Chapter 13. Spacecraft Navigation
Spacecraft navigation comprises two aspects: (1) knowledge and prediction of spacecraft position and velocity, which is orbit determination, and (2) firing the rocket motor to alter the spacecraft's velocity, which is flight path control.
Recall from Chapter 4 that a spacecraft on its way to a distant planet is actually in orbit about the sun, and the portion of its solar orbit between launch and destination is called the spacecraft's trajectory. Orbit determination involves finding the spacecraft's orbital elements and accounting for perturbations to its natural orbit. Flight path control involves commanding the spacecraft's propulsion system to alter the vehicle's velocity. Comparing the accurately determined spacecraft's trajectory with knowledge of the destination object's orbit is the basis for determining what velocity changes are needed.
Since the Earth's own orbital parameters and inherent motions are well known, the measurements we make of the spacecraft's motion as seen from Earth can be converted into the sun-centered or heliocentric orbital parameters needed to describe the spacecraft's trajectory. The meaningful measurements we can make from Earth of the spacecraft's motion are:
Some spacecraft can generate a fourth type of nav data,
By repeatedly acquiring these three or four types of data, a mathematical model may be constructed and maintained describing the history of a spacecraft's location in three-dimensional space over time. The navigation history of a spacecraft is incorporated not only in planning its future maneuvers, but also in reconstructing its observations of a planet or body it encounters. This is essential to constructing SAR (synthetic aperture radar) images, tracking the spacecraft's passage through planetary magnetospheres or rings, and interpreting imaging results.
Another use of navigation data is the creation of predicts, which are data sets predicting locations in the sky and radio frequencies for the Deep Space Network, DSN to use in acquiring and tracking the spacecraft.
Navigation Data Acquisition
The basic factors involved in acquiring the types of navigation data mentioned above are described below.
Spacecraft Velocity Measurement
Measurements of the Doppler shift of a coherent downlink carrier provide the radial component of a spacecraft's Earth-relative velocity. Doppler is a form of the tracking data type, TRK, provided by the DSN.
Spacecraft Distance Measurement
A uniquely coded ranging pulse can be added to the uplink to a spacecraft and its transmission time recorded. When the spacecraft receives the ranging pulse, it returns the pulse on its downlink. The time it takes the spacecraft to turn the pulse around within its electronics is known from pre-launch testing. For example, Cassini takes 420 nanoseconds, give or take 9 ns. There are many other calibrated delays in the system, including the several microseconds needed to go from the computers to the antenna within DSN, which is calibrated prior to each use. When the pulse is received at the DSN, its true elapsed time at light-speed is determined, corrections are applied for known atmospheric effects, and the spacecraft's distance is then computed. Ranging is also a type of TRK data provided by the DSN.
Distance may also be determined using angular measurement.
Fairly accurate determination of Right Ascension is a direct byproduct of measuring Doppler shift during a DSN pass of several hours. Declination can also be measured by the set of Doppler-shift data during a DSN pass, but to a lesser accuracy, especially when the Declination value is near zero, i.e., near the celestial equator. Better accuracy in measuring a distant spacecraft's angular position can be obtained by:
These techniques, combined with high-precision knowledge of DSN Station positions, a precise characterization of atmospheric refraction, and extremely stable frequency and timing references (F&T, which is another one of the DSN data types), makes it possible for DSN to measure spacecraft velocities accurate to within hundredths of a millimeter per second, and angular position on the sky to within 10 nano-radians.
The process of spacecraft orbit determination solves for a description of a spacecraft's orbit in terms of a state vector (position and velocity) at an epoch, based upon the types of observations and measurements described above. If the spacecraft is en route to a planet, the orbit is heliocentric; if it is in orbit about a planet, the orbit determination is made with respect to that planet. Orbit determination is an iterative process, building upon the results of previous solutions. Many different data inputs are selected as appropriate for input to computer software, which uses the laws of Newton. The inputs include the various types of navigation data described above, as well as data such as the mass of the sun and planets, their ephemeris and barycentric movement, the effects of the solar wind and other non-gravitational effects, a detailed planetary gravity field model (for planetary orbits), attitude management thruster firings, atmospheric friction, and other factors.
Flight Path Control
Trajectory Correction Maneuvers: Once a spacecraft's solar or planetary orbital parameters are known, they may be compared to those desired by the project. To correct any discrepancy, a Trajectory Correction Maneuver (TCM) may be planned and executed. This adjustment involves computing the direction and magnitude of the vector required to correct to the desired trajectory. An opportune time is determined for making the change. For example, a smaller
Orbit Trim Maneuvers: Small changes in a spacecraft's orbit around a planet may be desired for the purpose of adjusting an instrument's field-of-view footprint, improving sensitivity of a gravity field survey, or preventing too much orbital decay. Orbit Trim Maneuvers (OTMs) are carried out generally in the same manner as TCMs. To make a change increasing the altitude of periapsis, an OTM would be designed to increase the spacecraft's velocity when it is at apoapsis. To decrease the apoapsis altitude, an OTM would be executed at periapsis, reducing the spacecraft's velocity. Slight changes in the orbital plane's orientation may also be made with OTMs. Again, the magnitude is necessarily small due to the limited amount of propellant spacecraft typically carry.
Cassini provides an example of the accuracy achieved in rocket firings. The duration of a firing is executed within about 0.1% of the planned duration, and the pointing direction is executed within about 7 milliradians (0.4 degrees). Over the course of seven years from launch to arrival at Saturn, Cassini executed only seventeen of these planned, small velocity adjustments.
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1 The Solar System
2 Reference Systems
3 Gravity & Mechanics
5 Planetary Orbits
7 Mission Inception
9 S/C Classification
11 Onboard Systems
12 Science Instruments
17 Extended Operations
18 Deep Space Network