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### Physical propeties of the Sun and planets

Distance to the Sun How far away is the Sun from the Earth, and how fast is the Earth moving through space? Keplers model of planetary motion only provided a scale model for the relative distances of the planets from the Sun, and for a long time no one knew exactly how big the solar system was. The crucial unit of distance for the planets is the mean Sun-Earth distance, known as the astronomical unit and designated AU for short. It can be determined by first estimating the distance between Earth and a nearby planet, and then inferring the Sun-Earth distance from geometry and Kepler's third law. The planetary distances are themselves determined by triangulation from different points on the Earth.

The AU was established with increasing accuracy in the 19th and 20th centuries, by determining the distances of Mars and the nearby minor planet 433 Eros during their closest approaches to the Earth. The results (Fig. 1.19) converged toward a solar parallax of 8.80 seconds of arc. The quest for accuracy in the mean distance of the Sun from the Earth culminated in the 1960s, when radar (radio detection and ranging) was used to accurately determine the distance to Venus (Fig. 1.20). The round-trip travel time, T, for a radio pulse to travel from the Earth to Venus and back  about 276 seconds when Venus is closest to the Earth  was precisely measured. The distance to Venus was then obtained by multiplying half the round-trip time, T/2, by the speed of light, c = 2.99792458 x 108 m s-1. The radar measurements have determined the mean distance between the Sun and the Earth to an accuracy of about 1,000 meters.

Mass, radius and mass density of the Sun and major planets

Once an accurate value for the mean distance between the Earth and the Sun is known, one can use it with the orbital period of the Earth to infer the mass of the Sun from Newtons formulation of Keplers third law. The precise distance to a planet can also be combined with the angular separation of one of its satellite to determine the orbital distance of that satellite from its planet, which can then be combined with the satellites orbital period to establish the planets mass using a similar mathematical expression. When the mass of the Sun and planets are thus determined, we find that the Sun doesnt just lie at the heart of our solar system, it dominates it. Some 99.866 percent of all the matter between the Sun and halfway to the nearest star is contained in the Sun.

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Copyright 2010, Professor Kenneth R. Lang, Tufts University     