Physics 3/3/2013. Kepler s Three Laws of Planetary Motion. Distance, Velocity from the Sun at any given time: q=angle from perihelion

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1 Physics Kepler s Three Laws of Planetary Motion a=semi-major axis b=semi-minor axis e=eccentricity Focus, Foci Distance, Velocity from the Sun at any given time: a(1 e ) r 1 ecosq v 1 GM ro a q=angle from perihelion Kepler s second law rate of orbit changes (fast at perihelion, slow at aphelion) Kepler s third law: P = k a 3 Newton s version (correct version) P 3 4 a G( M M 1 ) 1

2 Orbits aren t that simple More terms needed a Semi major axis e - eccentricity i - inclination q perihelion distance W longitude of the ascending node w argument of the perihelion Non-elliptical/circular orbits Depends upon velocity, direction Velocities < Escape velocity = elliptical/circular GM v esc r Velocity = Escape Velocity Orbit becomes parabolic e=1, q=closest approach r q 1 cosq Velocity > Escape Velocity Orbit is hyperbolic e>1 q(1 e) r 1 ecosq

3 Gravity Current formula two objects Three objects disaster! 3-body problems 3-Body Effects Simplifications good! Perturbations Predicatable (periodic) Commensurable orientations (orbits) Beat Phenomena Ratios of orbits = ½, 1/3, ¼, /3, /5, etc. Increases influence examples: Asteroid belt, Planetary rings Lagrangian Points Gravitational Peaks Valleys associated with two objects. 3

4 L1, L, L3 Unstable L4, L5 Stable Lagrangian Objects Jupiter Sun system Trojan Asteroids Earth Moon system Dust Earth Sun system L1 - SOHO L - Satellites L4, L5 mainly dust, 1 Trojan Mars Sun system L4, L5 - about 3 asteroids Saturn Dione system L4, L5 - Helene, Polydeuces Saturn Tethys system L4, L5 - Calypso, Telesto Neptune - Sun system L4, L5 - about 9 asteroids 4

5 Horseshoes & Tadpoles Horseshoe orbits Not really how things move Matter of perspective Janus/Epimetheus Cruithne 00 AA 9 5

6 Tadpole Orbits Objects trapped in L4, L5 move around Who controls all of this? The Sun? Not necessarily sphere of influence Hill Sphere distance where an object controls motion of other objects R H a 1/ 3 ( m 1 ) 3( 1 ) e m m All satellites within each planet s Hill sphere 6

7 Tides Force that depends on object size/distance 3 Strong distance effect! Earth-Moon system High/Low tides Earth s rotation Synchronous rotation of Moon (1:1) Moon s migration away Sun contributes 0% Killer Tides! Not really When do they hurt? When you get within the Roche Limit No precise limit Tensile strength (Composition, density, etc) r R M m 1/3 R r R M.5 m 1/ 3 R Tidal Heating Io, Europa, Ganymede Enceladus Triton 7

8 Ring Resonances Perturbations Light/Gas Influences Does effect motion small objects mainly For sub-micron (~10-7 m or less): Corpuscular drag Solar Winds particles from the Sun Gas drag Atmospheric effect 8

9 For micron sized (~ 10-6 m): Radiation pressure Photons = energy = influence ( flux ) a Q c F rad =radiation force Q=correction factor a=particle size r=distance L=luminosity La Q 4r c F rad For centimeter sized objects (0.01 m): Poynting-Robertson Drag Relativity effect Motion of particle effects re-emission of light Causes decreasing orbit Decaying orbits Particles that make up the Zodiacal light Need to be replenished! For meter sized objects: Yarkovsky (Yarkovski) effect Hot objects give off light When they give off light alters motion Influenced by temperature variation across it diurnal effects (rotation) seasonal effects albedo/composition variations Yarkovsky-O'Keefe-Radzievskii-Paddack effect (YORP) Irregular shape alters motion 9

10 Light Other things you may have forgotten: Types of light wavelength order Radio longest - lowest energy Microwave Infrared Visible (ROYGBIV) Ultraviolet X-ray Gamma-ray shortest - highest energy c=lf Speed = wavelength x frequency Wien s law for black bodies Peak type of light emitted - temperature l max = 0.009/T Doppler effect Change of wavelength due to motion 10

11 Spectrum of planets Absorption due to atmosphere, surface material Element Spectra 11

12 Albedo How light is absorbed reflected measured by the albedo Bond Albedo averaged over all wavelengths, all directions most commonly used Total reflected/total absorbed If it equals 0, what does that mean? If it equals 1, what does that mean? Albedo effects temperature Light coming in = primarily visible Light emitted = primarily IR Difference of incoming/outgoing influences environment of object (Greenhouse effect) 1