Updating the ephemeris and physical properties of five long-period transiting exoplanets using TESS and CHEOPS
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This report presents an empirical investigation of earth-to-moon trajectories. The primary objective is to uncover relationships that result in the reduction of mission analysis or trajectory analysis problems to fundamentals. It is considered imperative that the results be accurate to the extent that any relationships that are uncovered are not brought about by simplifying or unrealistic assumptions. Consequently, the model used is as accurate as is presently available for use and the computations are performed under strict error controls. Procedures are reasonable from the engineering viewpoint. Some very helpful principles are uncovered. These may be briefly stated as follows: 1) Trajectories of constant flight time to the moon (in the 66 hour to 90 hour range), and arriving within a few minutes of the same time pass over a common point on the moon regardless of the arrival altitude and inclination, This common point of passage for such a family of trajectories is arbitrarily referred to as a VERTEX point; 2) These VERTEX points lie within a bounded region on the lunar surface as arrival time varies throughout the years, for a given flight time or flight time spread; 3) Increasing flight time results primarily in a longitude shift of the VERTEX point for a given arrival time; 4) Launch azimuth should be treated as a strong parameter regarding its influence on the vertex. Launch azimuth variations up to +/- 20 degrees about 90 degrees can shift the vertex as much as 3 degrees in latitude even when one is free to pick launch time, coast time, and S-IVB burn time appropriately with launch azimuth; and 5) The locus of periselenum, as arrival inclination takes on all possible values, is nearly circular about the vertex point for a given arrival altitude. A publication is now in preparation that applies these principles to much advantage in the solution of various trajectory analysis problems.
Trajectory calculation, reentry conditions, landing site, and injection conditions for return-to-earth from lunar orbit
Earth-moon trajectories and relationship between injection and periselenum conditions
Modification of Mod V programmed oscillator
Variations after one revolution in semimajor axis, period and eccentricity computed for orbit using variable drag coefficient involving satellite and air thermal speeds
The symbolic manipulation capabilities of the FORMAC (Formula Manipulation Compiler) language are employed to expand and analytically evaluate integrals. The program integration is effected by expanding the integral(s) into a series of subintegrals and then substituting a pre-derived and pre-coded solution for that particular subintegral. Derivation of the integral solutions necessary for precoding is included, as is a discussion of the FORMAC system limitations encountered in the programming effort.
In the special perturbation method, Cowell and variation-of-parameters formulations of the motion equations are implemented and numerically integrated. Variations in the orbital elements due to drag are computed using the 1970 Jacchia atmospheric density model, which includes the effects of semiannual variations, diurnal bulge, solar activity, and geomagnetic activity. In the general perturbation method, two-variable asymptotic series and automated manipulation capabilities are used to obtain analytical solutions to the variation-of-parameters equations. Solutions are obtained considering the effect of oblateness only and the combined effects of oblateness and drag. These solutions are then numerically evaluated by means of a FORTRAN program in which an updating scheme is used to maintain accurate epoch values of the elements. The atmospheric density function is approximated by a Fourier series in true anomaly, and the 1970 Jacchia model is used to periodically update the Fourier coefficients. The accuracy of both methods is demonstrated by comparing computed orbital elements to actual elements over time spans of up to 8 days for the special perturbation method and up to 356 days for the general perturbation method.
Observations of the white dwarf G195-19 made for over a year show that the periodic variation in circular polarization continues with constant frequency and amplitude; an accurate value of 1.3309 plus or minus 0.0004 days is obtained for the period. While the variation in blue-green light is sinusoidal, extensive measurements in red light show an asymmetric curve, reaching a minimum about 6 hours earlier than in the blue-green.
The current state of minor planet ephemerides was assessed, and the means for providing and updating these emphemerides for use by both the mission planner and the astronomer were developed. A system of obtaining data for all the numbered minor planets was planned, and computer programs for its initial mechanization were developed. The computer based system furnishes the osculating elements for all of the numbered minor planets at an adopted date of October 10, 1972, and at every 400 day interval over the years of interest. It also furnishes the perturbations in the rectangular coordinates relative to the osculating elements at every 4 day interval. Another computer program was designed and developed to integrate the perturbed motion of a group of 50 minor planets simultaneously. Sampled data resulting from the operation of the computer based systems are presented.
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The present paper deals with the problem of determining various solar eclipse variables as observed from a sounding rocket for various rocket trajectories. By applying the methods described to a set of trajectories, a set of boundary conditions, launch azimuth, quadrant elevation, and launch time may be selected to optimize any aspect of eclipse observation within the constraints imposed by rocket performance.
A recursive filter/smoother orbit determination program was developed to refine the ephemerides produced by a batch orbit determination program (e.g., CELEST, GEODYN). The program PREFER can handle a variety of ground and satellite to satellite tracking types as well as satellite altimetry. It was tested on simulated data which contained significant modeling errors and the results clearly demonstrate the superiority of the program compared to batch estimation.
PREFER is a recursive orbit determination program which is used to refine the ephemerides produced by a batch least squares program (e.g., GTDS). It is intended to be used primarily with GTDS and, thus, is compatible with some of the GTDS input/output files.
A number of applications exist in astronomical research for planetary and lunar ephemerides covering an extended length of time. This paper discusses such a set of ephemerides, DE102/LE51, produced at JPL, covering the time 1411 B.C. to 3001 A.D. The ephemerides are dynamically self-consistent, in that the equations of motion were integrated simultaneously. They also represent the most accurately known positions covering such a time span. They have already been used by a number of different users in a variety of different applications.
Accurate geocentric positions are tabulated at five day intervals for the Sun, Mercury, Venus, Mars, Jupiter, Saturn, Uranus and Neptune during the ten year period 1986 through 1995. The apparent angular diameters, radial velocities, declinations and mean times of meridian transit of the seven planets and the Sun are graphically depicted for each year in the interval. Appendices are included which discuss the theory of planetary orbits and a FORTRAN program for calculating planetary ephemerides.
From the analysis of eclipses observed with the HEAO-1, Einstein, Exosat and Ginga satellites, it is shown that the orbital period of X1822 - 371 is increasing on a time-scale of 2.9 million yr. The period change, one of only three determined amongst the LMXBs, is in the opposite sense to the expected evolutionary trend, but in the same sense as the period change of Cyg X-3. The observation of an eclipse simultaneously in the X-ray and optical bands shows that the optical eclipse is asymmetric and has a minimum 3 min later than that of the X-ray eclipse, reflecting a pronounced asymmetry in the optically emitting disk structure.
A technique is described for measuring the positions of landmarks in multiple SAR images of the surface of Venus taken aboard the Magellan spacecraft. These measurements are then used to improve the spacecraft orbit estimate. The Venus-fixed coordinates of the landmarks are also estimated, as are the low-order coefficients of the gravitational field. Sample results are shown for five-orbit and 13-orbit data arcs using hundreds of landmark measurements. Reasonably good fits to the data are obtained for the short-arc solutions, while the data fits over long arcs are poorer, possibly due to higher-order uncertainties in the gravitational field. A comparison of post-fit orbit uncertainties shows that the SAR data significantly improves the orbit estimate.