Design: Orbits and missions
In this section, we propose some contracts mirroring real-life mission objectives, highlighting relevant mission constraints and providing examples of the ways in which the objectives have been met in various missions.
This section is heavily inspired by Capderou’s 2012 book Satellites : de Kepler au GPS; the title of the section is drawn from Capderou’s earlier book).
Where a particular approach requires 𝑛-body or extended-body gravitation, we make a note of this; however, there are always alternative approaches, so that none of these contracts are Principia-specific.
We group the missions in three main categories:
A fourth section contains miscellaneous missions that did not really fit into that classification.
The primary constraint for a solar observatory is, obviously, that the spacecraft have a direct line of sight to the Sun.
A spacecraft which spends a significant amount of time in the dark can perform solar observation (e.g., the SOLAR experiment on the ISS), but this is less efficient. Note however that even some dedicated solar observatories (especially older ones) have used such orbits: OSO-1 through -8 were in low-Earth orbits inclined 33°, SOLRAD-8 through -10 were inclined between 50° and 60° (Capderou 2012).
Further, solar observatories can also have a space weather monitoring mission: the goal is then that the Sun be observed at all times, or at least most of the time.
For better monitoring, it may be required that the Sun be observed from multiple angles at all times.
the STEREO-A and STEREO-B spacecraft achieve that by being on heliocentric orbits below and above the Earth respectively. Combined with L1 or Earth orbit satellites, they can sometimes achieve a nearly complete view of the Sun.
One constraint can be continuity with previous missions.
To quote the PROBA2/SWAP & LYRA Science Management Plan:
Continuity. The EUV corona has been continuously imaged by EIT onboard SOHO since the beginning of the present solar cycle. SDO will be launched at the beginning of the next solar cycle. The risk is non-negligible that the SOHO or EIT operations fail before the launch of SDO. Without a temporal overlap between the two EUV imaging missions it will be hard to compare two solar cycles. This is the same problem as the measurement of the Solar Constant over several solar cycles. PROBA2/SWAP will provide an extra chance for continuously overlapping EUV observations from SOHO to SDO.
Many orbits are used for dedicated solar observatories.
Some orbit choices minimize or eliminate eclipse.
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Sun-synchronous crepuscular orbit; requires the least Δv, but, because of the axial tilt of the Earth, the spacecraft will still experience (short, up to 20 min per revolution) eclipse near the solstices. Requires extended-body gravity.
Examples:
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Earth-Sun L1; no eclipse, requires less Δv than going to a heliocentric orbit; however at this distance, the DSN is required for the downlink. Requires 𝑛-body gravity.
Examples:
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Heliocentric orbit; requires lots of Δv, can observe the sun from places other than Earth. The main example is STEREO. Note that probes such as Helios, Ulysses, or Parker Solar Probe are in heliocentric orbits, but are designed for altitude (and, for Ulysses, latitude coverage) constraints that are more akin to planetary science missions than to sustained solar observation missions.
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Earth-Sun L4/L5: An early plan for STEREO; see also LUCI aboard Lagrange. TODO(egg): elaborate.
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Inclined geosynchronous orbit; eclipse season (up to 72 min per revolution) twice a year. Example: SDO.
Other solar observatories are in miscellaneous low-Earth orbits that do not seek to minimize eclipse. Examples:
- OSO missions, inclined 33°;
- SOLRAD, inclined between 50° and 60°;
- Коронас-Фотон, inclined 82°;
- ようこう, inclined 31°;
- SORCE, inclined 40°.
TODO(egg): mention high latitudes and things like Ulysses.
All these contracts should be renewable, with better rewards for renewal, to encourage continuity.
The Sun must be observed with an X-ray photometer for a total of six months over one year.
The Sun must be observed with an extreme ultraviolet telescope 95 % of the time over one year.
The Sun must be observed with an ultraviolet spectrometer 100 % of the time over one year.
70 % of the surface of the Sun must be observed with a white-light coronagraph 95 % of the time over one year.
The most important features of a survey telescope are field of view and exposure duration. Orbits are chosen based off of a balance of availability of portions of the sky and ease of bringing data back down.
- TESS's 13.7 day Lunar Resonant Orbit (P/2) is a good exotic orbit case study:
- Extended observations
- Thermal stability (lack of eclipses, theoretically convenient earth and moon positions)
- Low Earth/Moon stray light level compared with LEO(!)
- Low radiation (never gets low enough to be inside the Van Allen belts)
- Excellent pointing stability (lack of atmospheric drag or gravity gradient, much like an earth leading/trailing orbit)
- Kozai mechanism induced stability(!?) here, meaning no need for stationkeeping
- High downlink rates (apogee is not much farther than the Moon, perigee is slightly closer than GEO, so very easy with 34 m dishes on the DSN) Notable slide: https://photos.app.goo.gl/4K8g8HG32cGENk8z9 sourced from an STScI talk: https://cloudproject.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=768b2761-a534-4026-b644-a9e40150ccd2
TODO(egg): look at https://www.iau.org/static/science/scientific_bodies/working_groups/267/report-uva-wg-20200730.pdf.
