1 Lecture 4: Motion, Energy, GravitySCI238 W07 Lecture 4: Motion, Energy, Gravity SOHO image of Sun (obscured) and 4 planets L4-Jan17/08 Motion, Energy, Gravity…
2 Motion, Energy, Gravity…This week’s events: the Moon: Full Moon Jan 22 Venus: visible low in east before sunrise; brightest “morning” star Mars: is visible all night, rises at sunset, occultation 20 January... not visible from Waterloo but Mars will be very close to the Moon Jupiter: not visible Saturn: rises at 10pm L4-January 17/08 Motion, Energy, Gravity…
3 Motion, Energy, Gravity…Today’s Lecture the European Development of astronomy Galileo Newton today’s topic: gravity the physics of Kepler’s Laws orbits conservation of energy circular velocity, escape velocity, perturbations tides modern physics gravity and General Relativity mass-energy, atoms and molecules, heat energy L4-January 17/08 Motion, Energy, Gravity…
4 European Development of Astronomy: new technologyuse of a telescope to do astronomy phases of Venus mountains on Moon sunspots moons of Jupiter Milky Way is made of stars Forced confrontation with Pope → confined to his home for life in 1633 for heresy “forgiven” in 1992 start here on 17 Jan, 2008 Galileo ( )) L4-January 17/08 Motion, Energy, Gravity…
5 Motion, Energy, Gravity…observed phases of Venus => Venus must orbit the Sun L4-January 17/08 Motion, Energy, Gravity…
6 Motion, Energy, Gravity… Galileo and the Moons of Jupiter page from Galileo’s notebook (1610) sketches show four “stars” near Jupiter different positions at different times, repeatable Galileo realized these were moons of Jupiter showed that objects could orbit a moving body L4-January 17/08 Motion, Energy, Gravity…
7 European Development of Astronomy: PhysicsNewton Laws of Motion (F=ma) Law of Gravity optics Calculus these “Laws” were the first to provide universal rules that governed motions of planets and of everyday objects on the Earth Isaac Newton ( ) L4-January 17/08 Motion, Energy, Gravity…
8 Motion, Energy, Gravity…universal law of gravity: describes the forces acting between bodies due to gravity G is the gravitational constant G=6.67 m3/(kg s2) L4-January 17/08 Motion, Energy, Gravity…
9 Properties of an ellipsesemimajor axis is the average distance of a body from the orbit’s focus an orbit’s focus is at the location of the centre of mass of the system L4-January 17/08 Motion, Energy, Gravity…
10 Properties of an ellipseamin = a(1-e) amax = a(1+e) Note: amin + amax = 2a L4-January 17/08 Motion, Energy, Gravity…
11 Motion, Energy, Gravity…Centre of Mass a1 a2 location of centre of mass depends on relative masses in an equal mass system, CM is midway between in SS MSun >> Mplanet and CM is inside the Sun m1 a1= m2 a2 more general form of KIII (m1+m2)P2 = a3 = (a1+a2)3 L4-January 17/08 Motion, Energy, Gravity…
12 Kepler’s Laws from Newton’s Equations: “Celestial Mechanics”use conservation of momentum, centripetal forces, and gravity to get general version of Kepler’s Third Law: use conservation of energy, polar coordinate equation of ellipse (and take time derivatives of position on ellipse) + a lot of algebra to get “vis viva” equation (velocity as a function of distance from the “barycentre”): L4-January 17/08 Motion, Energy, Gravity…
13 Why are there three “versions” of KIII?Kepler’s: P2 = a3 another Kepler’s?: (m1+m2)P2 = a3 = (a1+a2)3 Newton’s?: …units: mSun, AU, y …or… kg, m, s special case: m1+m2 = 1 semimajor axis for each object L4-January 17/08 Motion, Energy, Gravity…
14 Motion, Energy, Gravity…Example: mSun, AU, y (m1+m2)P2 = a3 = (a1+a2)3 A planet orbits a 1mSun star with a period of 20y. What is its orbital semimajor axis? m1+m2=1 since mplanet << mSun also can use a1+a2=a since aplanet >> aSun (1)(20)2=a3 and a=7.37AU remember a is the separation between the masses; is masses are more similar you need to find a1 and a2 explicitly to know the orbit of each what if the body orbits a 3mSun star with a 20y period? What is its semimajor axis? You can also do this with Newton’s form, SI units; give it a try L4-January 17/08 Motion, Energy, Gravity…
15 Motion, Energy, Gravity…Example: kg, m, s The Moon and the Earth are in mutual orbit with a period of 27.3d and a mean separation of 384,400km. We know (by other means) that mEarth= 5.97x1024kg. What is the mass of the Moon? What are the semimajor axes of the Moon’s and Earth’s orbits? KIII(Newton’s form) gives MEarth+MMoon = 6.043x1024 kg; subtracting mEarth => MMoon=7.31x1022 kg = MEarth since mEarth ~81.5 mMoon we have aMoon/aEarth = mEarth/mMoon ~81.5, giving aMoon ~4700km and aEarth~380000km. because mMoon << mEarth, result will depend on the # significant figures …better way to get Moon’s mass? spacecraft? artificial satellite? Why? L4-January 17/08 Motion, Energy, Gravity…
16 Motion, Energy, Gravity…Orbits and energy circular orbit (e=0): v = vcirc bound orbit (0
17 Escape velocity: rocket leaving EarthL4-January 17/08 Motion, Energy, Gravity…
18 Orbital energy and distance from centre of massv1AU =2v4AU etc… orbital kinetic energy (½mv2) also decreases with distance from centre of mass this pattern for orbital speed vs distance is valid in any system where orbits are dominated by a central mass L4-January 17/08 Motion, Energy, Gravity…
