Related papers: A geometric method to locate Neptune
We describe a geometrical method for tracing a planet's orbit using its velocity hodograph, that is, the path of the planet's velocity. The method requires only a straight edge, a compass, and the help of the hodograph. We also obtain…
In this article, we describe a very simple technique to locate naked-eye planets in the sky, to an accuracy of $\sim 1^{\circ}$. The procedure, comprising just three steps, involves very simple manual calculations for planetary orbits…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
Accurate gravity field calculations are necessary for landing on planets, moons, asteroids, minimoons, or other irregularly shaped bodies, but current methods become increasingly inaccurate and slow near the surface. We present high…
Searching for extrasolar planets by direct detection is extremely challenging for current instrumentation. Indirect methods, that measure the effect of a planet on its host star, are much more promising and have indeed led to the discovery…
The study of the differences detected between the observed and the predicted positions of Uranus taking only the ancient planets into account led to the discovery of planet Neptune in 1846. This event remains one of the best accomplishments…
Deming's method is applied for calculating matrix elements allowing to fit orbital parameters for planets. This work provides demonstrations which were missing in our previous paper of 2002.
Orbital parameters of planets are fitted directly to an appropriate set of observations. It is shown how to use the rigorous Deming method combined with a numerical integration of gravitation equations. In all, 65 parameters of the nine…
We present a procedure for determination of positions and orbital elements, and associated uncertainties, of outer Solar System planets. The orbit-fitting procedure is greatly streamlined compared to traditional methods because acceleration…
The new approach of the regular spacing of planetary orbits and planet mass distribution in the Solar system is considered. The relative planetary distances will be represented as the inverse composite probabilities of two discrete…
Past planetary missions have been broad and detailed for Gas Giants, compared to flyby missions for Ice Giants. Presently, a mission to Neptune using electrodynamic tethers is under consideration due to the ability of tethers to provide…
By observing the transits of exoplanets, one may determine many fundamental system parameters. I review current techniques and results for the parameters that can be measured with the greatest precision, specifically, the transit times, the…
A discrete and exact algorithm for obtaining planetary systems is derived in a recent article (Eur. Phys. J. Plus 2022, 137:99). Here the algorithm is used to obtain planetary systems with forces different from the Newtonian inverse square…
The holy grail of exoplanet searches is an exo-Earth, an Earth mass planet in the habitable zone around a nearby star. Mass is the most important parameter of a planet and can only be measured by observing the motion of the star around the…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…
This tutorial covers the use of absolute astrometry, in particular from the combination of the Hipparcos and Gaia missions, to identify faint companions to nearby stars and to measure the masses and orbits of those companions. Absolute…
Batygin and Brown (2016) have suggested the existence of a new Solar System planet supposed to be responsible for the perturbation of eccentric orbits of small outer bodies. The main challenge is now to detect and characterize this putative…
A local positional system (LPS) is proposed, in which particles are launched at given velocities, and a sensor system measures the trajectory of particles in the platform frame. These measurements allow us to restore the position and…
Armed with an astrolabe and Kepler's laws one can arrive at accurate estimates of the orbits of planets.
The identification of mean motion resonances in exoplanetary systems or in the Solar System might be cumbersome when several planets and large number of smaller bodies are to be considered. Based on the geometrical meaning of the resonance…