**Objectives:**- Upon completion of this chapter you will be able todescribe basic principles of spacecraft navigation, including spacecraft velocityand distance measurement, angular measurement, and orbit determination. Youwill be able to describe spacecraft trajectory correction maneuvers and orbit trimmaneuvers.

Navigating a spacecraft involves measuring its radial distance and velocity,the angular direction to it, and its velocity in the plane-of-sky. From thesedata, a mathematical model may be constructed and maintained, describing thehistory of a spacecraft's location in three-dimensional space over time. Anynecessary corrections to a spacecraft's trajectory or orbit may beidentified.based on the model. The navigation history of a spacecraft isincorporated in the reconstruction of its observations of the planet itencounters; it may be applied to the construction of SAR images. Some of thebasic factors involved in acquiring navigation data are described below.

The art of spacecraft navigation draws upon tracking data, which includesmeasurements of the Doppler shift of the downlink carrier and the pointingangles of DSN antennas. Navigation also uses data categorized as very longbaseline interferometry (VLBI), explained below. These data types differ fromthe telemetry data, generated by science instruments and spacecraft healthsensors, which is transmitted via modulated subcarrier.

In two-way coherent mode, recall from Chapter 10 that a spacecraft determines its downlink frequency based upon a veryhighly stable uplink frequency. This permits the measurement of the inducedDoppler shift to within 1 Hz, since the uplink frequency is known with greatprecision. The rates of movement of the Earth in its revolution about the sun andits rotation are known to a high degree of accuracy, and are removed. Theresulting Doppler shift is directly proportional to the radial component of thespacecraft's velocity, and the velocity is thus computed.

A uniquely coded ranging pulse may be added to the uplink to a spacecraft, andits transmission time is recorded. When the spacecraft receives the rangingpulse, it returns the pulse on its downlink. The time it takes the spacecraftto turn the pulse around within its electronics is known from pre-launchtesting. When the pulse is received at the DSN, its true elapsed time isdetermined, and the spacecraft's distance is then computed. Distance may alsobe determined as well as its angular position, using triangulation. This isdescribed below.

The angles at which the DSN antennas point are recorded with an accuracy ofthousandths of a degree. These data are useful, but even more precise angularmeasurements can be provided by VLBI, and by differenced Doppler. A VLBIobservation of a spacecraft begins when two DSN stations on separatecontinents, separated by a very long baseline, track a single spacecraftsimultaneously. High-rate recordings are made of the downlink's wave fronts byeach station, together with precise timing data. DSN antenna pointing anglesare also recorded. After a few minutes, and while still recording, both DSNantennas slew directly to the position of a quasar, which is an extragalacticobject whose position is known with high accuracy. Then they slew back to thespacecraft, and end recording a few minutes later. Correlation and analysis ofthe recorded data yields a very precise triangulation from which both angularposition and radial distance may be determined. This process requiresknowledge of each station's location with respect to the location of Earth'saxis with very high precision. Currently, these locations are known to within3 cm. Their locations must be determined repeatedly, since the location of theEarth's axis varies several meters over a period of a decade.

Differenced Doppler can provide a measure of a spacecraft's changingthree-dimensional position. To visualize this, consider a spacecraft orbitinga planet. If the orbit is in a vertical plane edge on to you, you wouldobserve the downlink to take a higher frequency as it travels towards you. Asit recedes away from you, and behind the planet, you notice a lower frequency.Now, imagine a second observer halfway across the Earth. Since the orbit planeis not exactly edge-on as that observer sees it, the other observer will recorda slightly different Doppler signature. If you and the other observer were tocompare notes and difference your data sets, you would have enough informationto determine both the spacecraft's changing velocity and position inthree-dimensional space. Two DSSs separated by a large baseline do exactlythis. One DSS provides an uplink to the spacecraft so it can generate a stabledownlink, and then it receives two-way. The other DSS receives a three-waydownlink. The differenced data sets are frequently called "two-way minusthree-way." High-precision knowledge of DSN Station positions, as well as ahighly precise characterization of atmospheric refraction, makes it possiblefor DSN to measure spacecraft velocities accurate to within hundredths of amillimeter per second, and angular position to within 10 nano-radians.

