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PLANETARY ORBITS Chapter 2 CONIC SECTIONS PLANETARY GEOMETRY Definition of a Circle A Circle is a figure for which all points on it are the same distance from the centre. Definition of an Ellipse An Ellipse is a figure for which the sum of the distances from any point on the figure to two points inside the figure is always the same HOW to DRAW an ELLIPSE HOW to DRAW an ELLIPSE (ellipticity e = distance between foci / major axis – eEarth 0.02, eJupiter 0.05, eMercury 0.21) Major Axis Focus Focus Minor Axis KEPLER’S THREE LAWS KEPLER’S THREE LAWS First Law: The orbit of each planet is an ellipse with the Sun at one focus Foci Planet Sun PLANETARY ORBITS KEPLER’S THREE LAWS First Law: The orbit of each planet is an ellipse with the Sun at one focus Second Law: The line joining the planet and the Sun sweeps out equal areas in equal times. KEPLER’S SECOND LAW B Area 1 = Area 2 C A Sun Area 2 Perihelion Aphelion Area 1 D FLASHCARD WHERE DOES A PLANET MOVE FASTEST IN ITS ORBIT? A) At A B A C Sun Aphelion Perihelion D B) At perihelion C) At aphelion D) At D KEPLER’S THREE LAWS First Law: The orbit of each planet is an ellipse with the Sun at one focus Second Law: The line joining the planet and the Sun sweeps out equal areas in equal times. Third Law: The squares of the planets’ periods of revolution are in proportion to the cubes of the semimajor axes of their orbits KEPLER’S THIRD LAW (period)2 = (distance)3 Eg. Mars: p = 1.88 year, d = 1.52 AU (1.88)2 = (1.52)3 Planet Semimajor Axis Sun KEPLER’S THIRD LAW COMET HALLEY’S ORBIT FLASHCARD WOULD YOU EXPECT HALLEY’S COMET TO OBEY KEPLER’S LAWS? A) Yes B) No FLASHCARD SPECIFICALLY, DOES HALLEY’S COMET OBEY KEPLER’S THIRD LAW? PERIOD = 76 YEARS, SEMI-MAJOR AXIS = 18 AU A) Yes B) No ORBITAL DATA Planet Semimaj Period Axis (years) (AU) d3 p2 Mercury 0.39 0.24 0.0593 0.0576 Venus 0.72 0.62 0.3732 0.3844 Erath 1.00 1.00 1.000 1.000 Mars 1.52 1.88 3.5118 3.5344 Asteroid 2.77 4.60 21.254 21.160 Jupiter 5.20 1.86 140.61 140.66 Saturn 9.54 29.4 868.25 867.89 Uranus 19.19 84.07 7,066 Neptune 30.06 164.80 27,162 27,159 7,068 KEPLER’S THREE LAWS First Law: The orbit of each planet is an ellipse with the Sun at one focus Second Law: The line joining the planet and the Sun sweeps out equal areas in equal times. Third Law: The squares of the planets’ periods of revolution are in proportion to the cubes of the semimajor axes of their orbits NEWTON’S THREE LAWS NEWTON’S THREE LAWS First Law: Every body continues what it is doing (at rest or in motion in a straight line) unless acted upon by an outside force. (Note break here with tradition) Second Law: Change in motion of a body is proportional to the force acting on it and is in the direction that the force is acting. Third Law: For every action there is an equal and opposite reaction. NEWTON’S UNIVERSAL LAW of GRAVITATION Force = GM1M2/D2 M1 and M2 are the masses of the two objects D is the distance between them G is a constant called the Gravitational Constant Newton found that the orbits derived from this force were exactly those found by Kepler Kepler’s 3rd Law becomes D3 = (M1 + M2) x P2