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Context. The PLAnetary Transits and Oscillations of stars (PLATO) mission will observe the same area of the sky continuously for at least two years in an effort to detect transit signals of an Earth-like planet orbiting a solar-like star.…

Recent dynamical studies indicate that the possibility of an Earth-like planet around $\alpha\;$Cen A or B should be taken seriously. Such a planet, if it exists, would perturb the orbital astrometry by $<10 \ {\mu}\rm as$, which is…

In order to perform high resolution astrometry of the solar diameter from the ground, through the observations of eclipses, the study of the limb darkening profile is described. Knowing the profile of the solar limb is useful both to…

Here we explore a novel approach in order to try to measure the post-Newtonian 1/c^2 Lense-Thirring secular effect induced by the gravitomagnetic field of the Sun on the planetary orbital motion. Due to the relative smallness of the solar…

The count rate at dark-matter direct-detection experiments should modulate annually due to the motion of the Earth around the Sun. We show that higher-frequency modulations, including daily modulation, are also present and in some cases are…

Using over 40 million muons collected since 1989 by the MACRO detector we have searched for a depletion of muons coming from the direction of the Moon due to primary cosmic rays striking the Moon. We observe this Moon shadow in the expected…

During the 17th century the idea of an orbiting and rotating Earth became increasingly popular, but opponents of this view continued to point out that the theory had observable consequences that had never, in fact, been observed. Why, for…

% context heading (optional) {Thanks to the Venus Express Mission, new data on the properties of Venus could be obtained in particular concerning its rotation.} % aims heading (mandatory) {In view of these upcoming results, the purpose of…

We present a method to correct for deflections of ultra-high energy cosmic rays in the galactic magnetic field. We perform these corrections by simulating the expected arrival directions of protons using a parameterization of the field…

The serendipitous detection of stellar occultations by Outer Solar System objects is a powerful method for ascertaining the small end ($r \lesssim 15$ km) of the size distribution of Kuiper Belt Objects and may potentially allow the…

The experiment proposed aims to evidence and to measure the deflection of light rays induced by the source speed upon emission, and to discern it from the aberration of light rays induced by the observer speed. The method stands in creating…

A new class of Kuiper belt objects that lie beyond Neptune with semimajor axes greater than 250 astronomical units show orbital anomalies that have been interpreted as evidence for an undiscovered ninth planet. We show that a modified…

The kinematics of the Solar zenith passage on the Earth was shown as a simple harmonic motion. This analytical model used the uniform circular motion to describe the Earth's rotation relative to its axis and relative to the Sun, also this…

The Lunar Laser Ranging (LLR) experiment provides precise observations of the lunar orbit that contribute to a wide range of science investigations. In particular, time series of highly accurate measurements of the distance between the…

We investigate the prospects for characterizing extrasolar giant planets by measuring planetary oblateness from transit photometry and inferring planetary rotational periods. The rotation rates of planets in the solar system vary widely,…

We study the effect of the scattering of gravitational waves on planetary motions, say the motion of the Moon around the Earth. Though this effect has a negligible influence on dissipation, it dominates fluctuations and the associated…

Many theories which unify gravity with the other known forces of nature predict the existence of an intermediate-range ``fifth force'' similar to gravity. Such a force could be manifest as a deviation from the gravitational inverse-square…

This paper provides an overview of the Lunar Laser Ranging (LLR) experiments. The measurement principle is explained and its theory is derived. Both contributions, the direct reflected light from retroreflectors as well as the scattered…

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…

A point mass at the center of an ellipsoidal homogeneous fluid is used as a simple model to study the effect of rotation on the shape and external gravitational field of planets and stars. Maclaurin's analytical result for a homogenous body…