Spacecraft which are equipped with imaging instruments can use them to observethe spacecraft's destination planet against a known background starfield.These images are called OPNAV images. Interpretation of them provides a veryprecise data set useful for refining knowledge of a spacecraft's trajectory.

The process of spacecraft orbit determination solves for a description of aspacecraft's orbit in terms of its Keplerian elements (described in Chapter 5 ) based upon the types of observations andmeasurementsdescribed above. If the spacecraft is enroute to a planet, the orbit is heliocentric;if it is in orbit about a planet, the orbit determination is made in reference to thatplanet. Orbit determination is an iterative process, building upon the results ofprevious solutions. Many different data inputs are selected as appropriate forinput to computer software which uses the laws of Newton and Kepler. Theinputs include the various types of navigation data described above, as well asdata such as the mass of the sun and planets, their ephemeris and barycentricmovement, the effects of the solar wind, a detailed planetary gravity fieldmodel, attitude management thruster firings, atmospheric friction, and otherfactors.

The highly automated process of orbit determination is fairly taken for grantedtoday. During the effort to launch America's first artificial Earth satellite,the JPL craft Explorer 1, a room-sized IBM computer was employed to figure anew satellite's trajectory using Doppler data acquired from Cape Canaveral anda few other tracking sites. The late Caltech physics professor Richard Feynmanwas asked to come to the Lab and assist with difficulties encountered inprocessing the data. He accomplished all of the calculations by hand,revealing the fact that Explorer 2 had failed to achieve orbit, and had comedown in the Atlantic ocean. The IBM mainframe was coaxed to reach the sameresult, hours after Professor Feynman had departed for the weekend.

Once a spacecraft's solar or planetary orbital parameters are known, they maybe compared to those desired by the project. To correct any discrepancy, aTrajectory Correction Maneuver (TCM) may be planned and executed. Thisinvolves computing the direction and magnitude of the vector required tocorrect to the desired trajectory. An opportune time is determined for makingthe change. For example, a smaller magnitude of change would be requiredimmediately following a planetary flyby, than would be required after thespacecraft had flown an undesirable trajectory for many weeks or months. Thespacecraft is commanded to rotate to the attitude in three-dimensional spacecomputed for implementing the change, and its thrusters are fired for adetermined amount of time. TCMs generally involve a velocity change (delta-V)on the order of meters or tens of meters per second. The velocity magnitude isnecessarily small due to the limited amount of propellant typically carried.

Small changes in a spacecraft's orbit around a planet may be desired for thepurpose of adjusting an instrument's field-of-view footprint, improvingsensitivity of a gravity field survey, or preventing too much orbital decay.Orbit Trim Maneuvers (OTMs) are carried out generally in the same manner asTCMs. To make a change increasing the altitude of periapsis, an OTM would bedesigned to increase the spacecraft's velocity when it is at apoapsis. Todecrease the apoapsis altitude, an OTM would be executed at periapsis, reducingthe spacecraft's velocity. Slight changes in the orbital plane's orientationmay also be made with OTMs. Again, the magnitude is necessarily small due tothe limited amount of propellant typically carried.

**Recap**

- Spacecraft navigation draws upon __________________________ data,whichincludes measurements of the Doppler shift of the spacecraft's downlinkcarrier.
- The resulting Doppler shift is directly proportional to the _______________component of the spacecraft's velocity.
- A VLBI observation of a spacecraft begins when two DSN stations onseparate____________________ track the spacecraft simultaneously.
- If the spacecraft is enroute to a planet, the orbit determined is________________________ .
- TCMs generally involve a velocity change (delta-V) on the order of_______________ or tens of _______________ per second.

*Tracking**radial**continents**heliocentric**meters - or tens of - meters*