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Transformation from proper time on earth to coordinate time in solar system barycentric space-time frame of reference. I. II

It is noted that in order to obtain accurate computed values of earth-based range and Doppler observables of a deep space probe, an expression is required for the difference between coordinate time (t) in the solar system barycentric space-time frame of reference and proper time (tau) recorded on a fixed atomic clock on earth. This is part 1 of a two-part article which obtains an expression for the coordinate time/proper time difference that can be used in deriving computed values of observations of a spacecraft or celestial body located anywhere in the solar system. The expression can also be used in computing Very Long Baseline Interferometry data types. In part 1, expression for the coordinate time/proper time difference is obtained that is a function of position and velocity vectors of the major celestial bodies of the solar system and the atomic clock on earth which reads proper time. This expression is transformed in part 2 to a function of time and the earth-fixed coordinates of the atomic clock.

Moyer, T. D.

Estimation of Timing Performance with Pulsed Laser Links for Small Satellite PNT

Satellite constellations are growing in size and in utility for applications as diverse as providing reliable, low-latency internet service to rural areas orEarth science missions.This expansion of satellite constellations brings attention to the need for responsive and reliable satellite communication.Current research in the PrecisionSpace Systems Laboratory at the University of Florida focuses on using pulsed laser communications as the method of relaying time signals instead of the radio frequency (RF)signals.The upcoming CLICK (CubeSat Laser Infrared CrosslinK) missions (Massachusetts Institute of Technology, University of Florida, NASA Ames Research Center) will demonstrate a spacecraft-to-spacecraft laser communication link and time-transfer.For pre-flight technology assessment of missions such as CLICK, a simulation of a spacecraft constellation in Earth orbit has been created to estimate clock synchronization and precision orbit determination based on measured instrumentation performance.We have developed a novel MATLAB-based numerical simulator to model spacecraft-to-spacecraft laser time-transfer and estimate the offset between the spacecraft clocks over time.This simulation includes timing errors associated with laser pulse generation and detection, as well as non-Gaussian clock drift models.The two on-board clocks modeled are a cesium-based Chip-Scale Atomic Clock (CSAC) and a rubidium-based Miniature Atomic Clock (MAC), both produced by Microchip.An example case of two spacecraft in a circular, low-Earth orbit receiving GPS position, GPS timing, and laser pulse time-of-flight measurements is simulated.The positions and velocities of the two spacecraft at a reference epoch and the constant clock model coefficients are estimated.Polynomial models of different orders were used as clock models. The effect of clock model order on the root-mean-square (RMS) of the clock error is apparent in the case using GPS and lasing measurements, showing that the clock model improves with increasing clock model order. Results compare the estimated clock model of a mission operation that only uses GPS measurements and a mission operation that uses both GPS and laser pulse time-of-flight measurements between spacecraft referenced to their on-board CSACs or on-board MACs. Including lasing measurements reduces the RMS clock model error by approximately 80% of the RMS of the cases with only GPS measurements.This simulation tool can be used to optimize the lasing operations schedule based on mission timing performance objectives. During this presentation, I will discuss the details of the simulation and clock model estimation, as well as discuss the results.I will compare the results of incorporating lasing timing measurements to using only GPS measurements and the outcomes of using different orders of polynomials.

Timing Performance

Rugged, Tunable Extended-Cavity Diode Laser

A rugged, tunable extended-cavity diode laser (ECDL) has been developed to satisfy stringent requirements for frequency stability, notably including low sensitivity to vibration. This laser is designed specifically for use in an atomic-clock experiment to be performed aboard the International Space Station (ISS). Lasers of similar design would be suitable for use in terrestrial laboratories engaged in atomic-clock and atomic-physics research.

Moore, Donald

Frequency shifts in a rubidium frequency standard due to coupling to another standard

Highly reliable timing system, such as used on board satellites, may incorporate a hot standby atomic clock besides the active one. RF couplings between them may affect the performance of the active clock. The effect of such couplings between two rubidium atomic clocks was investigated, and it was found that they will add an oscillatory term to the Allan Variance of the active clock, degrading its frequency stability, and that under certain circumstances they may also shift the active clock's operating frequency. These two effects are discussed in detail, and the level of isolation required to render them negligible is established.

