Notes on Space Navigation

'''Such a spacecraft navigates using precisely timed radio signals sent back and forth to Earth. Navigators on Earth track its location and speed and transmit course adjustments. These techniques allow navigators to guide a probe to a planetary rendezvous or a pinpoint landing. Navigating a spacecraft to distant locations in the solar system requires a team of scientists and engineers using sophisticated radios, large antennas, computers, and precise timing equipment.'''

'''Before and during a mission, the team carefully plots the spacecraft’s course and maps the locations of planets and moons whose gravitational forces will affect its trajectory. Using the large dish antennas of the Deep Space Network, they locate the spacecraft by sending precisely timed signals to it and measuring the time it takes for the signals to be received and retransmitted back to Earth. If the spacecraft is not on course, they send signals instructing it to adjust its trajectory. Using these techniques, the team can bring a spacecraft to a precise landing on Mars or into an orbit around a moon of Saturn after a journey of millions of kilometers.'''

Gravity Assist
To reach destinations beyond the Moon, space navigators learned to take advantage of gravity.

'''A spacecraft can use the gravity of one celestial body to propel it toward another. While the trajectory is longer than a more direct route, a “gravity assist” saves fuel. But it requires complex calculations, precise navigation, and atomic clocks for timing. Many planetary missions would be impractical without gravity assist because of the extra fuel and larger rockets they would otherwise need.'''

Helping Hand from Gravity

Launched in 1973, Mariner 10 used the gravity of Venus to propel it to Mercury with minimal use of fuel.

'''To reach Mercury, Mariner 10 first passed by Venus, threading through a narrow 400-kilometer (250-mile) “window” of space a few thousand kilometers above the surface. That level of accuracy had not been possible with the navigation systems available for the Pioneer 4 mission in 1959. After a gravitational assist from Venus, Mariner 10 entered an orbit around the Sun that allowed it to pass by Mercury three times in 1974 and 1975.'''

HEMISPHERICAL RESONATOR GYROSCOPE
Most inertial navigation devises use a gyro that measures motion by the change in vibration of a cup-shaped device.

Resonator Gyroscope

'''Spacecraft traversing the solar system carry inertial navigation devices to supplement Earth-based radio navigation. Most use a simple but accurate gyro that measures motion by the change in vibration of a cup-shaped device—similar to how a wine glass “hums” when you rub a wet finger around its rim.'''

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:'''

Its distance or range from Earth,

The component of its velocity that is directly toward or away from Earth, and

To the extent discussed below, its position in Earth's sky.

Some spacecraft can generate a fourth type of nav data,

Optical navigation
, wherein the spacecraft uses its imaging instrument to view a target planet or body against the background stars.

'''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.

No single measurement directly yields the lateral motion of a spacecraft deep in the solar system (if lateral motion is any component of motion except directly toward or away from Earth.)

'''But we do have a very good understanding of how things move in space -- orbit models of spacecraft are built based on equations of motion from the likes of Kepler and Newton. There aren't many ways of moving (in other words, trajectories) that match up with a big batch of range and range-rate data acquired from various DSN station locations over a period or days, weeks or months.'''

'''The task is to apply measurements of Doppler and range to a model of a trajectory, and update that model to match all your measurements reasonably well, to obtain a solution to the orbit determination problem. Gaining knowledge of lateral motion is an iterative process.'''

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.

Spacecraft Angular Measurement
'''The spacecraft's position in the sky is expressed in the angular quantities Right Ascension and Declination. While the angles at which the DSN antennas point are monitored with an accuracy of thousandths of a degree, they are not accurate enough to be used in determining a distant interplanetary spacecraft's position in the sky for navigation. DSN tracking antenna angles are useful only for pointing the antenna to the predicts given for acquiring the spacecraft's signal.'''

'''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:'''

VLBI
'''Extremely accurate angular measurements can be provided by a process independent from Doppler and range, VLBI, Very Long Baseline Interferometry. A VLBI observation of a spacecraft begins when two DSN stations on different continents (separated by a VLB) track a single spacecraft simultaneously. High-rate recordings are made of the downlink's wave fronts by each station, together with precise timing data. After a few minutes, both DSN antennas slew directly to the position of a quasar, which is an  VLBI extragalactic object whose position on the plane of the sky is known to a high precision. Recordings are made of the quasar's radio-noise wavefronts.'''

'''Correlation and analysis of the recorded wavefronts yields a very precise triangulation from which the angular position may be determined by direct comparison to the position of a quasar whose RA and DEC are well known. VLBI is considered a distinct DSN data type, different from TRK and TLM. This VLBI observation of a spacecraft is called a "delta DOR," DOR meaning differenced one-way ranging, and the "delta" meaning the difference between spacecraft and quasar positions.'''

