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Exploring the Solar System Lecture 1 Exploring the Solar System Lecture 1: Overview of the Solar System - Introduction Professor Paul Sellin Department of Physics University of Surrey Guildford UK Page 1 Paul Sellin Lecture 1 Page 1 Course Schedule Session 1: 10-11 Session 2: 11-12 Week 1 L1: Introduction to the Solar System 11 Feb Week 2 L2: Physical Properties of the Solar system 18 Feb Lectures are in TB01 No lecture on 25th Feb - Week 3 Week 4 L3: Structure of the Moon Computing Computing sessions 4 March are in 32BB03 Give out CW1 exercise Week 5 L4: Exploration of the Moon Computing 11 March There are 2 pieces of Computing Week 6 L5: Formation of the Solar System Coursework, plus a 18 March Submit CW1 exercise final examination Week 7 L6: Terrestrial Planets: Mercury 25 March Coursework deadlines Week 8 L7: Terrestrial Planets: Venus Computing are Friday at 4pm 1 April Computing Give out CW2 exercise Week 9 L8: Terrestrial Planets: Mars Computing Recommended Text: 8 April ‘Universe’ by Easter Holiday Freedman and Kaufmann Week 10 L9: Jovian Planets: Jupiter and Saturn 13 May Submit CW2 exercise Week 11 L10: Jovian Planets: Uranus and Neptune 20 May Page 2 Paul Sellin Lecture 1 Page 2 Contents Planetary motion and basic orbital data Titus-Bodes or planetary orbits Kepler’s Laws Observed orbits The layout of the Solar System View of the solar system to scale Some key definitions Sidereal rotation Astronomical units Rotational motion of the planets Rotational data Rotational measurements using Radar Summary Page 3 Paul Sellin Lecture 1 Page 3 The Planets Nine major planets have been discovered in orbit around the Sun. In order of increasing heliocentric distance these are: Mercury, Venus, Earth and Mars (the so- called terrestrial planets); Jupiter, Saturn, Uranus, and Neptune (the so-called gas-giants or Jovian planets); and finally the small and rather odd planet Pluto, discovered in 1930. Page 4 Paul Sellin Lecture 1 Page 4 Planetary Moons Earth’s satellite (the Moon) is unusually large compared to its parent body and so it is also sometimes classed as a terrestrial planet - thus, the Earth- Moon system can be thought of as a double-planet. Similarly, Pluto’s satellite Charon is also relatively large, and so this may also be classed as a double-planet. Planet Sidereal Period Semi-Major Axis Eccentricity Inclination Tropical Years AU 106 km to Ecliptic Mercury 0.241 (87.96d) 0.387 57.9 0.206 7.00° Venus 0.615 (224.70d) 0.723 108.2 0.007 3.39° Earth 1.000 (365.26d) 1.000 149.6 0.017 0.00° Mars 1.88 (686.98d) 1.524 228.0 0.093 1.85° Jupiter 11.86 5.203 778.3 0.048 1.31° Saturn 29.46 9.54 1427 0.056 2.49° Uranus 84.01 19.18 2871 0.047 0.77° Neptune 164.8 30.06 4497 0.009 1.77° Pluto 248.6 39.44 5913 0.249 17.15° Page 5 Paul Sellin Lecture 1 Page 5 1.1 Planetary Orbits and Motion* The planets orbit the Sun under the influence of gravity according to Newton’s and Kepler’s laws - i.e. the planets follow elliptical paths. Bode’s Law- The size of the semi-major axes (SMA’s) of the planetary orbits form an approximately regular pattern, discovered empirically by Titius of Wittenburg in 1766 (before Uranus. Neptune and Pluto were discovered), and publicised by Johann Bode in 1772. The Titius-Bode Rule or Bode’s law concerns the sequence: Dividing the numbers in this sequence by 10 gives a remarkable fit to the SMA’s of the planets, when these are expressed in terms of Astronomical Units (AU) Page 6 Paul Sellin Lecture 1 Page 6 The Titus-Bode sequence* The Titius-Bode Sequence gives (only 6 planets known at the time): and the actual planetary SMA’s are: The fit to the six planets (known since ancient times) was good, however there seemed to be a missing planet at 2.8 AU. This prediction was confirmed in 1801 when Giuseppe Piazzi discovered the small planet Cees in exactly the right place. However, it was soon discovered that this was only one (albeit the largest) of numerous small bodies orbiting between 2.3 and 3.3 AU, now known as minor planets or asteroids. Page 7 Paul Sellin It can be seen that the empirical Titius-Bode Rule works remarkably well for most of the planets. When William Herschel discovered Uranus in 1781 at 19.2 AU, nine years after Bode’s publication, the predictive power of the rule must have seemed remarkable. Shortly after its discovery, minor perturbations in the predicted orbit of Uranus suggested that an eighth planet waited to be discovered beyond Uranus - was it to be found at 38.8 AU? Calculations based on Newtonian mechanics