Compared with optical telescopes, the primary problem is cooling. Aside perhaps from Hubble (which only goes out to 1.6 μm, and only gained that ability after the second servicing mission) and early iterations of SIRTF (which would have been brought back to earth for maintenance and refilling coolant every few weeks), infrared instruments make extensive use of passive cooling, and are exclusively placed in orbits to mitigate heating from the Earth and Sun. Several orbits are used to this end.
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Sun-Synchronous orbit; Requires the least ΔV, and keeps the sun in a consistent location (if somewhat away from the earth). Requires extended-body gravity. Examples:
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Earth-Sun L2; Keeps the Earth and Sun (and Moon!) all in one direction, so that they can be easily blocked with a sunshield. Earth is also always in the same direction, making pointing and antenna design easier. The greater distance requires using the DSN for downlink. Requires 𝑛-body gravity.
Examples:
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Earth-Trailing orbit; At sufficiently large distances from Earth, it can be ignored as a thermal source, so the spacecraft merely has to deal with the Sun. Requires less station-keeping than a Lagrange point and less ΔV than HEO, but requires using the DSN, and regularly repointing the spacecraft to downlink. Long duration missions present problems of increasing distances (reduced data rates in real life, probably just DSN upgrades here), and increasingly unfavorable pointings. (Sun angle presents both heating and power issues in the case of Spitzer's Beyond Phase)
Examples:
TODO: discuss misc orbits (ISO's highly eccentric 24 hour orbit, the high earth orbit planned at one point for Spitzer), better research sun-synchronous ones. (These seem to also be crepuscular?), radiation effects on sensors (both IR and X-ray sats have periods of uselessness from passing through the van Allen belts)
TODO: the constraints for CoRoT are well documented, e.g., https://corot.cnes.fr/fr/COROT/Fr/contraintes_mission.htm; mention that.
Many kinds of instruments are involved in Earth observation, and some of the constraints that affect the choice of orbit come from intrinsic properties of the instruments.
High resolution imaging, as well as most non-imaging Earth observation instruments (radars, scatterometers, lidars, etc.) require that the satellite be at LEO altitudes; while some sets of constraints (especially in meteorology) are better satisfied by GEO, most solutions are LEO.
Some instruments are power-hungry (radars, scatterometers), and require that eclipse (where the solar panels cannot provide power) be rare and brief. For low orbits, this favours a crepuscular sun-synchronous orbit.
Together with considerations of cycle and sub-cycle length, this is one of the main constraints on phasing: one generally requires that most of the Earth be observed at regular interval, so that the interval between neighbouring ground tracks should be less than the swath.
For some satellites, the orbit should not be sun-synchronous: in particular oceanographic satellites that perform altimetry, such as TOPEX/Poséidon, Jason-1 and -2, or SWOT (planned), need to observe the oceans under varied solar angles so as not to be biased by tides.
This is one of the main reason for non-crepuscular sun-synchronous orbits: imaging requires sunlight at a reasonably high angle (minimal solar elevations considered usable range from 10° to 30° depending on the application).
At latitudes far from the equator, there is a narrower window of mean solar time around noon that is suitable to observation, so the satellite should pass there at local noon to observe these latitudes.
When the observation targets are in the northern hemisphere, this favours either of two choices for the (local) mean solar time of the ascending node—see figure:
- around 22:30, with a descending node around 10:30, going down the northern latitudes between 11:30 and 10:30, with good morning illuminations towards the descending node;
- around 13:30, with a descending node around 01:30, going up the northern latitudes between 13:30 and 12:30, with good afternoon illuminations towards the ascending node.
These have sunlit imaging passes crossing the equator either side of noon, and closer to noon in the north.
The morning option (ascending node around 22:30) is the one most often chosen, to avoid afternoon clouds.
Note that solar elevation not only depends on latitude and mean solar time, but also varies with the seasons; observation is possible at higher latitudes during northern summer (but images will be more affected by glint; see the next section).
Some (but not all) instruments can be used for imaging at night as well as in sunlight.
Thermal infrared on MODIS or the day/night panchromatic band on VIIRS are examples.
Note that night-time imaging is also subject to nontrivial solar elevation constraints; it is not enough for the sun to be below the horizon, twilight has to be over, which means that there is a (negative) maximum solar elevation. See the figure below for the civil (-6°), nautical (-12°) and astronomical (-18°) twilights along the orbit of EROS B on the equinoxes and solstices.
Night-time imagery from EROS B is commercially available. This chart lists the availability of this product by latitude over the year; comparing the solstices with the figure above hints to a maximum solar elevation of about -15°.
Night-time imaging should probably be considered a separate experiment from the KSP point of view: even if done in the same band, the products of nighttime observation generally have distinct uses, and are not substitutes for daytime imaging; daytime imaging has broader uses, and should probably be worth more in contracts and science all other things being equal.
See https://www.ion.org/museum/files/TransitBooklet.pdf.