Precision Ranging
'''precision RNG Precision ranging refers to a set of procedures to ensure that range measurements are accurate to about 1 meter. Knowledge of the spacecraft's Declination can be improved with Range measurements from two stations that have a large north-south displacement, for example between Spain and Australia, via triangulation.'''

Differenced Doppler
'''Differenced Doppler can provide a measure of a spacecraft's changing three-dimensional position. To visualize this, consider a spacecraft orbiting a distant planet. If the orbit is in a vertical plane exactly edge on to you at position A, you would observe the downlink to take a higher frequency as it travels towards you. As it recedes away from you to go behind the planet, you observe a lower frequency.'''

'''Differenced Doppler Now, imagine a second observer way across the Earth, at position B. Since the orbit plane is not exactly edge-on as that observer sees it, that person will record a slightly different Doppler signature. If you and the other observer were to compare notes and difference your data sets, you would have enough information to determine both the spacecraft's changing velocity and position in three-dimensional space.'''

'''Two DSSs separated by a large baseline can do basically this. One DSS provides an uplink to the spacecraft so it can generate a coherent downlink, and then it receives two-way. The other DSS receives a three-way coherent downlink. The differenced data sets are frequently called "two-way minus three-way."'''

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.

Optical Navigation
'''Spacecraft that are equipped with imaging instruments can use them to observe the spacecraft's destination planet or other body, such as a satellite, against a known background starfield. These images are called opnav images. The observations are carefully planned and uplinked far in advance as part of the command sequence development process. The primary body often appears overexposed in an opnav, so that the background stars will be clearly visible. When the opnav images are downlinked in telemetry (TLM) they are immediately processed by the navigation team. Interpretation of opnavs provides a very precise data set useful for refining knowledge of a spacecraft's trajectory as it approaches a target. Note that this form of navigation data resides in the TLM data type.'''

Orbit Determination
'''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.'''

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

More on this story in Genius: The Life and Science

of Richard Feynman by James Gleick.

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 '''

'''An interplanetary spacecraft's course is mostly set once the launch vehicle has fallen away. From that point on, the spacecraft can make only very small corrections in its trajectory by firing small engines or thrusters. Often the largest complement of propellant that a spacecraft carries is reserved for orbit insertion at its destination.'''

'''magnitude of change would be required immediately following a planetary flyby, than would be required after the spacecraft had flown an undesirable trajectory for many weeks or months. The spacecraft is commanded to rotate to the attitude in three-dimensional space computed for implementing the change, and its thrusters are fired for a determined amount of time. TCMs generally involve a velocity change (delta-V) on the order of meters, or sometimes tens of meters, per second. The velocity magnitude is necessarily small due to the limited amount of propellant typically carried.'''

'''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.'''

Chapter 13. Spacecraft Navigation
'''Do you want to travel to another planet? Or perhaps even another star system?'''

'''Then you can use this calculator to work out how long it will take you, how much energy your spacecraft needs and what your maximum velocity will be. If you travel close to the speed of light, you can also see how much time it will take from your point of view and from the point of view of the people on earth. You can also see how the length of your spacecraft will shorten for observers watching it from earth, if only they had powerful enough telescopes.'''

This is the simplest way to use the space travel calculator:

'''Enter a distance to a planet or star. Don't know any? Then type Pr and press the down arrow. The distance to Proxima Centauri appears. Select it and the distance will be filled in. Try other places in space.'''

'''Click Calculate. The calculator determines the remaining unfilled values.'''

'''Click Run. Watch the space rocket travel from earth to your destination. Also watch the clocks of the observer and the traveler.'''

Distance ?+

Acceleration ?+

Maximum velocity ?+

Observer time elapsed during journey ?+

Traveler time elapsed during journey ?+

Spacecraft mass at launch ?+

Energy ?+

Fuel conversion rate ?+

Fuel mass ?+

Length of spacecraft at start of journey ?+

Shortest length of spacecraft for observer ?+

Calculate Clear

'''The closest star to the sun is Proxima Centauri, but its brighter neighbor Alpha Centauri, a double star, is so nearly the same distance that data about it are usually given. It is about 4 light years distance, or about 3.8x1016 m.'''

380,000,000,000,000,000

Oh what a great question and here is my answer

Let’s calculate a trip to Proxima Centauri

'''For that we need some data. '''

First: Distance  Earth / Proxima

39734219300000000  meters