Jaduszliwer, Bernardo

Laser retroreflector experiment on NAVSTAR 35 and 36

In GPS one of the primary errors contributing to positioning inaccuracy is the performance of the on-board atomic clock. To determine and predict the performance of this atomic clock has been a problem due to the ambiguity of the orbital position error and clock uncertainty in the Radio Frequency (RF) tracking of the navigation signals. The Laser Retroreflector Experiment (LRE) on-board NAVSTAR 35 and 36 provides a means of separating these ambiguous errors by enabling highly precise and accurate satellite positions to be determined independently of the RF signals. The results of examining onboard clock behavior after removing the orbital position signatures will be discussed. GPS RF tracking data from various DOD and other sites are used to reconstruct the onboard clock data and examine the clock behavior. From these data, the effects of clock performance on GPS positioning performance can examined.

Pavlis, E. C.

Future Laser-Cooled Microwave Clock Performance

Limitations to the performance of laser-cooled earth and space-based Cs clocks will be critically discussed. The most significant limitation to the stability and accuracy of laser-cooled atomic clocks is the frequency shift due to cold collisions. Because of it, laser-cooled Cs clocks must be operated at low density and this implies that space based Cs clock performance will not be significantly better than earth based. To regain some of the high accuracy and stability lost to the low density, clocks can be designed to multiply launch (or juggle) atoms. Clocks based on other atoms, in particular Rb-87 or possibly Rb-85, may have much smaller cold collision frequency shifts and therefore be capable of higher stability and accuracy, especially in a space environment.

Gibble, Kurt

Technology Demonstration Missions

Technology Demonstration Missions (TDM) is in its third year of execution, being initiated in 2010 and baselined in January of 2012. There are 11 projects that NASA Marshall Space Flight Center (MSFC) has contributed to or led: (1) Evolvable Cryogenics (eCryo): Cyrogenic Propellant Storage and Transfer Engineering Development Unit (EDU), a proof of manufacturability effort, used to enhance knowledge and technology related to handling cryogenic propellants, specifically liquid hydrogen. (2) Composites for Exploration Upper Stage (CEUS): Design, build, test, and address flight certification of a large composite shell suitable for the second stage of the Space Launch System (SLS). (3) Deep Space Atomic Clock (DSAC): Spaceflight to demo small, low-mass atomic clock that can provide unprecedented stability for deep space navigation. (4) Green Propellant Infusion Mission (GPIM): Demo of high-performance, green propellant propulsion system suitable for Evolved Expendable Launch Vehicle (EELV) Secondary Payload Adapter (ESPA)-class spacecraft. (5) Human Exploration Telerobotics (HET): Demonstrating how telerobotics, remote control of a variety of robotic systems, can take routine, highly repetitive, dangerous or long-duration tasks out of human hands. (6) Laser Communication Relay Demo (LCRD): Demo to advance optical communications technology toward infusion into deep space and near Earth operational systems, while growing the capabilities of industry sources. (7) Low Density Supersonic Decelerator (LDSD): Demo new supersonic inflatable decelerator and parachute technologies to enable Mars landings of larger payloads with greater precision at a wider range of altitudes. (8) Mars Science Laboratory (MSL) Entry Descent & Landing Instrumentation (MEDLI): Demo of embedded sensors embedded in the MSL heat shield, designed to record the heat and atmospheric pressure experienced during the spacecraft's high-speed, hot entry in the Martian atmosphere. (9) Solar Electric Propulsion (SEP): 50-kW class spacecraft that uses flexible blanket solar arrays for power generation and an electric propulsion system that delivers payload from low-Earth orbit to higher orbits. (10) Solar Sail Demonstration (SSD): Demo to validate sail deployment techniques for solar sails that are propelled by the pressure of sunlight. (11) Terrestrial HIAD Orbit Reentry (THOR): Demo of a 3.7-m Hypersonic Inflatable Aerodynamic Decelerator (HIAD) entry vehicle to test second generation aerothermal performance and modeling.