by J.C Adams (in 1843) and independently by U.J Leverrier (in 1846), deduced the probable mass and orbit of the unknown planet, and in 1846 Johann G. Galle at the Berlin Observatory found the planet (later to be called Neptune) within 1° of its predicted position - but unfortunately not where the Titius-Bode rule said it would be. However, perturbations observed in Neptune’s orbit suggested that yet another planet existed beyond Neptune (the so-called “PlanetX’). However, predicting the orbit and mass of this planet was very difficult! Eventually, in 1930 Clyde W. Tombaugh found the planet Pluto close to the position calculated by Percival Lowell. Unfortunately this was just a fluke as Pluto is too small to perturb Neptune’s orbit. So is Planet X still out there waiting to be discovered? Has the TitiusBode Rule got any real physical basis? We just don’t know! Lecture 1 Page 7 Kepler’s empirical laws of planetary motion* Keppler’s 1st Law: The orbit of each planet is an ellipse, with the Sun at one of the foci (published 1609). Note that the Sun is one focus of a planet’s elliptical orbit, with nothing at the other focus An ellipse can be drawn using a string of fixed length: A series of ellipses with the same major axis, and varying eccentricities: Page 8 Paul Sellin By 1621, Kepler had shown that these laws also applied to the Galilean satellites, with Jupiter as the primary body, and with a different value of k. Newton, in Principia (1687), explained these empirical observations through his theory of Universal Gravitation. In this theory, an attractive force - gravity - is supposed to exist between all bodies, with a magnitude proportional to the product of the masses of the bodies, and inversely proportional to the square of their distance apart: F=G Mm I r2 A Lecture 1 Page 8 Conic Sections* The ellipse is one form of conic section, which have the general expression: where: e is the eccentricity p is a length ordinate: The 4 possible conics are: Circle: Ellipse Parabola Hyperbola Here a is the semi-major axis, and b the semi- minor axis. For an ellipse: For a parabola, q is defined as the distance to the COM at closed approach. Page 9 Paul Sellin The type of conic section is determined by the angle the plane makes with the horizontal. If the plane is horizontal, the resulting curve is a circle. If the plane is at an angle which is less than the slope angle of the cone, the curve is an ellipse. If the plane is parallel to the slope angle of the cone, the curve is a parabola. If the plane is anywhere between the slope angle of the cone and the vertical, the curve is a hyperbola. For a 2 body planetary orbit (eg. a planet around the Sun) the motion is elliptical, hence Keppler’s first law is a result of the inverse square law of force. In such an orbit one of the masses occupies one focus of the ellipse, whilst the other focal point is empty. Some cometary orbits are parabola, with e ~ 1 although most permanent members of the solar system follow elliptical orbits with e<<1. Exceptions to this are Pluto (e=0.25) and Mercury (e=0.21). Lecture 1 Page 9 Kepler’s 2nd Law* Keppler’s 2nd Law: The radius vector to a planet sweeps out equal areas in equal times (the Equal Areas Law). A planet moves fastest at Perihelion and slowest at Aphelion, such that the equal areas are swept out over equal time. The semimajor axis a is the orbiting body’s mean distance from the Sun An elliptical orbit is defined in terms of the semimajor axis and the eccentricity e. The perihelion distance q is the distance from the perihelion to the Sun, and similarly the aphelion distance Q: Page 10 Paul Sellin Lecture 1 Page 10 Orbital Period* Circular orbital motion is derived from equating centripetal and gravitational forces: Hence the orbital period T is proportional to r3/2 Page 11 Paul Sellin Lecture 1 Page 11 Kepler’s 3rd Law* Kepler’s 3rd law connects the planet’s sideral period p with the semimajor axis a: More generally we can write: where k is a constant which depends on the mass of the central body. k is the same for all planets orbiting around the Sun For calculations in our solar system it is convenient to use units of years and AU. Hence calculate k for our solar system using Earth data: Page 12 Paul Sellin In the special case of an object orbiting the Sun, where p is in years and a is in AU, then: Lecture 1 Page 12 Orbital Motion of the Planets Direction – Most of the planets orbit counter-clockwise around the Sun seen from above the Earth’s orbit plane (North = Up).
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