellites can harness the energy of these perturbations to maintain configuration rather than struggle against them. Both identified constellations, identified by green crosses lie in these advantageous regions of the space. In addition, the constellations lie in inclination regions with relatively flat contouring in the direction of RAAN. This contrasts with the contouring at the Draim inclination of \(31.{3}^{\circ }\), indicated by white circles, which at both orbit periods passes through regions with relatively high annual station-keeping requirements. By positioning satellites in inclinations with more benign variations in station-keeping requirements across RAAN, the satellites do not experience significant coverage-degrading differential motion between one another. This allows the satellites to forego RAAN station-keeping without adversely affecting the constellation’s coverage performance. The constellations reported here represent only two of many designs identified during the search process. Details regarding the broader results of the search are available in Supplementary Figs. 1 and 2. The orbital elements for the reported constellations are shown in Supplementary Tables 1 and 2.