Eduqas Physics for A Level Year 2: Student Bk

101 2.8 Orbits and the wider universe Section 2.6 discussed Newton’s law of gravitation. The investigation into the properties of gravity and gravitational mass and the motion of bodies under their influence has led to many important developments in our understanding of the universe. The story of Johannes Kepler’s 1 development of these revolutionary laws, which not only debunked the philosophical notion that celestial (and therefore perfect) objects could only travel in perfect (i.e. circular) paths but also dethroned the Earth from its central position in the universe, is well worth looking into. The observational and experimental work of Galileo and mathematical work of Newton would eventually explain them and consolidate the idea that the whole of the universe was subject to the same physical laws. 2.8.1 Kepler’s laws of planetary motion Using the very accurate observations of the Danish astronomer, Tycho Brahe, Kepler was able to promulgate three laws which sum up how planets move relative to the Sun. These were purely empirical laws, i.e. they did not explain the motion but they described it to a much greater precision than Copernicus. In fact, they also apply to comets, dwarf planets, TNOs and asteroids, etc., i.e. all objects in orbit around the Sun; they also apply separately to objects in orbit around planets. (a) Kepler’s 1st and 2nd laws As with Newton’s laws we shall refer to Kepler’s laws as K1, K2 and (later) K3. The first two laws can be written as: K1:The orbit of a planet is an ellipse with the Sun at one focus. K2:The line joining the planet to the Sun sweeps out equal areas in equal intervals of time. For most planets it is difficult to tell that the orbit is not circular. Mars has the most eccentric of any of the easily observed planets; its path drawn in Fig. 2.8.2 departs from circular by about the thickness of the line! F 1 Fig. 2.8.2 Orbit of Mars In Fig. 2.8.2, the yellow and black discs represent the Sun and Mars (not to scale) and the red pecked line, the orbit of the Earth. The Sun is at, F 1 , one of the foci of the ellipse – the other focus is shown by the small grey circle. Fig. 2.8.1 Kepler’s portrait on a German postage stamp A TNO (trans-Neptunian object) is a minor planet which orbits the Sun with an average distance (i.e. semi-major axis) greater than that of Neptune. This category includes Pluto, Eris and Sedna. Terms & definitions Study point When applying Kepler’s laws to moon systems, we replace planet with moon and Sun with planet . Thus: The orbit of a moon is an ellipse with the planet at one focus. Study point Note that K2 refers to an individual planet (comet, TNO…) in its orbit. It doesn’t compare the areas swept out by different bodies. The movement of different objects in orbit around the same central body is the subject of Kepler’s third law (K3). 1 He was a mathematician, astronomer and astrologer who successfully defended his mother from a charge of witchcraft. MATHS TIP See the Maths section for the terminology and mathematical properties of ellipses.