McDougal, John

A Transportable Gravity Gradiometer Based on Atom Interferometry

A transportable atom interferometer-based gravity gradiometer has been developed at JPL to carry out measurements of Earth's gravity field at ever finer spatial resolutions, and to facilitate high-resolution monitoring of temporal variations in the gravity field from ground- and flight-based platforms. Existing satellite-based gravity missions such as CHAMP and GRACE measure the gravity field via precise monitoring of the motion of the satellites; i.e. the satellites themselves function as test masses. JPL's quantum gravity gradiometer employs a quantum phase measurement technique, similar to that employed in atomic clocks, made possible by recent advances in laser cooling and manipulation of atoms. This measurement technique is based on atomwave interferometry, and individual laser-cooled atoms are used as drag-free test masses. The quantum gravity gradiometer employs two identical atom interferometers as precision accelerometers to measure the difference in gravitational acceleration between two points (Figure 1). By using the same lasers for the manipulation of atoms in both interferometers, the accelerometers have a common reference frame and non-inertial accelerations are effectively rejected as common mode noise in the differential measurement of the gravity gradient. As a result, the dual atom interferometer-based gravity gradiometer allows gravity measurements on a moving platform, while achieving the same long-term stability of the best atomic clocks. In the laboratory-based prototype (Figure 2), the cesium atoms used in each atom interferometer are initially collected and cooled in two separate magneto-optic traps (MOTs). Each MOT, consisting of three orthogonal pairs of counter-propagating laser beams centered on a quadrupole magnetic field, collects up to 10(exp 9) atoms. These atoms are then launched vertically as in an atom fountain by switching off the magnetic field and introducing a slight frequency shift between pairs of lasers to create a moving rest frame for the trapped atoms. While still in this moving-frame molasses, the laser frequencies are further detuned from the atomic resonance (while maintaining this relative frequency shift) to cool the atom cloud's temperature to 2 K or below, corresponding to an rms velocity of less than 2 cm/s. After launch, the cold atoms undergo further state and velocity selection to prepare for atom interferometry. The atom interferometers are then realized using laser-induced stimulated Raman transitions to perform the necessary manipulations of each atom, and the resulting interferometer phase is measured using laser-induced fluorescence for state-normalized detection. More than 20 laser beams with independent controls of frequency, phase, and intensity are required for this measurement sequence. This instrument can facilitate the study of Earth's gravitational field from surface and air vehicles, as well as from space by allowing gravity mapping from a low-cost, single spacecraft mission. In addition, the operation of atom interferometer-based instruments in space offers greater sensitivity than is possible in terrestrial instruments due to the much longer interrogation times available in the microgravity environment. A space-based quantum gravity gradiometer has the potential to achieve sensitivities similar to the GRACE mission at long spatial wavelengths, and will also have resolution similar to GOCE for measurement at shorter length scales.

Yu, Nan

Noise in state of the art clocks and their impact for fundamental physics

In this paper a review of the use of advanced atomic clocks in testing the fundamental physical laws will be presented. Noise sources of clocks will be discussed, together with an outline their characterization based on current models. The paper will conclude with a discussion of recent attempts to reduce the fundamental, as well as technical noise in atomic clocks.

noise state-of-the-art clocks fundamental physics

Precision Clocks in Space and alpha-Variations

Important developments of both in theoretical and observational cosmology have fueled considerable interest in searches for variations of the fine structure constant. Experimentally, Webb et. al. have found evidence for a cosmological variation of the fine structure constant through an analysis of the absorption lines in galactic halos from quasar-emitted light. Recently developed small ion atomic clocks enable Solar System tests for equivalence principle (EP) violating (alpha)-variations by way of rate-comparisons of three ultra-stable atomic clocks near-to and far-from the sun where gravitational red-shift changes are more than 10(exp 4) larger than in low Earth orbit. No space tests of the EP have been made in nearly 30 years, since the GP-A hydrogen maser reached a 10,000 km apogee confirming EP red-shift predictions ~1 part in 10(exp 4). Today's small ion clocks, nearly 100x more stable and 100x smaller then the GP-A H-maser, could probe for EP violating scalar fields near the sun for mission costs comparable to low Earth orbiters and improve the GP-A sensitivity by 5 to 6 orders of magnitude.