19 Motion, Energy, Gravity…m1=m2 as centre of mass location depends on mass ratio… m1=2m2 so does relative orbital size m1>>m2 L4-January 17/08 Motion, Energy, Gravity…
20 Conservation of Energyenergy can be neither created nor destroyed. energy merely changes its form or is exchanged between objects. this principle (or law) is fundamental physics/science the total energy content of the Universe was determined in the Big Bang and remains the same today! L4-January 17/08 Motion, Energy, Gravity…
21 Conservation of energy: PE+KE=constant …if no external forces!gravitational potential energy ↑ as distance ↑ orbital kinetic energy ↑ as distance ↓ L4-January 17/08 Motion, Energy, Gravity…
22 Orbits: can be altered by exchange of energysuch as… collisions near encounters examples: comets and Jupiter spacecraft star clusters L4-January 17/08 Motion, Energy, Gravity…
23 Orbits: can be altered by exchange of energygalaxies and more… L4-January 17/08 Motion, Energy, Gravity…
24 Tides: caused by differential forces across a bodyremember: the force of gravity varies as distance2 L4-January 17/08 Motion, Energy, Gravity…
25 OceanTides on Earth: vary with alignment of Earth, Moon, SunL4-January 17/08 Motion, Energy, Gravity…
26 Motion, Energy, Gravity…Tidal friction: is slowing Earth’s rotation also increasing Earth/Moon distance L4-January 17/08 Motion, Energy, Gravity…
27 Tides not just Earth/Moon effect…Tidal forces are important wherever differential gravitational forces are large enough SS examples: planetary rings, jovian moons and more binary stars: close pairs, large envelopes… vicinity of black holes galaxies: tidal streams from encounters, warped disks etc. L4-January 17/08 Motion, Energy, Gravity…
28 Einstein’s Theories of RelativitySpecial Relativity: speed of light is independent of the motion of the observer General Relativity: a theory of gravity curved spacetime … there is no “gravitational field”. mass simply curves spacetime and objects move along the curvature L4-January 17/08 Motion, Energy, Gravity…
29 Motion, Energy, Gravity…Mass versus Energy energy is stored in matter itself this mass-energy is what would be released if an amount of mass, m, were converted into energy Albert Einstein ( ) E = mc2 L4-January 17/08 Motion, Energy, Gravity…
30 Motion, Energy, Gravity…Atomic Theory of Matter atoms consist of a nucleus, made of protons and neutrons, plus a set of electrons that surround it in a normal atom the number of electrons is equal to the number of protons (defines the“element”) the number of neutrons is similar to the number of protons, but often slightly different (“isotopes”) there are many other “sub-atomic” particles. (quarks, muons, neutrinos…) L4-January 17/08 Motion, Energy, Gravity…
31 Motion, Energy, Gravity…the structure of an atom: mass mostly in nucleus; electron “cloud” >> in size L4-January 17/08 Motion, Energy, Gravity…
32 Motion, Energy, Gravity…Atom nucleus electron p+ e- n proton neutron L4-January 17/08 Motion, Energy, Gravity…
33 Motion, Energy, Gravity…Hydrogen e- atomic number = 1 p+ atomic mass number = 1 L4-January 17/08 Motion, Energy, Gravity…
34 Motion, Energy, Gravity…Helium e- p+ p+ atomic number = 2 n n e- atomic mass number = 4 L4-January 17/08 Motion, Energy, Gravity…
35 Motion, Energy, Gravity…we distinguish different elements by the number of protons in the nucleus: hydrogen with one proton, no neutrons; deuterium (heavy hydrogen) has one proton and one neutron) helium has two protons, two neutrons carbon has six protons, six neutrons L4-January 17/08 Motion, Energy, Gravity…
36 What if two or more atoms combine to form a particle?=> molecule p+ p+ 8p+ 8n H2O (water) L4-January 17/08 Motion, Energy, Gravity…
37 Motion, Energy, Gravity…Electron Orbits electrons can gain or lose energy while orbiting nucleus. if electrons have lowest possible energy → atom is in the ground state. electrons with > lowest energy → atom in an excited state. electrons with enough energy to escape the nucleus → atom is ionized. L4-January 17/08 Motion, Energy, Gravity…
38 Electron Energy Levelsbut, electrons cannot have just any energy while orbiting the nucleus. only certain energy values are allowed. electrons may gain or lose only certain specific amounts of energy. each element (atom and ion) has its own distinctive set or pattern of energy levels. this diagram depicts the energy levels of Hydrogen. L4-January 17/08 Motion, Energy, Gravity…
39 Motion, Energy, Gravity…a measure of heat energy content per particle temperature normally measured in the “Kelvin scale” zero is “Absolute Zero”; no negative temperature each Kelvin degree same size as “Celsius” or “Centigrade” freezing point of water is 273° above Absolute Zero (i.e. 273° K) boiling point of water is 373° above Absolute Zero (i.e. 373° K) “room temperature” (20° C) at 293° K Temperature L4-January 17/08 Motion, Energy, Gravity…
40 Motion, Energy, Gravity…Temperature vs. Heat Temperature is the average kinetic energy. Heat (thermal energy) is the total kinetic energy. less heat more heat lower T higher T same T L4-January 17/08 Motion, Energy, Gravity…
41 Motion, Energy, Gravity…phase of an element depends on temperature solid, liquid, or gas L4-January 17/08 Motion, Energy, Gravity…