revieww09 - April 2, 2009 review A survey of the solar...

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Unformatted text preview: April 2, 2009 review A survey of the solar system Course Review April 2, 2009 review Course Outline Part I: basic physical concepts; properties of the solar system; Part II: formation and evolution of the Solar System; using knowledge of SS to develop and test models Part III: searching for extrasolar planets comparing known extrasolar planets with our SS value for future studies/SS formation models etc. Text: Moons and Planets : W. Hartmann UWACE Website: lecture notes, assignments, announcements etc.; check it at least once/week April 2, 2009 review Geometry, Distances, Orbits Skinny triangle -> distance, scale Geometry of relative orbits Early knowledge of orbital scale, sizes of Earth, Moon, Sun Eratosthenes, Aristarchus, Hipparcos Properties of an ellipse Keplers Laws gravity, angular momentum, distance Forms of KIII: P 2 = a 3 (m 1 +m 2 )P 2 = (a 1 + a 2 ) 3 (m 1 + m 2 )P 2 = 4 2 a 3 /G circular velocity, escape velocity, vis viva equation Tidal forces April 2, 2009 review What is an ellipse? a r r 2 = + Definition: An ellipse is a closed curve defined by the locus of all points such that the sum of the distances from the two foci is a constant : Ellipticity: Relates the semi- major (a) and semi-minor (b) axes: 2 2 2 2 2 1 e a b b e a a = + = Equation of an ellipse: ( ) 2 2 2 2 cos 2 sin r ae r r + + = Substituting and rearranging we get: a r r 2 = + ( ) cos 1 1 2 e e a r + = r p = a(1-e) r a =a(1+e) April 2, 2009 review Keplers Third Law ) ( ) ( 4 3 2 2 m M G a a P m M + + = 3 2 a P ) ( 4 3 2 2 m M G a P + = The general form of Keplers third law can be derived from Newtons laws. But since a=a M +a m we can write it even more generally and precisely because the mean separation between the two masses is the sum of their semimajor axes And, of course, Keplers original form (or slightly modified) is valid if working in units of: M sun , AU,yr 3 2 ) ( ) ( M m a a P M m + = + And thus April 2, 2009 review Circular Velocity A body in circular motion will have a constant velocity determined by the force it must balance to stay in orbit. By equating the circular acceleration and the acceleration of a mass due to gravity: r GM v circ = where M is the mass of the central body and r is the separation between the orbiting body and the central mass. This is convenient and useful for our purposes because most planet and satellite orbits are close to circular. April 2, 2009 review Escape velocity Escape velocity is the velocity a mass must have to escape the gravitational pull of the mass to which it is attracted . We define a mass as being able to escape if it can move to an infinite distance just when its velocity reaches zero. At this point its net energy is zero and so we have: 2 2 1 esc mv r GMm = r GM v esc 2 = Note: circ esc v v 2 = April 2, 2009 review 1. Gravitating objects orbit one another in an ellipse of eccentricity e and semimajor axis length a. and semimajor axis length a....
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revieww09 - April 2, 2009 review A survey of the solar...

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