(alpha)-variation

Optical Time Transfer for Bistatic SAR Spacecraft

A spacecraft-to-spacecraft optical time-transfer simulation has been developed as a tool for informing NASA’s Surface Deformation and Change (SDC) mission architecture. The SDC mission will combine radar images from multiple spacecraft to improve understanding of the Earth’s sea-level and landscape changes. Spacecraft must be precisely synchronized in order to create sharp radar images. Simulation of multiple spacecraft time-synchronizing via laser communication can inform technology choices of a mission by providing a picosecond-precision level estimate of clock error. This timing and ranging simulation has been combined with a radar system performance analysis pipeline. The simulated timing errors are used to predict performance of bistatic SAR systems in the presence of oscillator noise and time synchronization in accuracy. This analysis includes both analytic approximation equations from existing literature, and a numerical radar simulation to extract key system performance parameters like phase error and signal-to-noise ratio (SNR)degradation. Precision time-transfer techniques facilitate the accurate synchronization of clocks between any combination of terminals. Most time-transfer technology for comparing two clocks at different terminals use radio frequencies (RF) to measure the time delay between the sending and receiving of signals. Laser technology offers the capability to transmit high data rates with systems that are of smaller size and lower power than comparable RF systems. The clocks on independent spacecraft will have some phase and frequency errors between them that result in clock drift. The two clock models that are included in this bi-directional MATLAB simulation are a cesium-based Chip-Scale Atomic Clock (CSAC) and a rubidium-based Miniature Atomic Clock (MAC). The CSAC has flown as hardware for small satellite missions such as the University of Florida’s CHOMPTT mission. A study of example orbits, including that of NASA NASA-ISRO Synthetic Aperture Radar Mission (NISAR) mission, and lasing rates demonstrate the impact of flight configuration parameters on the synchronization error between two spacecraft. The MATLAB timing simulation uses a Runge-Kutta 4th-order method to propagate spacecraft orbits and computes the light-travel time estimate between them. The simulation outputs the estimated range and estimated clock error based on a user-defined spacecraft cluster configuration. The radar simulation and analytic approximations are applied to evaluate a potential future NASA bistatic SAR constellation architecture. In the proposed architecture, satellites follow each other in the same orbit at 800 km altitude, with a 210 km baseline. We also baseline the CSAC as an ultra stable oscillator, and use NASA’s NISAR for baseline radar system parameters to compute a clock-system introduced phase error of 5.6 degrees without synchronization by frequent time transfer. We build on this base case with a sensitivity analysis of radar performance over a proposed range of constellation and radar system parameters. With this analysis pipeline, we comment on which radar parameters should or should not be changed to minimize synchronization requirements. This analysis technique could be extended or modified to evaluate the timing requirements of other geometries for other future multistatic SAR missions, or other interferometric satellite missions.

Surface Deformation and Change

Probing Curved Spacetime with a Distributed Atomic Processor Clock

Quantum dynamics on curved spacetime has never been directly probed beyond the Newtonian limit. Although we can describe such dynamics theoretically, experiments would provide empirical evidence that quantum theory holds even in this extreme limit. The practical challenge is the minute spacetime curvature difference over the length scale of the typical extent of quantum effects. Here, we propose a quantum network of alkaline earth (like) atomic processors for constructing a distributed quantum state that is sensitive to the differential proper time between its constituent atomic processor nodes, implementing a quantum observable that is affected by post-Newtonian curved spacetime. Conceptually, we propose to delocalize one clock between three locations by encoding the presence or absence of a clock into the state of the local atoms. By separating three atomic nodes over approximately kilometer-scale elevation differences and distributing one clock between them via a 𝑊 state, we demonstrate that the curvature of spacetime is manifest in the interference of the three different proper times that give rise to three distinct beat notes in our nonlocal observable. We further demonstrate that 𝑁-atom entanglement within each node enhances the interrogation bandwidth by a factor of 𝑁. We discuss how our proposed system can probe new facets of fundamental physics, such as the linearity, unitarity, and probabilistic nature of quantum theory on curved spacetime. Our protocol combines several recent advances with neutral atom and trapped ions to realize a novel quantum probe of gravity uniquely enabled by quantum networks.

