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The Sun and Planets Lecture Notes 1. Spring Semester 2017 Prof Dr Ravit Helled Lecture 1 Introduction to Planetary Science Units in Planetary Science S.I. Units (“Systeme Internationale”) length unit: time unit: mass unit: meter second kilogram (m) (s) (kg) Table — Astronomical Units Unit light-year astronomical unit Abb. ly AU S.I. Equivalent 9.461 × 1015 m 1.496 × 1011 m Description distance that light travels in one year average Sun-Earth distance Note that it is also common in planetary science to report measurements in units of a particular object (e.g., Earth radii, Jupiter masses, etc.). An example of these units would be: 1 AU = 215 R (solar radii). Basic Astronomical Objects star — A large, glowing ball of gas that generates heat and light through nuclear fusion in its core. The Sun is a star. planet — A moderately large object that orbits a star and shines primarily by reflecting light from its star. According to the 2006 definition of the IAU (International Astronomical Union), an object can be considered a planet only if it: 1. orbits a star 2. is large enough for its own gravity to make it round 3. has cleared most other objects from its orbital path An object that meets the first two criteria, but has not cleared its orbital path, is a “dwarf planet” (e.g. Pluto). 1 exoplanet — A moderately large object that orbits a star and shines primarily by reflecting light from its star. According to the 2006 definition of the IAU (International Astronomical Union), an object can be considered an exoplanet only if it: 1. orbits a star (or stellar remnant) 2. has a mass lower than the mass required for deuterium burning 3. fulfils the mass/size criteria of planets in the solar system moon (or satellite) — An object that orbits a planet. The term satellite is also used more generally to refer to any object orbiting another object. asteroid — A relatively small and rocky object that orbits a star. Asteroids are “small solar system bodies” comet — A relatively small and ice-rich object that orbits a star. Like asteroids, comets are considered “small solar system bodies”. The Solar System The Sun — An average star at the center of the solar system. The Sun is a G-class star with a surface temperature of 5’800 K and a central temperature of 15 million K. The Planets — Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune The Asteroid Belt — A ring of small bodies between Mars and Jupiter with a combined mass of ∼ 3 × 1021 kg. The largest asteroid in the belt, Ceres, accounts for 1/3 13 of the asteroid belt’s mass. The Comets — The two reservoirs (sources) of comets in the solar system are the Kuiper belt (35–1’000 AU) and Oort cloud (30’000–100’000 AU). Age The age of the solar system is approx. 4.567 Gyr. Most of the objects in the solar system show a similar age. Mass The Sun contains most of the mass in the solar system: Sun 99.85%, Planets 0.135%, Comets 0.01%, Satellites 0.00005%. The planets account for less than 0.2% of the solar system’s mass. The outer planets (Jupiter, Saturn, Uranus, Neptune) are much more massive than the inner planets (Mercury, Venus, Earth, Mars). 2 Orbits The orbits of the planets are ellipses with the Sun at one focus. The orbits of the planets are all more or less in the same plane (this plane is called the ecliptic). The planets orbits are prograde (i.e., they orbit in the same direction as the Sun rotates) and roughly circular. All of the planets’ orbits lie within approx. 30 AU of the Sun. The spacing between the planets is large. Angular Momentum Over 98% of the angular momentum in the solar system is found in the orbital motions of the giant planets, whereas 99% of the mass is found in the Sun. Composition Planets differ in composition, with a definite trend with distance from the Sun. Planets closer to the Sun are denser and have higher metal contents. H and He abundances in the giant planets decrease with distance from the Sun. The asteroids are mostly rocky. The moons of the outer planets, as well as Kuiper belt objects, consist of rock and ice. Kepler’s Laws Kepler’s 1st Law Planets travel in an ellipse with the Sun at one focus. Kepler’s 2nd Law The planet sweeps out equal areas in equal times (the planet goes faster when nearer the Sun). Kepler’s 3rd Law The square of the orbital period P of any planet is proportional to the cube of the planet’s average distance from the Sun: a3 = kP 2 If a is expressed in Astronomical Units (AU) and P in Julian (i.e. Earth) years, then the constant of proportionality is k = 1. Newton’s Laws Newton’s 1st Law Every object in a state of uniform motion tends to remain in that state of motion unless acted on by an external force. Newton’s 2nd Law The relationship between an object’s mass m, its acceleration α, and the force F applied upon it is F = mα. Newton’s 3rd Law For every action there is an equal and opposite reaction. 3 Gravitation Newton’s law of universal gravitation states that an object attracts another object using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them: F1 = F2 = Gm1 m2 , r2 where G = 6.67428 × 10−11 m3 kg−1 s−2 is Newton’s Gravitational Constant, m1 and m2 are the masses of the objects, and r is the distance between the objects. Both objects feel the same force. Gravity is a central force, meaning that the force depends on the distance from the center [of mass]. This is why massive objects are round. 4