Satellites in a formation might need to maneuver to avoid potential collisions that may occur when foreign objects enter the formation, or when a satellite within the formation drifts into the path of another. In either case we seek to determine the probability of a future collision based on current state knowledge and the uncertain dynamic environment, and further to determine a control strategy to reduce the collision probability to an acceptable level while minimizing the ΔV required for the maneuver. The approach taken in this paper is to propagate the uncertainty covariance using linear theory and determine the probability that the relative displacement between two objects is less than some "collision metric." This probability will be a function of the initial conditions, the uncertainty in the initial state and disturbing acceleration, and the time-to-go before closest approach. The intent of the paper is to examine the evolution of this probability and to determine an effective maneuver algorithm that can minimize the probability of collision while reducing the energy expenditure in the maneuver. Numerical values are used for satellites in a tightly spaced, low-Earth-orbit formation. For satellites in a close formation, it is demonstrated that the uncertain disturbance environment can make efficient ΔV maneuvers difficult to determine, as collision probabilities can vary rapidly (on the orbital timescale.) Remarks and some sample calculations on the total ΔV required for an evasion maneuver are presented.

An outgassing jet model is presented in support of spacecraft navigation for future missions to comets. The outgassing jet is modeled as an emission cone while the comet is modeled as a uniform density triaxial ellipsoid. The comet's motion about the sun is included in the model. The model is used to explore the effects on a spacecraft passing through an outgassing jet field. The outgassing jet model is also used for simulation and estimation of the physical outgassing properties of jets at and near the surface of a comet. Methods for estimating the locations and sizes of multiple outgassing jets are presented. Nomenclature a = semimajor axis a p = outgassing jet acceleration vector a t , b t , c t = chord lengths in inscribed triangle B= spacecraft mass-to-area ratio c 1 , c 2 , c 3 = constants E = orbital energy e = eccentricitŷ e jet = unit vector in direction of jet orientation e surf = unit vector in direction of jet center on comet surfacê= principle axes moments of inertia J = jet cone half-angle cost function Kk = complete elliptic integral of the first kind k, n = elliptic function parameters M = mean anomaly P = comet period p = orbital parameter p = pressure vector p 0 = effective jet pressure at comet surface Q j = mass ejection rate per unit area Q = mass ejection rate of plane with equal area to the comet perpendicular to the sun at 1 AU q = radius of periapsis Rt = rotation matrix r = spacecraft position r j = spacecraft position relative to jet's virtual center r og = jet outgassing centerline r p = jet surface cross-section's radius r s = comet heliocentric distance r s0 = constant r vc = jet virtual center r 0 = radius at surface of comet S = relative intensity with respect to Q s = time since ejection T = kinetic energy T m = transformation matrix t = time t 0 = initial epoch U = comet gravitational potential u c = jet center at comet surface unit vector u i = jet boundary crossing at comet surface unit vector V og = jet outgassing velocity v = orbital velocity = thermal inertia err = simulation angle error = jet cone half-angle = nutation angle rel = angle between jet and spacecraft sun = angle between jet and the sun 0 = jet latitude com = comet gravitational parameter = true anomaly ; n = elliptical integral of the third kind ; n = modified elliptical integral of the third kind = elliptical function parameter = elliptical function parameter related to time 0 = elliptical function parameter related to initial epoch = spin angle 0 = longitude of jet = precession angle = longitude of ascending nodes = angular velocity vector ! = argument of periapsis ! com = comet rotation rate ! l = effective rotation rate ! x , ! y , ! z = principle axes angular velocity components Prefix = small change

No abstract

Satellites in a formation might need to maneuver to avoid potential collisions that may occur when foreign objects enter the formation, or when a satellite within the formation drifts into the path of another. In either case we seek to determine the probability of a future collision based on current state knowledge and the uncertain dynamic environment, and further to determine a control strategy to reduce the collision probability to an acceptable level while minimizing the ΔV required for the maneuver. The approach taken in this paper is to propagate the uncertainty covariance using linear theory and determine the probability that the relative displacement between two objects is less than some "collision metric." This probability will be a function of the initial conditions, the uncertainty in the initial state and disturbing acceleration, and the time-to-go before closest approach. The intent of the paper is to examine the evolution of this probability and to determine an effective maneuver algorithm that can minimize the probability of collision while reducing the energy expenditure in the maneuver. Numerical values are used for satellites in a tightly spaced, low-Earth-orbit formation. For satellites in a close formation, it is demonstrated that the uncertain disturbance environment can make efficient ΔV maneuvers difficult to determine, as collision probabilities can vary rapidly (on the orbital timescale.) Remarks and some sample calculations on the total ΔV required for an evasion maneuver are presented.

The United States Naval Observatory (USNO) produces GPS-based estimates of satellite orbits, satellite-and receiver-clock time corrections, and earth-orientation parameters five times per day: once in a daily "rapid" process, the results of which are available with approximately 16-hour latency, and four times in an every-six-hours "ultra-rapid" process, the results of which are available with 3-hour latency. The rapid products supply 24 hours of post-processed estimates; the ultra-rapid products supply 24 hours of post-processed estimates with 24 hours of predictions. As is, the ultra-rapid products are suited for real-time systems where high-accuracy GPS orbits are required. In addition to providing high precision and low latency, these products are available on an extremely reliable basis. USNO is one of the few DoD providers of these GPS-based estimates and performs duties as an Analysis Center (AC) of the International GNSS Service (IGS). Recently, the USNO has begun to test the incorporation of GLONASS observational data into a non-operational "rapids" processing. The resulting solutions from this case study will be compared to a USNO's GPS-based control solution as well as to the combination rapid products produced by the IGS. It is shown that the network stations used in the GLONASS test case have a noticeable improvement in in their position estimate RMS in comparison to the control solution. Performing a 7-parameter Helmert transformation indicates that the Z-direction rotational values appear to have the most improvement from the inclusion of the GLONASS observations.