Covey, Jacob P. [Univ. of Illinois at Urbana-Champ

Geodetic positioning using a global positioning system of satellites

Geodetic positioning using range, integrated Doppler, and interferometric observations from a constellation of twenty-four Global Positioning System satellites is analyzed. A summary of the proposals for geodetic positioning and baseline determination is given which includes a description of measurement techniques and comments on rank deficiency and error sources. An analysis of variance comparison of range, Doppler, and interferometric time delay to determine their relative geometric strength for baseline determination is included. An analytic examination to the effect of a priori constraints on positioning using simultaneous observations from two stations is presented. Dynamic point positioning and baseline determination using range and Doppler is examined in detail. Models for the error sources influencing dynamic positioning are developed. Included is a discussion of atomic clock stability, and range and Doppler observation error statistics based on random correlated atomic clock error are derived.

Fell, P. J.

Clock Technology Development for the Laser Cooling and Atomic Physics (LCAP) Program

The Time and Frequency Sciences and Technology Group at Jet Propulsion Laboratory (JPL) has developed a laser cooling capability for flight and has been selected by NASA to support the Laser-Cooling and Atomic Physics (LCAP) program. Current work in the group includes design and development for tee two laser-cooled atomic clock experiments which have been selected for flight on the International Space Station.

Klipstein, W. M.

Microwave Cavity Clocks On Space Station

We describe the status of a microwave cavity clock experiment to perform improved tests of Local Position Invariance and Lorentz Invariance on the International Space Station in conjunction with atomic clocks. Significant improvements over present bounds are expected in both cases. The oscillators can also be used to enhance the performance of atomic clocks at short time scales for other experiments.

Lipa, J. a.

Evolution of the International Atomic Time TAI computation

The computation of the International Atomic Time (TAI), a worldwide time reference, is briefly examined. The types of atomic clocks, computation procedures, and time intercomparison between clocks utilizing navigation satellites are addressed. Changes in the system would essentially depend on the improvement of the atomic clocks.

Granveaud, M.

Integrity Monitoring of Mercury Discharge Lamps

Mercury discharge lamps are critical in many trapped ion frequency standard applications. An integrity monitoring system can be implemented using end-of-life signatures observed in operational mercury discharge lamps, making it possible to forecast imminent failure and to take action to mitigate the consequences (such as switching to a redundant system). Mercury lamps are used as a source of 194-nm ultraviolet radiation for optical pumping and state selection of mercury trapped ion frequency standards. Lamps are typically fabricated using 202Hg distilled into high-purity quartz, or other 194-nm transmitting material (e.g., sapphire). A buffer gas is also placed into the bulb, typically a noble gas such as argon, neon, or krypton. The bulbs are driven by strong RF fields oscillating at .200 MHz. The lamp output may age over time by two internal mechanisms: (1) the darkening of the bulb that attenuates light transmission and (2) the loss of mercury due to migration or chemical interactions with the bulb surface. During fabrication, excess mercury is placed into a bulb, so that the loss rate is compensated with new mercury emanating from a cool tip or adjacent reservoir. The light output is nearly constant or varies slightly at a constant rate for many months/years until the mercury source is depleted. At this point, the vapor pressure abruptly falls and the total light output and atomic clock SNR (signal-to-noise ratio) decrease. After several days to weeks, the light levels decrease to a point where the atomic clock SNR is no longer sufficient to stay in lock, or the lamp self-extinguishes. This signature has been observed in four separate end-of-life lamp failures while operating in the Deep Space Network (DSN). A simple integrator circuit can observe and document steady-state lamp behavior. When the light levels drop over a predetermined time interval by a specified amount (e.g., 20 percent), an alarm is set. For critical operational applications, such as the DSN or in space flight, this warning provides notice that a failure may be imminent, and for operators or control algorithm to take action.

Tjoelker, Robert L.