A usable satellite pass will be above the horizon between 10 and 18 minutes, which determines the number of Doppler counts acquired. Typically 20 to 40 counts will be collected by modern equipment.
The requirement is roughly "At latitudes lower than φ (or perhaps within some geographic region), within any Δt period (max time between fixes), be able to see a satellite for at least δt (pass duration), and during that time its radial velocity should change by Δv". There is a complication induced by the requirement of known altitude for positioning: passes at higher elevations will lead to a higher position error from the same error in altitude, so there is some sort of DOP thingy going on here. TODO(egg): derive a formula for that.
https://en.wikipedia.org/wiki/Dilution_of_precision_(navigation)
https://gssc.esa.int/navipedia/index.php/Positioning_Error HPDOP, VPDOP can be used to estimate the horizontal and vertical position error from the pseudorange error, where G is the matrix from https://gssc.esa.int/navipedia/index.php/Code_Based_Positioning_(SPS) (or equivalently the matrix A from the Wikipedia article). We will ignore pseudorange error correlations, but the errors may differ in magnitude if the satellites are meaningfully different (clock accuracy, ability to correct for the ionosphere with dual-frequency signals, etc.). For that, see equation (8) of https://gssc.esa.int/navipedia/index.php/Parameters_adjustment, with a diagonal R whose entries are the squared pseudorange errors (the error is then the square root of the trace of the relevant submatrix).
TODO(egg): I am not completely sure how to compute reasonable pseudorange errors; we should probably add several contributions together, and reduce some under some conditions; e.g., if the satellite broadcasts in two frequencies, the ionospheric error vanishes; in the presence of WAD SBAS, it should be somewhat reduced. See https://gssc.esa.int/navipedia/index.php/Ionospheric_Delay, https://gssc.esa.int/navipedia/index.php/SBAS_Fundamentals.
TODO(egg): Note in particular the difference in stationkeeping strategies between GPS, whose orbits are heavily perturbed by resonances with the geopotential, and whose planes are not kept (variation in Ω by a couple of degrees within satellites that are nominally part of the same plane, irregular spacing along-plane), and the more tightly-controlled ГЛОНАСС and Galileo (which have longer recurrence cycles). This makes it clear that a contract ought not require closely adhering to specific orbits (lest the real GPS fail such a contract).
Telecommunication missions require providing some bandwidth (possibly under some latency constraint) between points on the surface, generally with high availability (with the exception of very early systems, e.g. Telstar). These points may be predefined ground stations (Telstar 1, Early Bird, Молния) or arbitrary individual customers in the serviced area (TVRO and then DTH TV, Iridium, etc.). Individual customers equipped with a dish—rather than an omnidirectional antenna—may require fixed pointing.
For intermittent links (Telstar 1 and 2, Relay 1 and 2) the requirements are likely on pass length and frequency, i.e., x minutes of uninterrupted signal at the requisite bandwidth in any y-hour period (maybe with time of day requirements so the requirement isn’t fulfilled by offering live television at 4 in the morning).
For continuous links (be that via one or multiple satellites, with ground stations that are tracking or not) the requirement should instead be availability percentage (signal at the requisite bandwidth and latency at least x% of the time).
It may make sense to combine this with time-of-day constraints, e.g., broadcast TV with 99% availability between the hours of 07:00 and 01:00, allowing for a gap during night-time; this would only be exploitable in the long run by sun-synchronous orbits or Earth-Sun L1/L2 relays, both of which seem like strange platforms for television, but at the very least it would allow for at earlier start of service on synchronous/semisynchronous networks by launching current-daytime satellites first.
An open question is the extent to which the player should be able to define ground infrastructure. The location of fixed ground stations and geographic area of individual receivers should be part of the contract, but it may make sense for the bands to be the player’s choice (with an incentive for reusing existing infrastructure, e.g., Экран did direct-to-home TV on UHF so existing terrestrial TV antennas could be reused).
Comments from DRVeyl:
[14:04] DRVeyl: Letting the player have choice over, if not definition of, the communication band sounds good IMO. As a content provider, you just demand data rate. As a service provider, you tend to provide the ground equipment to receive your stuff. There's nothing stopping K band SATCOM service, and the hardware for the RF front end equipment isn't large, certainly not compared to the dish.
[14:04] DRVeyl: You may or may not want to incentivize smaller ground user equipment.
[14:06] DRVeyl: (User more likely to buy a 0.6m dish for service than a 3m dish. Unless they really want the higher max data rate. Or you might incentivize running at lower transmission powers. (Nobody cares about 1W continuous, but get above 200W and you start having power bill effects!)
A player-chosen band makes it possible to do, e.g., direct-to-home TV using non-stationary orbits (in S band, with 1 m fixed dishes pointing to the apogee, 5 satellites in молния orbit or 4 in supertundra will provide constant 24 h coverage), which may be interesting for customers and launch sites at higher latitudes.
Probably requires Principia to do right, could then have a direct effect by improving predictions. A rabbit hole for another day.