PLANETARY ORBITS Chapter 2

CONIC SECTIONS

PLANETARY GEOMETRY l Definition of a Circle äA Circle is a figure for which all points on it are the same distance from the centre. l Definition of an Ellipse äAn 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

Major Axis FocusFocus Minor Axis  (ellipticity e = distance between foci / major axis – e Earth 0.02, e Jupiter 0.05, e Mercury 0.21)

KEPLER’S THREE LAWS

l First Law:  The orbit of each planet is an ellipse with the Sun at one focus Sun Planet Foci

PLANETARY ORBITS

KEPLER’S THREE LAWS l First Law:  The orbit of each planet is an ellipse with the Sun at one focus l Second Law:  The line joining the planet and the Sun sweeps out equal areas in equal times.

KEPLER’S SECOND LAW Sun AphelionPerihelion A B C D Area 1 = Area 2 Area 1 Area 2

FLASHCARDFLASHCARD WHERE DOES A PLANET MOVE FASTEST IN ITS ORBIT? A) At A B) At perihelion C) At aphelion D) At D Sun Aphelion Perihelion A B C D

KEPLER’S THREE LAWS First Law: First Law:  The orbit of each planet is an ellipse with the Sun at one focus Second Law: Second Law:  The line joining the planet and the Sun sweeps out equal areas in equal times. Third Law: Third Law:  The squares of the planets’ periods of revolution are in proportion to the cubes of the semimajor axes of their orbits

Sun Planet Semimajor Axis KEPLER’S THIRD LAW (period) 2 = (distance) 3 Eg. Mars: p = 1.88 year, d = 1.52 AU (1.88) 2 = (1.52) 3

KEPLER’S THIRD LAW

COMET HALLEY’S ORBIT

FLASHCARDFLASHCARD WOULD YOU EXPECT HALLEY’S COMET TO OBEY KEPLER’S LAWS? A) Yes B) No

FLASHCARDFLASHCARD 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 Axis (AU) Period (years) d3d3 p2p2 Mercury Venus Erath Mars Asteroid Jupiter Saturn Uranus ,0667,068 Neptune ,16227,159 Pluto ,0991,802

KEPLER’S THREE LAWS First Law: First Law:  The orbit of each planet is an ellipse with the Sun at one focus Second Law: Second Law:  The line joining the planet and the Sun sweeps out equal areas in equal times. Third Law: 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

l 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) l 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. l Third Law:  For every action there is an equal and opposite reaction.

NEWTON’S UNIVERSAL LAW of GRAVITATION l Force = GM 1 M 2 /D 2 äM 1 and M 2 are the masses of the two objects äD is the distance between them äG is a constant called the Gravitational Constant l Newton found that the orbits derived from this force were exactly those found by Kepler l Kepler’s 3rd Law becomes D 3 = (M 1 + M 2 ) x P 2