Orbital Mechanics
Simple Explanation
The MPS system consists of 18 active satellites divided into 3 constellations of 6 satellites. They orbit at an inclination of 56° and have an orbital period of 21/20ths of a Mars sidereal day. The image to the right shows the orbital configuration with cones to show signal coverage. Animations at the bottom of this page illustrate satellite coverage in more detail.
Decision process
While developing our satellite constellation, many factors were considered. The need for global coverage, the specifications of our antenna's gain pattern, system maintenance/calibration and the extensive cost of putting satellites around mars all have been considered. The extreme cost of putting satellites around mars dictates that an arrangement that minimizes the number of satellites is necessary. To create the most coverage per satellite, the specifications of our antenna were modified to help minimize the elevation angle at which the antenna had sufficient gain to see the satellites, thereby greatly helping to reduce the number of required satellites. Also, the orbits of the satellites were increased to expand the area covered by each individual satellite further helping reduce the necessary number of satellites.
The final consideration for the orbit is how the orbital period affects the resolving power of the positioning system. GPS systems rely on satellites with precisely defined orbits so that the receivers might make accurate assumption as to the satellite's location, which forms the basis of determining the receiver's location. Because of this requirement, the orbital period of a satellite must be a well defined multiple of a sidereal day to make it easy to calculate satellite positions. In earth based GPS, the orbital period is designed to be ½ a sidereal day. For our MPS system, we chose to define an orbital period of 21/20 of a sidereal day. The significantly longer orbital period was chosen so that the satellites would be in a high orbit, allowing each to cover a significantly larger area. While an orbital period of 1 sidereal day would be an obvious alternative, it has several limitations. In such an arrangement, each satellite would be confined to a narrow band of longitudes for the entirety of their orbit. This is undesirable, as it greatly complicates system calibration and any failure of satellites beyond the number of spares would leave a few large coverage gaps that would move slowly across latitude but stay within the same wide range of longitudes. Combined with the long time it would take to get a replacement satellite from earth, this means that users within a static range of longitudes would have intermittent service for well over a year and a half.
Resulting numbers
The system of satellites will orbit mars at an altitude of 17708 km above the surface with an eccentricity of 0.0 and a period of 21/20 sidereal days, or 25 hours, 51 minutes, 14.8 seconds. The satellites will be arranged into 3 constellations spaced equally around mars with 6 active satellites in each constellation. Each constellation will be inclined 56° above the equatorial plane of Mars. Each constellation should have at least one spare satellite as a backup in case an active satellite fails.
Description of orbit properties and effects on system performance
The odd orbital period of 21/20 sidereal days has the benefit of wide coverage area from a high orbit, but does not have the downside described above of a 1 sidereal day orbit. Instead each satellite slowly advances in longitude, circling the planet in 21 days. There are two main benefits of this: First, by arranging for each satellite to circle the planet every 21 days, any outages in coverage would not be permanently confined to a given area, but slowly move across the planet every 21 days. In this fashion, the users in a given region won't have to suffer from an outage for the entire time it takes for a satellite to be replaced, but instead the burden of the outage would be distributed over all users, with the outage for each user being much shorter than it otherwise would. A cheap altimeter built into each receiver could be used to provide an estimate of the receiver’s altitude provide the missing reference point in a “reduced accuracy” mode during this outage period.
The second and more important benefit of the orbital period being 21/20 sidereal days is that it greatly simplifies the calibration process. A planet-side station, with a well defined longitude and latitude will eventually see all 18 MPS satellites over the course of 21 days. This allows a single station to measure any error in the satellites' locations in orbit for the entire MPS system. Such a calibration mechanism would not be possible if the satellites had an orbital period of 1 sidereal day due to the longitudinal confinement mention previously. Over the course of 21 days, a single ground station will measure the location error of all 18 active satellites and upload data to the MPS almanac to be distributed among all satellites and receivers for station-keeping corrections and so receivers can calculate their own ephemeris error.
Of course, increasing the altitude of our orbit and decreasing the minimum elevation visable to the antenna degrades decreases the power received by the antenna. Increasing the orbit from a period of ½ sidereal day to 21/20 sidereal days causes received power to drop by 5dB. This is balanced by the high quality of our coding system, which creates 9dB in processing gain.
Orbital Animations
The coverage map shows the number of satellites visible on the surface of Mars over a span of 26 hours (one orbital period). Green lines indicate ground tracks for satellites. The left circle is the western hemisphere, and the right circle is the eastern hemisphere of Mars. Mouseover the image to activate the video playback controls. Animations require Adobe Flash 9.
One problem with Earth GPS is poor coverage at the poles. The animation below shows satellite coverage at the North Pole of Mars to be satisfactory.
The next video, below, shows an animation of the orbital track for each satellite.
Earth-to-mars journey
Finding launch windows for sending satellites to mars via gravity assisted trajectory via Venus or Earth is difficult and the inherent irregularity in when they occur is undesirable. We decided that it would be more effective to travel to Mars with Hohmann transfer orbits as they provide a much more predictable launch window and are simpler to use. With Hohmann transfers to Mars, launch windows present themselves every 26 months and take approximately 8.5 months to complete. [http://www-istp.gsfc.nasa.gov/stargaze/Smars1.htm]
Budget
Satellite cost = $101.61 per satellite, or $2,134 million for a set of 21 in 2008 dollars (based on numbers from The Global Positioning System: Assessing National Policies table B.1 and adjusted for inflation